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This is PART 29: Centers X(56001) - X(58000)

PART 1: Introduction and Centers X(1) - X(1000) PART 2: Centers X(1001) - X(3000) PART 3: Centers X(3001) - X(5000)
PART 4: Centers X(5001) - X(7000) PART 5: Centers X(7001) - X(10000) PART 6: Centers X(10001) - X(12000)
PART 7: Centers X(12001) - X(14000) PART 8: Centers X(14001) - X(16000) PART 9: Centers X(16001) - X(18000)
PART 10: Centers X(18001) - X(20000) PART 11: Centers X(20001) - X(22000) PART 12: Centers X(22001) - X(24000)
PART 13: Centers X(24001) - X(26000) PART 14: Centers X(26001) - X(28000) PART 15: Centers X(28001) - X(30000)
PART 16: Centers X(30001) - X(32000) PART 17: Centers X(32001) - X(34000) PART 18: Centers X(34001) - X(36000)
PART 19: Centers X(36001) - X(38000) PART 20: Centers X(38001) - X(40000) PART 21: Centers X(40001) - X(42000)
PART 22: Centers X(42001) - X(44000) PART 23: Centers X(44001) - X(46000) PART 24: Centers X(46001) - X(48000)
PART 25: Centers X(48001) - X(50000) PART 26: Centers X(50001) - X(52000) PART 27: Centers X(52001) - X(54000)
PART 28: Centers X(54001) - X(56000) PART 29: Centers X(56001) - X(58000) PART 30: Centers X(58001) - X(60000)
PART 31: Centers X(60001) - X(62000) PART 32: Centers X(62001) - X(64000) PART 33: Centers X(64001) - X(66000)
PART 34: Centers X(66001) - X(68000) PART 35: Centers X(68001) - X(70000) PART 36: Centers X(70001) - X(72000)

X(56001) = KP2(X(3)) OF X(2) AND X(29)

Barycentrics    a^2*(a+b)*(a+c)*(b^5-a^3*b*c-b^3*c^2-b^2*c^3+c^5+a^4*(b+c)+a*b*c*(b+c)^2-a^2*(2*b^3+b^2*c+b*c^2+2*c^3)) : :

X(56001) lies on these lines: {2, 6}, {21, 7078}, {27, 651}, {28, 3157}, {29, 3562}, {34, 41723}, {58, 1167}, {73, 4225}, {110, 2299}, {212, 4184}, {222, 1817}, {284, 2003}, {580, 34148}, {581, 5889}, {648, 2988}, {1172, 3173}, {1409, 3101}, {2193, 53819}, {3193, 3194}, {3219, 3990}, {4641, 18603}, {8021, 22117}, {8757, 31902}, {9536, 21767}, {16049, 19349}, {16054, 20744}, {18604, 40214}, {18605, 41332}, {23070, 52012}, {23071, 36011}, {23131, 37265}, {38832, 40958}, {45924, 50435}

X(56001) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 28788}, {661, 41906}
X(56001) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 28788}, {36830, 41906}
X(56001) = X(i)-Ceva conjugate of X(j) for these {i, j}: {44130, 4225}
X(56001) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(1167)}}, {{A, B, C, X(73), X(14055)}}, {{A, B, C, X(394), X(2988)}}, {{A, B, C, X(837), X(1262)}}, {{A, B, C, X(37652), X(55999)}}
X(56001) = barycentric quotient X(i)/X(j) for these (i, j): {3, 28788}, {110, 41906}, {14055, 3142}
X(56001) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {212, 54411, 4184}

X(56002) = KP2(X(3)) OF X(2) AND X(54)

Barycentrics    a^2*(a^8+b^2*(b^2-c^2)^3-a^6*(4*b^2+3*c^2)+3*a^4*(2*b^4+b^2*c^2+c^4)-a^2*(4*b^6-3*b^4*c^2+2*b^2*c^4+c^6))*(a^8+c^2*(-b^2+c^2)^3-a^6*(3*b^2+4*c^2)+3*a^4*(b^4+b^2*c^2+2*c^4)-a^2*(b^6+2*b^4*c^2-3*b^2*c^4+4*c^6)) : :

X(56002) lies on these lines: {2, 47731}, {24, 3060}, {54, 12095}, {254, 1147}, {1609, 1993}, {1994, 52505}, {5012, 55159}, {6515, 7763}, {11547, 37192}, {43756, 52032}

X(56002) = isogonal conjugate of X(9722)
X(56002) = trilinear pole of line {10540, 13557}
X(56002) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 9722}, {19, 12359}, {91, 50647}
X(56002) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 9722}, {6, 12359}, {34116, 50647}
X(56002) = X(i)-cross conjugate of X(j) for these {i, j}: {2501, 110}
X(56002) = intersection, other than A, B, C, of these circumconics: {{A, B, C, X(2), X(24)}}, {{A, B, C, X(3), X(6504)}}, {{A, B, C, X(6), X(1609)}}, {{A, B, C, X(57), X(32760)}}, {{A, B, C, X(74), X(13579)}}, {{A, B, C, X(83), X(288)}}, {{A, B, C, X(97), X(2986)}}, {{A, B, C, X(193), X(5422)}}, {{A, B, C, X(249), X(275)}}, {{A, B, C, X(394), X(5504)}}, {{A, B, C, X(459), X(38534)}}, {{A, B, C, X(588), X(41516)}}, {{A, B, C, X(589), X(41515)}}, {{A, B, C, X(1073), X(16867)}}, {{A, B, C, X(1176), X(2987)}}, {{A, B, C, X(1790), X(2990)}}, {{A, B, C, X(1994), X(3580)}}, {{A, B, C, X(10559), X(44828)}}, {{A, B, C, X(11449), X(14919)}}, {{A, B, C, X(11538), X(14483)}}, {{A, B, C, X(11595), X(34986)}}, {{A, B, C, X(12095), X(52032)}}, {{A, B, C, X(13585), X(16835)}}, {{A, B, C, X(14518), X(40393)}}, {{A, B, C, X(30528), X(46639)}}, {{A, B, C, X(32654), X(41271)}}, {{A, B, C, X(34545), X(41628)}}, {{A, B, C, X(42410), X(55982)}}, {{A, B, C, X(43705), X(44175)}}
X(56002) = barycentric quotient X(i)/X(j) for these (i, j): {3, 12359}, {6, 9722}, {571, 50647}

X(56003) = KP2(X(3)) OF X(2) AND X(63)

Barycentrics    a^2*(a^3-a^2*b-a*b^2+b^3+c^3)*(a^3+b^3-a^2*c-a*c^2+c^3) : :

X(56003) lies on these lines: {6, 26690}, {31, 3190}, {81, 33113}, {219, 608}, {394, 1407}, {579, 604}, {1462, 3662}, {2203, 26893}, {2273, 2298}, {2287, 5016}

X(56003) = isogonal conjugate of X(3772)
X(56003) = trilinear pole of line {667, 8676}
X(56003) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 3772}, {2, 3924}, {4, 26934}, {6, 17861}, {7, 40968}, {8, 36570}, {19, 41004}, {37, 17189}, {42, 16749}, {57, 1837}, {81, 21935}, {226, 40980}, {514, 53279}
X(56003) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 3772}, {6, 41004}, {9, 17861}, {5452, 1837}, {32664, 3924}, {36033, 26934}, {40586, 21935}, {40589, 17189}, {40592, 16749}
X(56003) = X(i)-cross conjugate of X(j) for these {i, j}: {1946, 100}, {6589, 101}
X(56003) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1175)}}, {{A, B, C, X(2), X(284)}}, {{A, B, C, X(3), X(1257)}}, {{A, B, C, X(6), X(31)}}, {{A, B, C, X(8), X(283)}}, {{A, B, C, X(9), X(1021)}}, {{A, B, C, X(28), X(39945)}}, {{A, B, C, X(35), X(39708)}}, {{A, B, C, X(37), X(33113)}}, {{A, B, C, X(59), X(77)}}, {{A, B, C, X(63), X(5279)}}, {{A, B, C, X(71), X(321)}}, {{A, B, C, X(72), X(5016)}}, {{A, B, C, X(75), X(4570)}}, {{A, B, C, X(88), X(1436)}}, {{A, B, C, X(103), X(4373)}}, {{A, B, C, X(219), X(394)}}, {{A, B, C, X(270), X(55991)}}, {{A, B, C, X(279), X(3451)}}, {{A, B, C, X(323), X(35192)}}, {{A, B, C, X(346), X(15629)}}, {{A, B, C, X(572), X(14964)}}, {{A, B, C, X(596), X(10623)}}, {{A, B, C, X(672), X(3056)}}, {{A, B, C, X(909), X(15474)}}, {{A, B, C, X(941), X(2259)}}, {{A, B, C, X(947), X(1219)}}, {{A, B, C, X(989), X(18772)}}, {{A, B, C, X(1037), X(1280)}}, {{A, B, C, X(1169), X(2215)}}, {{A, B, C, X(1172), X(2990)}}, {{A, B, C, X(1174), X(34260)}}, {{A, B, C, X(1433), X(34040)}}, {{A, B, C, X(1795), X(51497)}}, {{A, B, C, X(2273), X(2300)}}, {{A, B, C, X(2297), X(2364)}}, {{A, B, C, X(2316), X(55989)}}, {{A, B, C, X(2997), X(37142)}}, {{A, B, C, X(3415), X(38813)}}, {{A, B, C, X(3450), X(39946)}}, {{A, B, C, X(3681), X(4388)}}, {{A, B, C, X(3765), X(5360)}}, {{A, B, C, X(3868), X(54125)}}, {{A, B, C, X(4257), X(41434)}}, {{A, B, C, X(4271), X(17281)}}, {{A, B, C, X(8769), X(28471)}}, {{A, B, C, X(13404), X(30712)}}, {{A, B, C, X(16667), X(17745)}}, {{A, B, C, X(17754), X(27678)}}, {{A, B, C, X(22122), X(22123)}}, {{A, B, C, X(22131), X(22132)}}, {{A, B, C, X(23707), X(40424)}}, {{A, B, C, X(25306), X(32937)}}, {{A, B, C, X(30457), X(41798)}}, {{A, B, C, X(36101), X(40802)}}
X(56003) = barycentric product X(i)*X(j) for these (i, j): {1, 40436}, {3, 34406}, {34399, 55}, {55994, 63}
X(56003) = barycentric quotient X(i)/X(j) for these (i, j): {1, 17861}, {3, 41004}, {6, 3772}, {31, 3924}, {41, 40968}, {42, 21935}, {48, 26934}, {55, 1837}, {58, 17189}, {81, 16749}, {604, 36570}, {692, 53279}, {2194, 40980}, {6056, 53850}, {34399, 6063}, {34406, 264}, {40436, 75}, {55994, 92}
X(56003) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {219, 608, 38875}

X(56004) = KP2(X(3)) OF X(2) AND X(69)

Barycentrics    a^2*(a^4-2*a^2*b^2+b^4+c^4)*(a^4+b^4-2*a^2*c^2+c^4) : :

X(56004) lies on these lines: {3, 14601}, {6, 6393}, {24, 511}, {32, 1993}, {69, 34138}, {76, 6531}, {99, 9289}, {155, 36998}, {183, 36952}, {213, 42700}, {297, 315}, {323, 20065}, {525, 1975}, {626, 11060}, {637, 13429}, {638, 13440}, {729, 42297}, {1078, 42313}, {1147, 3425}, {2794, 11441}, {2979, 28724}, {5017, 46288}, {5028, 26206}, {5422, 6680}, {7592, 13335}, {7851, 44415}, {7857, 42295}, {9468, 43183}, {9753, 36747}, {10316, 51439}, {14585, 36790}, {16266, 46319}, {20576, 36749}, {22416, 30541}, {28710, 34148}, {35431, 46308}, {35910, 40354}, {39238, 44499}

X(56004) = isogonal conjugate of X(3767)
X(56004) = trilinear pole of line {669, 684}
X(56004) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 3767}, {4, 2083}, {6, 17871}, {19, 1899}, {31, 41760}, {63, 41762}, {75, 42295}, {92, 40947}, {158, 39643}, {426, 6520}, {661, 1632}, {1096, 6389}, {1910, 2450}, {1973, 41009}, {2156, 41761}, {2168, 27362}
X(56004) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 41760}, {3, 3767}, {6, 1899}, {9, 17871}, {206, 42295}, {1147, 39643}, {3162, 41762}, {6337, 41009}, {6503, 6389}, {11672, 2450}, {22391, 40947}, {36033, 2083}, {36830, 1632}, {37867, 426}
X(56004) = X(i)-cross conjugate of X(j) for these {i, j}: {2485, 110}, {17994, 10425}, {39201, 99}
X(56004) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(24)}}, {{A, B, C, X(3), X(76)}}, {{A, B, C, X(4), X(2987)}}, {{A, B, C, X(6), X(32)}}, {{A, B, C, X(25), X(7807)}}, {{A, B, C, X(39), X(5017)}}, {{A, B, C, X(59), X(30701)}}, {{A, B, C, X(64), X(671)}}, {{A, B, C, X(68), X(18876)}}, {{A, B, C, X(69), X(315)}}, {{A, B, C, X(74), X(2996)}}, {{A, B, C, X(99), X(1975)}}, {{A, B, C, X(183), X(1078)}}, {{A, B, C, X(193), X(26206)}}, {{A, B, C, X(257), X(3422)}}, {{A, B, C, X(287), X(15316)}}, {{A, B, C, X(323), X(14385)}}, {{A, B, C, X(335), X(7163)}}, {{A, B, C, X(394), X(801)}}, {{A, B, C, X(598), X(3527)}}, {{A, B, C, X(626), X(44558)}}, {{A, B, C, X(694), X(2353)}}, {{A, B, C, X(1016), X(42019)}}, {{A, B, C, X(1173), X(5395)}}, {{A, B, C, X(1297), X(40824)}}, {{A, B, C, X(1350), X(30270)}}, {{A, B, C, X(1351), X(13335)}}, {{A, B, C, X(1384), X(44499)}}, {{A, B, C, X(1504), X(12968)}}, {{A, B, C, X(1505), X(12963)}}, {{A, B, C, X(1691), X(43183)}}, {{A, B, C, X(1994), X(5422)}}, {{A, B, C, X(2076), X(32452)}}, {{A, B, C, X(2139), X(3926)}}, {{A, B, C, X(2165), X(42406)}}, {{A, B, C, X(2979), X(8024)}}, {{A, B, C, X(3053), X(5028)}}, {{A, B, C, X(3095), X(35424)}}, {{A, B, C, X(3289), X(14585)}}, {{A, B, C, X(3398), X(35431)}}, {{A, B, C, X(3407), X(14495)}}, {{A, B, C, X(3426), X(53105)}}, {{A, B, C, X(3431), X(18840)}}, {{A, B, C, X(3435), X(17946)}}, {{A, B, C, X(3531), X(53107)}}, {{A, B, C, X(3532), X(32901)}}, {{A, B, C, X(3978), X(32542)}}, {{A, B, C, X(5162), X(44453)}}, {{A, B, C, X(5359), X(34945)}}, {{A, B, C, X(5392), X(34439)}}, {{A, B, C, X(5485), X(11270)}}, {{A, B, C, X(5504), X(14376)}}, {{A, B, C, X(5976), X(38907)}}, {{A, B, C, X(6664), X(34436)}}, {{A, B, C, X(8266), X(41262)}}, {{A, B, C, X(8743), X(41363)}}, {{A, B, C, X(8770), X(39644)}}, {{A, B, C, X(8781), X(40801)}}, {{A, B, C, X(9217), X(30496)}}, {{A, B, C, X(9515), X(27375)}}, {{A, B, C, X(9605), X(41413)}}, {{A, B, C, X(10159), X(14528)}}, {{A, B, C, X(11610), X(40358)}}, {{A, B, C, X(11824), X(11825)}}, {{A, B, C, X(13334), X(50685)}}, {{A, B, C, X(13472), X(18841)}}, {{A, B, C, X(14483), X(18845)}}, {{A, B, C, X(14491), X(18843)}}, {{A, B, C, X(16835), X(38259)}}, {{A, B, C, X(17743), X(52186)}}, {{A, B, C, X(17811), X(37672)}}, {{A, B, C, X(18532), X(43678)}}, {{A, B, C, X(22151), X(41614)}}, {{A, B, C, X(22334), X(53106)}}, {{A, B, C, X(23128), X(32661)}}, {{A, B, C, X(31360), X(43725)}}, {{A, B, C, X(32640), X(44767)}}, {{A, B, C, X(34401), X(44717)}}, {{A, B, C, X(37128), X(39945)}}, {{A, B, C, X(39201), X(39643)}}, {{A, B, C, X(39396), X(47643)}}, {{A, B, C, X(40403), X(56003)}}, {{A, B, C, X(40421), X(40708)}}, {{A, B, C, X(40436), X(52378)}}, {{A, B, C, X(40830), X(54973)}}, {{A, B, C, X(40832), X(54114)}}, {{A, B, C, X(42354), X(43679)}}, {{A, B, C, X(43527), X(43908)}}, {{A, B, C, X(43714), X(46140)}}, {{A, B, C, X(46164), X(52568)}}, {{A, B, C, X(46321), X(50659)}}, {{A, B, C, X(52518), X(53109)}}
X(56004) = barycentric product X(i)*X(j) for these (i, j): {3, 34405}, {42297, 512}, {42407, 6}
X(56004) = barycentric quotient X(i)/X(j) for these (i, j): {1, 17871}, {2, 41760}, {3, 1899}, {6, 3767}, {22, 41761}, {25, 41762}, {32, 42295}, {48, 2083}, {52, 27362}, {69, 41009}, {110, 1632}, {184, 40947}, {394, 6389}, {418, 6751}, {511, 2450}, {577, 39643}, {1092, 426}, {1993, 41770}, {3313, 52532}, {3964, 44141}, {20806, 28405}, {34405, 264}, {42297, 670}, {42407, 76}, {44175, 41765}

X(56005) = KP2(X(3)) OF X(2) AND X(77)

Barycentrics    a^2*(a+b-c)*(a-b+c)*(a^3-a^2*b-a*b^2+b^3-c^3)*(a^3-b^3-a^2*c-a*c^2+c^3) : :

X(56005) lies on these lines: {35, 255}, {41, 2003}, {81, 34398}, {220, 394}, {222, 607}, {651, 17181}, {1433, 10394}, {1437, 45963}, {2287, 34016}, {18604, 40214}

X(56005) = isogonal conjugate of X(46835)
X(56005) = trilinear pole of line {2605, 8641}
X(56005) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 46835}, {2, 4336}, {6, 17860}, {9, 1836}, {33, 17073}, {37, 17188}, {190, 2520}, {281, 20277}, {1172, 21912}, {2341, 51462}, {4162, 27833}
X(56005) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 46835}, {9, 17860}, {478, 1836}, {32664, 4336}, {40589, 17188}, {55053, 2520}
X(56005) = X(i)-cross conjugate of X(j) for these {i, j}: {1946, 934}, {6586, 109}, {20122, 7}
X(56005) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1262)}}, {{A, B, C, X(2), X(1167)}}, {{A, B, C, X(3), X(36101)}}, {{A, B, C, X(6), X(41)}}, {{A, B, C, X(7), X(1803)}}, {{A, B, C, X(21), X(37378)}}, {{A, B, C, X(35), X(57)}}, {{A, B, C, X(54), X(44178)}}, {{A, B, C, X(56), X(34056)}}, {{A, B, C, X(58), X(279)}}, {{A, B, C, X(59), X(7131)}}, {{A, B, C, X(60), X(271)}}, {{A, B, C, X(73), X(45963)}}, {{A, B, C, X(81), X(222)}}, {{A, B, C, X(85), X(52378)}}, {{A, B, C, X(102), X(10405)}}, {{A, B, C, X(189), X(1790)}}, {{A, B, C, X(277), X(36052)}}, {{A, B, C, X(284), X(41894)}}, {{A, B, C, X(514), X(3417)}}, {{A, B, C, X(593), X(1422)}}, {{A, B, C, X(693), X(17181)}}, {{A, B, C, X(1255), X(53995)}}, {{A, B, C, X(1257), X(40802)}}, {{A, B, C, X(1819), X(10394)}}, {{A, B, C, X(34028), X(46882)}}, {{A, B, C, X(38690), X(54232)}}, {{A, B, C, X(40403), X(56003)}}
X(56005) = barycentric product X(i)*X(j) for these (i, j): {3, 34398}, {57, 55965}, {4131, 52776}, {23224, 54968}, {34409, 56}, {37741, 7}
X(56005) = barycentric quotient X(i)/X(j) for these (i, j): {1, 17860}, {6, 46835}, {31, 4336}, {56, 1836}, {58, 17188}, {73, 21912}, {222, 17073}, {603, 20277}, {667, 2520}, {1464, 51462}, {7335, 53847}, {34398, 264}, {34409, 3596}, {37741, 8}, {38828, 27833}, {55965, 312}
X(56005) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {222, 607, 38877}

X(56006) = KP2(X(3)) OF X(2) AND X(98)

Barycentrics    (a^8-a^6*(b^2+4*c^2)+(b^2+c^2)*(-(b^2*c)+c^3)^2+a^4*(-b^4+3*b^2*c^2+6*c^4)+a^2*(b^6-4*b^4*c^2+3*b^2*c^4-4*c^6))*(a^8-a^6*(4*b^2+c^2)+(b^2+c^2)*(b^3-b*c^2)^2+a^4*(6*b^4+3*b^2*c^2-c^4)+a^2*(-4*b^6+3*b^4*c^2-4*b^2*c^4+c^6)) : :

X(56006) lies on the MacBeath circumconic and on these lines: {110, 6353}, {193, 571}, {524, 43755}, {648, 8745}, {895, 55121}, {1331, 4028}, {1353, 54034}, {1993, 4563}, {5392, 39109}, {44768, 51481}

X(56006) = trilinear pole of line {3, 3566}
X(56006) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 34382}
X(56006) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 34382}, {35067, 31842}
X(56006) = X(i)-cross conjugate of X(j) for these {i, j}: {6132, 99}, {32654, 98}
X(56006) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(193)}}, {{A, B, C, X(5), X(1353)}}, {{A, B, C, X(6), X(571)}}, {{A, B, C, X(69), X(5392)}}, {{A, B, C, X(83), X(13472)}}, {{A, B, C, X(94), X(18947)}}, {{A, B, C, X(95), X(42354)}}, {{A, B, C, X(98), X(46039)}}, {{A, B, C, X(110), X(287)}}, {{A, B, C, X(141), X(41628)}}, {{A, B, C, X(249), X(38534)}}, {{A, B, C, X(323), X(37784)}}, {{A, B, C, X(394), X(40318)}}, {{A, B, C, X(524), X(3580)}}, {{A, B, C, X(671), X(30477)}}, {{A, B, C, X(847), X(7763)}}, {{A, B, C, X(1972), X(35511)}}, {{A, B, C, X(1992), X(37645)}}, {{A, B, C, X(2996), X(34386)}}, {{A, B, C, X(4590), X(16081)}}, {{A, B, C, X(6339), X(6504)}}, {{A, B, C, X(8548), X(19139)}}, {{A, B, C, X(13567), X(40316)}}, {{A, B, C, X(15316), X(19141)}}, {{A, B, C, X(15988), X(40571)}}, {{A, B, C, X(30535), X(56002)}}, {{A, B, C, X(35142), X(51481)}}, {{A, B, C, X(42313), X(42410)}}, {{A, B, C, X(44174), X(51776)}}
X(56006) = barycentric product X(i)*X(j) for these (i, j): {40120, 69}
X(56006) = barycentric quotient X(i)/X(j) for these (i, j): {3, 34382}, {3564, 31842}, {40120, 4}, {42065, 53787}

X(56007) = KP2(X(3)) OF X(2) AND X(111)

Barycentrics    a^2*(a^6+2*b^6-3*b^4*c^2-4*b^2*c^4+c^6-a^4*(4*b^2+c^2)-a^2*(3*b^4-12*b^2*c^2+c^4))*(a^6+b^6-4*b^4*c^2-3*b^2*c^4+2*c^6-a^4*(b^2+4*c^2)-a^2*(b^4-12*b^2*c^2+3*c^4)) : :

X(56007) lies on the MacBeath circumconic and on these lines: {110, 19118}, {126, 193}, {648, 6392}, {1332, 21874}, {3053, 4558}, {3291, 37784}, {3926, 15525}, {6391, 15369}, {14273, 41909}, {41617, 43755}

X(56007) = trilinear pole of line {3, 8651}
X(56007) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(40324)}}, {{A, B, C, X(6), X(193)}}, {{A, B, C, X(67), X(6096)}}, {{A, B, C, X(69), X(40318)}}, {{A, B, C, X(110), X(287)}}, {{A, B, C, X(111), X(126)}}, {{A, B, C, X(524), X(1177)}}, {{A, B, C, X(1297), X(35511)}}, {{A, B, C, X(1992), X(1993)}}, {{A, B, C, X(2996), X(55977)}}, {{A, B, C, X(3580), X(41617)}}, {{A, B, C, X(3926), X(6338)}}, {{A, B, C, X(4590), X(8749)}}, {{A, B, C, X(5505), X(25322)}}, {{A, B, C, X(6515), X(31626)}}, {{A, B, C, X(32240), X(34898)}}, {{A, B, C, X(36792), X(52234)}}, {{A, B, C, X(38263), X(52041)}}

X(56008) = KP2(X(3)) OF X(2) AND X(112)

Barycentrics    a^2*(a-b)*(a+b)*(a-c)*(a+c)*(a^6+a^4*(b^2-c^2)-a^2*(b^2-c^2)^2-(b^2-c^2)*(b^2+c^2)^2)*(a^6-a^2*(b^2-c^2)^2+a^4*(-b^2+c^2)+(b^2-c^2)*(b^2+c^2)^2) : :

X(56008) lies on the MacBeath circumconic and on these lines: {32, 23974}, {110, 39417}, {112, 44766}, {193, 46767}, {287, 6515}, {895, 32262}, {1993, 40358}, {2986, 50188}, {2987, 40144}, {4563, 4611}, {14919, 52041}, {44770, 52917}

X(56008) = isogonal conjugate of X(47125)
X(56008) = trilinear pole of line {3, 206}
X(56008) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 47125}, {75, 52588}, {159, 1577}, {512, 21582}, {523, 18596}, {656, 41361}, {661, 1370}, {3162, 14208}, {4041, 18629}, {23115, 24006}, {24018, 41766}, {24019, 55069}
X(56008) = X(i)-vertex conjugate of X(j) for these {i, j}: {32713, 44766}
X(56008) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 47125}, {206, 52588}, {35071, 55069}, {36830, 1370}, {39054, 21582}, {40596, 41361}, {55047, 53822}
X(56008) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(1301)}}, {{A, B, C, X(110), X(287)}}, {{A, B, C, X(112), X(4611)}}, {{A, B, C, X(520), X(23974)}}, {{A, B, C, X(1304), X(44326)}}, {{A, B, C, X(1993), X(34211)}}, {{A, B, C, X(2421), X(6515)}}, {{A, B, C, X(2966), X(13398)}}, {{A, B, C, X(3580), X(50188)}}, {{A, B, C, X(5468), X(40318)}}, {{A, B, C, X(35575), X(46134)}}, {{A, B, C, X(40173), X(46963)}}
X(56008) = barycentric product X(i)*X(j) for these (i, j): {110, 13575}, {163, 39733}, {1576, 40009}, {4558, 52583}, {34207, 99}, {39129, 827}, {39417, 69}, {40144, 4563}, {40358, 44766}, {52041, 648}
X(56008) = barycentric quotient X(i)/X(j) for these (i, j): {6, 47125}, {32, 52588}, {110, 1370}, {112, 41361}, {163, 18596}, {520, 55069}, {662, 21582}, {1576, 159}, {1624, 41602}, {4558, 28419}, {4565, 18629}, {4630, 8793}, {8673, 53822}, {13575, 850}, {32661, 23115}, {32713, 41766}, {34207, 523}, {39129, 23285}, {39172, 8673}, {39417, 4}, {39733, 20948}, {40009, 44173}, {40144, 2501}, {40358, 33294}, {46767, 2485}, {52041, 525}, {52583, 14618}

X(56009) = KP2(X(1)) OF X(6) AND X(44)

Barycentrics    a*(a^2+3*b*c-2*a*(b+c)) : :

X(56009) lies on these lines: {1, 3689}, {2, 2177}, {3, 6048}, {6, 43}, {9, 6181}, {10, 4256}, {31, 14997}, {36, 31855}, {42, 4038}, {44, 9324}, {55, 15485}, {78, 24440}, {88, 17449}, {100, 238}, {106, 519}, {165, 2348}, {200, 982}, {210, 17596}, {239, 4434}, {244, 3935}, {404, 3214}, {474, 50581}, {511, 3030}, {515, 38471}, {517, 5529}, {518, 1054}, {528, 51415}, {536, 24398}, {612, 17600}, {650, 1734}, {726, 3699}, {740, 5205}, {750, 3240}, {846, 3740}, {908, 24715}, {936, 37598}, {940, 42043}, {978, 5687}, {984, 17593}, {1155, 1757}, {1215, 17116}, {1386, 17779}, {1429, 3507}, {1574, 41239}, {1698, 16844}, {1722, 16485}, {1738, 6745}, {1961, 3723}, {1979, 20669}, {2226, 52925}, {2291, 53891}, {2345, 4070}, {2550, 17717}, {2664, 3230}, {2802, 45763}, {2999, 16491}, {3035, 33140}, {3068, 41421}, {3158, 5272}, {3216, 5255}, {3218, 21805}, {3247, 3290}, {3257, 41461}, {3293, 16474}, {3306, 49490}, {3452, 33095}, {3550, 4383}, {3570, 41142}, {3619, 33174}, {3620, 33084}, {3621, 32577}, {3631, 33085}, {3634, 33771}, {3679, 16499}, {3685, 24003}, {3687, 33079}, {3693, 3731}, {3711, 17595}, {3720, 9342}, {3722, 7292}, {3742, 3979}, {3749, 16487}, {3752, 3961}, {3792, 51377}, {3811, 24174}, {3823, 29862}, {3826, 29640}, {3828, 4653}, {3836, 26073}, {3840, 3996}, {3870, 17063}, {3871, 27627}, {3880, 13541}, {3911, 49772}, {3913, 16486}, {3936, 31151}, {3952, 32845}, {4000, 17725}, {4023, 33082}, {4090, 32939}, {4220, 8296}, {4257, 5247}, {4358, 4693}, {4384, 16497}, {4420, 24443}, {4421, 8616}, {4447, 4489}, {4511, 4695}, {4551, 9364}, {4578, 4947}, {4640, 15492}, {4651, 32918}, {4660, 5233}, {4674, 4867}, {4685, 14829}, {4716, 17763}, {4849, 32913}, {4860, 49498}, {5121, 5853}, {5211, 17765}, {5212, 5847}, {5297, 46904}, {5363, 36741}, {5400, 5537}, {5432, 33138}, {5741, 32948}, {6174, 35466}, {6686, 32942}, {6765, 11512}, {7081, 17117}, {7186, 23638}, {7963, 11519}, {8298, 31073}, {8649, 52959}, {8715, 17749}, {9352, 32912}, {9355, 17613}, {10327, 32855}, {10448, 46933}, {10563, 16189}, {11499, 37570}, {15604, 37508}, {16468, 37540}, {16477, 17126}, {16489, 48696}, {16602, 29820}, {16788, 41416}, {17018, 17124}, {17020, 17469}, {17021, 21806}, {17261, 42056}, {17278, 29675}, {17356, 29860}, {17490, 32920}, {17495, 17780}, {17740, 33165}, {17764, 17777}, {19746, 43997}, {19804, 29670}, {19998, 32919}, {20103, 24210}, {20368, 33878}, {21008, 21868}, {21026, 27757}, {21241, 27759}, {21747, 32911}, {21870, 37520}, {22313, 50362}, {24169, 33126}, {24582, 31210}, {24627, 49457}, {24988, 29632}, {25269, 27538}, {25568, 33103}, {25882, 47296}, {26582, 30837}, {27131, 33094}, {30577, 49701}, {31137, 49460}, {31197, 42819}, {32783, 34573}, {32922, 43290}, {33104, 37651}, {33106, 34612}, {33109, 37662}, {37674, 42042}, {37684, 49497}, {37789, 53531}, {40091, 49992}, {40663, 43056}, {41684, 51402}, {43055, 51463}, {49984, 54391}

X(56009) = midpoint of X(i) and X(j) for these {i,j}: {1054, 5524}
X(56009) = reflection of X(i) in X(j) for these {i,j}: {18201, 1054}, {39343, 44}
X(56009) = trilinear pole of line {21343, 23650}
X(56009) = perspector of circumconic {{A, B, C, X(932), X(2346)}}
X(56009) = X(i)-Dao conjugate of X(j) for these {i, j}: {4928, 1647}
X(56009) = X(i)-Ceva conjugate of X(j) for these {i, j}: {40400, 1}
X(56009) = intersection, other than A, B, C, of these circumconics: {{A, B, C, X(87), X(9325)}}, {{A, B, C, X(1120), X(21343)}}, {{A, B, C, X(1266), X(24216)}}, {{A, B, C, X(2162), X(2382)}}, {{A, B, C, X(2319), X(4900)}}
X(56009) = barycentric product X(i)*X(j) for these (i, j): {100, 4928}, {101, 21433}, {190, 21343}, {22437, 6335}, {23650, 668}
X(56009) = barycentric quotient X(i)/X(j) for these (i, j): {4928, 693}, {21343, 514}, {21433, 3261}, {22437, 905}, {23650, 513}
X(56009) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 2177, 16484}, {42, 17122, 4038}, {43, 1376, 171}, {55, 16569, 17123}, {100, 37680, 902}, {100, 899, 238}, {244, 3935, 49675}, {518, 1054, 18201}, {750, 3240, 4649}, {899, 902, 37680}, {978, 5687, 37588}, {1054, 5524, 518}, {1738, 6745, 17719}, {2177, 16484, 3750}, {3158, 5272, 17715}, {3218, 21805, 49712}, {3218, 54309, 21805}, {3550, 36634, 4383}, {3689, 16610, 1}, {3711, 17595, 49448}, {3752, 3961, 17598}, {4421, 37679, 8616}, {17495, 17780, 32927}, {24988, 29632, 31252}, {34612, 37663, 33106}, {37662, 49732, 33109}

X(56010) = KP2(X(1)) OF X(6) AND X(45)

Barycentrics    a*(2*a^2+3*b*c-a*(b+c)) : :

X(56010) lies on these lines: {1, 88}, {2, 902}, {6, 43}, {8, 37608}, {9, 2243}, {10, 4257}, {31, 16569}, {35, 13738}, {36, 16499}, {37, 17601}, {38, 9352}, {42, 14996}, {46, 5293}, {55, 16059}, {57, 3961}, {58, 6048}, {75, 4434}, {81, 42043}, {142, 29675}, {165, 846}, {200, 32913}, {210, 4650}, {238, 4413}, {474, 5255}, {498, 26027}, {519, 37684}, {528, 24217}, {612, 17596}, {748, 9342}, {752, 5233}, {899, 14997}, {940, 42042}, {964, 1698}, {978, 5264}, {982, 49465}, {984, 1155}, {996, 1150}, {1055, 40790}, {1086, 17725}, {1201, 17572}, {1480, 6911}, {1621, 17124}, {1707, 3973}, {1738, 29658}, {1742, 44425}, {1961, 3247}, {2108, 31073}, {2209, 25528}, {2223, 16497}, {2330, 5197}, {2550, 33140}, {2664, 8621}, {3035, 17717}, {3052, 8692}, {3098, 20368}, {3158, 3979}, {3218, 49448}, {3242, 18201}, {3246, 31197}, {3474, 33099}, {3501, 5277}, {3570, 50127}, {3619, 32783}, {3620, 33085}, {3631, 33084}, {3632, 32919}, {3689, 37520}, {3699, 32935}, {3711, 49712}, {3723, 4682}, {3729, 16997}, {3740, 7262}, {3742, 17715}, {3744, 17063}, {3749, 5437}, {3750, 4421}, {3751, 5524}, {3752, 17716}, {3790, 49994}, {3836, 29858}, {3911, 29676}, {3915, 17531}, {3920, 17591}, {3923, 5205}, {3935, 49498}, {3938, 27003}, {3971, 25269}, {3980, 7081}, {4188, 10459}, {4216, 5010}, {4315, 51301}, {4334, 9364}, {4362, 17117}, {4396, 4659}, {4414, 5297}, {4428, 37682}, {4429, 29856}, {4432, 30829}, {4450, 25960}, {4598, 17105}, {4640, 16814}, {4653, 41451}, {4671, 24344}, {4676, 24003}, {4685, 37683}, {4781, 31035}, {4860, 49675}, {4867, 53115}, {4954, 34747}, {5096, 5363}, {5212, 51196}, {5218, 29640}, {5219, 23703}, {5235, 19875}, {5241, 50296}, {5247, 9709}, {5263, 29827}, {5266, 16498}, {5269, 16491}, {5272, 16487}, {5432, 33111}, {5687, 37607}, {5718, 6174}, {5880, 17719}, {6015, 28841}, {6649, 9312}, {6745, 50307}, {8167, 21000}, {8296, 18235}, {8693, 29352}, {9082, 40780}, {9335, 29818}, {9350, 32911}, {9780, 51674}, {10327, 33167}, {10456, 55094}, {11112, 37716}, {11246, 33101}, {13588, 18169}, {16371, 37617}, {16474, 37522}, {16475, 17779}, {16485, 37552}, {16486, 25524}, {16489, 37610}, {16490, 48696}, {16571, 20964}, {17051, 53534}, {17282, 29860}, {17284, 24602}, {17336, 42056}, {17602, 33149}, {17696, 30063}, {17720, 24715}, {17740, 32847}, {17752, 33062}, {17763, 49474}, {18792, 35983}, {19740, 43997}, {21242, 49720}, {24169, 29634}, {24342, 29828}, {24397, 45140}, {24440, 37539}, {24452, 27747}, {24620, 50023}, {24627, 36480}, {24850, 46937}, {25590, 37670}, {27002, 29668}, {29571, 51300}, {29649, 32932}, {29662, 33110}, {29683, 33131}, {29825, 50302}, {30039, 33839}, {30644, 35342}, {30811, 31151}, {31137, 32941}, {31242, 32942}, {32845, 49445}, {32865, 37646}, {32927, 49532}, {33141, 34612}, {33174, 34573}, {37699, 51340}

X(56010) = perspector of circumconic {{A, B, C, X(932), X(3257)}}
X(56010) = X(i)-Dao conjugate of X(j) for these {i, j}: {4389, 33934}
X(56010) = X(i)-Ceva conjugate of X(j) for these {i, j}: {40401, 1}
X(56010) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(48344)}}, {{A, B, C, X(87), X(88)}}, {{A, B, C, X(106), X(2162)}}, {{A, B, C, X(996), X(4792)}}, {{A, B, C, X(1320), X(2319)}}, {{A, B, C, X(4674), X(16606)}}, {{A, B, C, X(9025), X(40780)}}, {{A, B, C, X(9082), X(40753)}}
X(56010) = barycentric product X(i)*X(j) for these (i, j): {100, 47779}, {190, 48344}
X(56010) = barycentric quotient X(i)/X(j) for these (i, j): {47779, 693}, {48344, 514}
X(56010) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3550, 8616}, {2, 902, 15485}, {55, 17122, 26102}, {100, 37633, 2177}, {100, 750, 1}, {165, 5268, 846}, {171, 1376, 43}, {474, 5255, 21214}, {750, 2177, 37633}, {899, 21747, 14997}, {1621, 17124, 25502}, {3550, 15485, 902}, {3689, 37520, 49490}, {3749, 5437, 29820}, {3750, 9337, 4421}, {3751, 46917, 5524}, {4413, 37540, 238}, {4421, 37674, 3750}, {9350, 32911, 36634}, {14997, 17126, 21747}, {14997, 21747, 16468}, {34612, 37634, 33141}, {37675, 41423, 3731}

X(56011) = KP2(X(1)) OF X(6) AND X(81)

Barycentrics    a*(a^2*(b-c)+b*c^2-a*c*(2*b+c))*(a^2*(b-c)-b^2*c+a*b*(b+2*c)) : :

X(56011) lies on these lines: {6, 40720}, {43, 7121}, {81, 27044}, {595, 2209}, {727, 3293}, {932, 20971}, {2176, 4393}, {20332, 20691}, {21760, 27644}, {21904, 34077}

X(56011) = isogonal conjugate of X(16604)
X(56011) = trilinear pole of line {4057, 4782}
X(56011) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 16604}, {6, 24165}, {42, 16710}, {75, 21757}, {86, 21827}, {87, 17459}, {92, 22378}, {101, 48406}, {330, 20971}, {2162, 34832}, {2176, 52573}, {7121, 20899}, {21128, 34071}
X(56011) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 16604}, {9, 24165}, {206, 21757}, {1015, 48406}, {22391, 22378}, {40592, 16710}, {40598, 20899}, {40600, 21827}, {40610, 21128}
X(56011) = X(i)-cross conjugate of X(j) for these {i, j}: {1919, 100}
X(56011) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4393)}}, {{A, B, C, X(2), X(979)}}, {{A, B, C, X(6), X(904)}}, {{A, B, C, X(31), X(41396)}}, {{A, B, C, X(42), X(41240)}}, {{A, B, C, X(43), X(53675)}}, {{A, B, C, X(58), X(1016)}}, {{A, B, C, X(81), X(83)}}, {{A, B, C, X(87), X(32095)}}, {{A, B, C, X(88), X(25439)}}, {{A, B, C, X(213), X(1924)}}, {{A, B, C, X(256), X(39722)}}, {{A, B, C, X(257), X(39979)}}, {{A, B, C, X(330), X(39969)}}, {{A, B, C, X(1002), X(5395)}}, {{A, B, C, X(1170), X(18772)}}, {{A, B, C, X(1220), X(39971)}}, {{A, B, C, X(1222), X(40432)}}, {{A, B, C, X(1255), X(43531)}}, {{A, B, C, X(1432), X(6630)}}, {{A, B, C, X(1509), X(41434)}}, {{A, B, C, X(1575), X(20691)}}, {{A, B, C, X(2334), X(14621)}}, {{A, B, C, X(3224), X(40735)}}, {{A, B, C, X(3293), X(27044)}}, {{A, B, C, X(3500), X(38247)}}, {{A, B, C, X(3795), X(46032)}}, {{A, B, C, X(5559), X(17946)}}, {{A, B, C, X(9309), X(54123)}}, {{A, B, C, X(23617), X(35105)}}, {{A, B, C, X(32008), X(37128)}}, {{A, B, C, X(32009), X(39748)}}, {{A, B, C, X(32012), X(39797)}}, {{A, B, C, X(32014), X(40434)}}, {{A, B, C, X(39952), X(39970)}}
X(56011) = barycentric product X(i)*X(j) for these (i, j): {1, 55997}, {35572, 4083}
X(56011) = barycentric quotient X(i)/X(j) for these (i, j): {1, 24165}, {6, 16604}, {32, 21757}, {43, 34832}, {81, 16710}, {87, 52573}, {184, 22378}, {192, 20899}, {213, 21827}, {513, 48406}, {2176, 17459}, {2209, 20971}, {4083, 21128}, {20691, 21040}, {35572, 18830}, {55997, 75}

X(56012) = KP2(X(1)) OF X(6) AND X(105)

Barycentrics    a*(a^3*(b-c)-a^2*c^2-b^2*c*(b+c)+a*(b^3+2*b*c^2))*(a^2*b^2+a^3*(b-c)+b*c^2*(b+c)-a*(2*b^2*c+c^3)) : :

X(56012) lies on these lines: {6, 20532}, {101, 978}, {644, 2176}, {645, 27644}, {666, 39930}, {904, 20971}, {932, 20467}, {1575, 34077}, {1743, 20370}, {2209, 3169}, {3009, 33854}, {7121, 17754}, {20332, 40848}, {32911, 52136}

X(56012) = trilinear pole of line {55, 8640}
X(56012) = X(i)-isoconjugate-of-X(j) for these {i, j}: {727, 20343}, {3226, 20467}, {20332, 20366}, {20443, 34077}
X(56012) = X(i)-Dao conjugate of X(j) for these {i, j}: {17793, 20343}, {20532, 20443}
X(56012) = intersection, other than A, B, C, of these circumconics: {{A, B, C, X(6), X(904)}}, {{A, B, C, X(8), X(978)}}, {{A, B, C, X(43), X(17754)}}, {{A, B, C, X(55), X(4383)}}, {{A, B, C, X(83), X(713)}}, {{A, B, C, X(87), X(41527)}}, {{A, B, C, X(101), X(294)}}, {{A, B, C, X(105), X(33295)}}, {{A, B, C, X(239), X(292)}}, {{A, B, C, X(257), X(39798)}}, {{A, B, C, X(291), X(7261)}}, {{A, B, C, X(672), X(39930)}}, {{A, B, C, X(1016), X(1438)}}, {{A, B, C, X(1126), X(1178)}}, {{A, B, C, X(1575), X(20532)}}, {{A, B, C, X(3108), X(40394)}}, {{A, B, C, X(3212), X(25311)}}, {{A, B, C, X(7035), X(9082)}}, {{A, B, C, X(17033), X(41268)}}, {{A, B, C, X(17752), X(20971)}}, {{A, B, C, X(18785), X(27810)}}, {{A, B, C, X(28317), X(37680)}}, {{A, B, C, X(36125), X(43531)}}
X(56012) = barycentric quotient X(i)/X(j) for these (i, j): {726, 20443}, {1575, 20343}, {3009, 20366}, {20777, 20738}, {21760, 20467}

X(56013) = KP2(X(2)) OF X(4) AND X(20)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(5*a^4+b^4+6*b^2*c^2+c^4-6*a^2*(b^2+c^2)) : :

X(56013) lies on these lines: {2, 15851}, {4, 193}, {6, 32000}, {20, 15312}, {53, 6144}, {69, 648}, {112, 32817}, {141, 40138}, {144, 1897}, {196, 1943}, {239, 1119}, {253, 441}, {264, 1992}, {281, 3879}, {297, 20080}, {317, 11008}, {376, 3164}, {385, 6353}, {393, 524}, {394, 14361}, {458, 51170}, {459, 34410}, {653, 53997}, {894, 7046}, {1092, 41425}, {1350, 15258}, {1944, 7003}, {1990, 40341}, {2322, 3945}, {3087, 3629}, {3172, 32830}, {3618, 5702}, {3793, 37460}, {3855, 17035}, {4416, 7952}, {6103, 37690}, {6527, 15905}, {6616, 11441}, {6617, 20213}, {6620, 46444}, {6748, 15534}, {7490, 37683}, {7493, 35311}, {7774, 8889}, {10002, 15069}, {10299, 43980}, {14552, 41083}, {15143, 22152}, {15262, 20806}, {15589, 45141}, {16264, 54132}, {16318, 37668}, {17008, 52290}, {18848, 33893}, {21447, 44146}, {36794, 52710}, {37667, 38282}, {37765, 50992}, {37766, 45794}, {40330, 42873}, {41370, 52713}

X(56013) = reflection of X(i) in X(j) for these {i,j}: {32001, 393}, {6527, 15905}
X(56013) = anticomplement of X(40995)
X(56013) = X(i)-Dao conjugate of X(j) for these {i, j}: {40995, 40995}
X(56013) = X(i)-Ceva conjugate of X(j) for these {i, j}: {14944, 441}, {18848, 2}
X(56013) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {18848, 6327}, {41894, 4329}
X(56013) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2996), X(34410)}}, {{A, B, C, X(6330), X(34208)}}, {{A, B, C, X(6391), X(36609)}}, {{A, B, C, X(8778), X(14248)}}
X(56013) = barycentric product X(i)*X(j) for these (i, j): {75, 8765}, {76, 8778}
X(56013) = barycentric quotient X(i)/X(j) for these (i, j): {8765, 1}, {8778, 6}
X(56013) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 32000, 52288}, {69, 1249, 52283}, {69, 648, 1249}, {193, 43981, 27377}, {193, 9308, 4}, {253, 36413, 441}, {264, 1992, 40065}, {9308, 27377, 43981}

X(56014) = KP2(X(2)) OF X(4) AND X(21)

Barycentrics    (a+b)*(a+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^2+2*b*c-a*(b+c)) : :

X(56014) lies on these lines: {4, 193}, {19, 18206}, {21, 20222}, {25, 17002}, {27, 4373}, {28, 330}, {29, 10405}, {81, 92}, {86, 281}, {144, 3559}, {225, 4416}, {264, 34283}, {273, 2287}, {278, 333}, {283, 45738}, {286, 648}, {314, 46108}, {385, 4231}, {469, 31034}, {524, 1865}, {653, 1014}, {860, 1654}, {894, 41013}, {1068, 17257}, {1119, 16054}, {1396, 31623}, {1783, 27644}, {1792, 25252}, {1812, 1943}, {1826, 3879}, {1957, 38832}, {2303, 54314}, {2322, 15149}, {2331, 54308}, {3164, 6906}, {3194, 26735}, {3651, 18666}, {4227, 41676}, {4658, 39585}, {5136, 17379}, {5235, 17923}, {5333, 52412}, {10446, 46011}, {14571, 16696}, {17037, 37434}, {17913, 27164}, {23602, 54107}, {31917, 31925}, {31923, 53238}, {38810, 44129}

X(56014) = trilinear pole of line {4885, 22091}
X(56014) = X(i)-isoconjugate-of-X(j) for these {i, j}: {71, 9309}, {72, 9315}, {228, 9311}, {810, 30610}, {1214, 9439}, {2200, 32023}
X(56014) = X(i)-Dao conjugate of X(j) for these {i, j}: {4885, 53560}, {39062, 30610}
X(56014) = intersection, other than A, B, C, of circumconics {{A, B, C, X(330), X(2481)}}, {{A, B, C, X(1814), X(6180)}}, {{A, B, C, X(8751), X(14248)}}, {{A, B, C, X(9311), X(44735)}}, {{A, B, C, X(19607), X(38810)}}, {{A, B, C, X(34208), X(54235)}}
X(56014) = barycentric product X(i)*X(j) for these (i, j): {27, 3729}, {29, 9312}, {162, 20907}, {1376, 286}, {4449, 811}, {4885, 648}, {16759, 46102}, {17218, 1897}, {18110, 41676}, {18199, 6335}, {20980, 6331}, {22091, 6528}, {31623, 6180}, {44129, 9310}, {44130, 9316}
X(56014) = barycentric quotient X(i)/X(j) for these (i, j): {27, 9311}, {28, 9309}, {286, 32023}, {648, 30610}, {1376, 72}, {1474, 9315}, {2299, 9439}, {3729, 306}, {3967, 3695}, {4014, 18210}, {4449, 656}, {4513, 3694}, {4885, 525}, {6180, 1214}, {9310, 71}, {9312, 307}, {9316, 73}, {16283, 52370}, {16759, 26932}, {17218, 4025}, {18110, 4580}, {18199, 905}, {20907, 14208}, {20980, 647}, {21052, 4064}, {21139, 4466}, {22091, 520}
X(56014) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {81, 92, 44734}, {286, 1172, 31926}, {286, 648, 1172}

X(56015) = KP2(X(2)) OF X(4) AND X(22)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^6+2*b^2*c^2*(b^2+c^2)-a^2*(b^2+c^2)^2) : :

X(56015) lies on circumconic {{A, B, C, X(2996), X(46140)}} and on these lines: {3, 41676}, {4, 193}, {6, 1235}, {24, 385}, {69, 19595}, {76, 648}, {112, 1975}, {148, 35490}, {183, 39575}, {194, 378}, {232, 7751}, {253, 28425}, {264, 7760}, {297, 45794}, {315, 5523}, {339, 26226}, {458, 1994}, {524, 27376}, {538, 1968}, {1593, 22253}, {1594, 7774}, {2207, 44146}, {2904, 39931}, {3147, 37667}, {3162, 8024}, {3164, 10323}, {3520, 31859}, {3788, 6103}, {3933, 16318}, {4235, 8778}, {6240, 20065}, {7547, 7785}, {7777, 52296}, {7783, 35477}, {7784, 19221}, {7793, 32534}, {7803, 44134}, {7805, 10311}, {7823, 35480}, {7839, 37337}, {7890, 27371}, {7893, 40889}, {7894, 36794}, {9605, 37125}, {10018, 17008}, {10312, 14614}, {12251, 41204}, {15014, 20081}, {15073, 39646}, {17037, 52404}, {17907, 41366}, {18018, 28701}, {19124, 41622}, {20806, 43678}, {23115, 30737}, {28695, 52058}, {28717, 36413}, {28728, 40888}, {32451, 39588}, {34507, 39604}

X(56015) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {76, 648, 8743}, {7754, 9308, 4}

X(56016) = KP2(X(2)) OF X(4) AND X(23)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^6+2*b^2*c^2*(b^2+c^2)-a^2*(b^4+3*b^2*c^2+c^4)) : :

X(56016) lies on circumconic {{A, B, C, X(2996), X(14364)}} and on these lines: {4, 193}, {25, 9870}, {112, 538}, {186, 385}, {194, 3520}, {297, 37779}, {339, 52058}, {378, 22253}, {458, 11004}, {511, 41377}, {524, 5523}, {648, 8744}, {732, 41363}, {892, 52490}, {1235, 7760}, {1236, 22151}, {2914, 39931}, {3793, 10295}, {5971, 44467}, {6103, 7813}, {7577, 7774}, {7751, 39575}, {7775, 50718}, {7785, 54001}, {7793, 17506}, {7805, 10312}, {7839, 37125}, {10311, 41748}, {11580, 34336}, {17037, 34621}, {20065, 34797}, {31859, 35473}, {40889, 50248}, {41253, 51481}

X(56016) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {385, 41676, 186}, {648, 44146, 8744}

X(56017) = KP2(X(2)) OF X(4) AND X(24)

Barycentrics    a^8-2*b^2*c^2*(b^2-c^2)^2-a^6*(b^2+c^2)-a^4*(b^2+c^2)^2+a^2*(b^6+b^4*c^2+b^2*c^4+c^6) : :
X(56017) = -3*X[2]+2*X[52347]

X(56017) lies on these lines: {2, 52347}, {4, 193}, {6, 311}, {22, 385}, {69, 41237}, {148, 52842}, {155, 44145}, {194, 7503}, {264, 275}, {393, 467}, {524, 44128}, {648, 8745}, {1316, 23163}, {1609, 14570}, {1654, 37156}, {2165, 39113}, {3580, 17907}, {5133, 7774}, {5889, 33971}, {7494, 37667}, {7495, 17008}, {7566, 7785}, {7777, 19577}, {7783, 43980}, {8553, 44376}, {9723, 44375}, {9818, 22253}, {11441, 43976}, {12220, 39646}, {19221, 40341}, {19588, 53350}, {20806, 41238}, {25051, 34777}, {26206, 40814}, {31859, 35921}, {35360, 52439}, {40393, 54636}, {41375, 41767}

X(56017) = anticomplement of X(52347)
X(56017) = X(i)-Dao conjugate of X(j) for these {i, j}: {52347, 52347}
X(56017) = X(i)-Ceva conjugate of X(j) for these {i, j}: {8884, 2}
X(56017) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {1096, 2888}, {2148, 6527}, {2190, 1370}, {8795, 21275}, {8882, 4329}, {8884, 6327}, {15422, 21294}, {16813, 17217}, {42405, 21305}
X(56017) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2996), X(34385)}}, {{A, B, C, X(5392), X(27364)}}, {{A, B, C, X(14248), X(41525)}}, {{A, B, C, X(34208), X(42354)}}
X(56017) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 311, 41231}, {1993, 5392, 52253}, {7754, 9308, 193}, {20806, 41760, 41238}

X(56018) = KP2(X(2)) OF X(4) AND X(27)

Barycentrics    (a+b)*(a+c)*(a^2+2*a*(b+c)-(b+c)^2) : :
X(56018) = -3*X[2]+2*X[41014], -3*X[3017]+2*X[3454], -4*X[8258]+3*X[33160]

X(56018) lies on these lines: {1, 333}, {2, 41014}, {3, 20018}, {4, 193}, {6, 10449}, {8, 81}, {10, 86}, {20, 20019}, {21, 145}, {27, 3187}, {28, 39696}, {29, 1069}, {30, 20077}, {40, 4229}, {55, 37296}, {58, 519}, {65, 1943}, {69, 387}, {72, 1999}, {78, 18465}, {99, 28527}, {100, 37288}, {110, 4248}, {190, 2901}, {192, 3927}, {238, 35633}, {239, 942}, {283, 41575}, {284, 24391}, {314, 989}, {320, 23537}, {341, 30939}, {385, 6998}, {386, 14829}, {404, 37639}, {405, 37652}, {442, 17778}, {447, 44698}, {474, 37684}, {496, 37373}, {517, 37422}, {518, 18178}, {524, 1330}, {643, 1780}, {648, 8747}, {740, 1046}, {758, 18719}, {849, 30606}, {859, 20037}, {894, 5295}, {938, 2287}, {940, 9534}, {944, 7415}, {958, 18185}, {964, 37685}, {986, 17206}, {999, 20036}, {1014, 53997}, {1150, 19270}, {1193, 32919}, {1203, 32942}, {1210, 27398}, {1326, 49609}, {1408, 41687}, {1412, 4848}, {1434, 3339}, {1654, 4205}, {1698, 25507}, {1706, 18164}, {1714, 18134}, {1724, 33309}, {1737, 31631}, {1743, 35629}, {1778, 14974}, {1788, 14868}, {1812, 18391}, {1817, 20043}, {1897, 3559}, {1993, 11109}, {2049, 17379}, {2292, 41813}, {2303, 5839}, {2322, 3562}, {2475, 20086}, {2476, 31034}, {2650, 27368}, {2784, 54160}, {2895, 5051}, {2907, 14054}, {2975, 37303}, {3017, 3454}, {3167, 16066}, {3180, 37144}, {3181, 37145}, {3241, 4921}, {3244, 4653}, {3286, 3913}, {3293, 29766}, {3555, 5208}, {3578, 26064}, {3616, 5235}, {3617, 8025}, {3621, 4720}, {3622, 17557}, {3623, 17588}, {3633, 52352}, {3634, 28620}, {3679, 25526}, {3695, 6542}, {3710, 50292}, {3714, 4663}, {3736, 49497}, {3769, 3811}, {3786, 34790}, {3870, 54356}, {3871, 4184}, {3874, 32922}, {3875, 8822}, {3931, 40773}, {3936, 24883}, {3945, 37153}, {3996, 5264}, {4018, 19642}, {4042, 19853}, {4201, 48847}, {4202, 32863}, {4221, 12245}, {4225, 20040}, {4228, 19993}, {4256, 50588}, {4259, 50633}, {4260, 50628}, {4267, 12513}, {4273, 50131}, {4276, 8666}, {4278, 8715}, {4340, 48816}, {4417, 5292}, {4442, 14450}, {4641, 7283}, {4646, 16696}, {4678, 17589}, {4701, 4803}, {5015, 5847}, {5047, 19742}, {5247, 38832}, {5278, 37035}, {5333, 9780}, {5361, 16342}, {5554, 26637}, {5687, 13588}, {5706, 13727}, {5708, 17490}, {5739, 52258}, {5752, 50579}, {5767, 37088}, {5774, 16738}, {5786, 10446}, {5814, 17363}, {5815, 17183}, {5844, 15952}, {5889, 37420}, {5904, 18417}, {5965, 37823}, {6175, 50256}, {6515, 17555}, {6646, 50067}, {6762, 10461}, {6996, 10441}, {7380, 7774}, {7410, 37667}, {7413, 48909}, {7419, 20041}, {7474, 20045}, {8258, 33160}, {8728, 17300}, {10453, 16466}, {10471, 35616}, {10916, 33071}, {11024, 17169}, {11108, 17349}, {11851, 31900}, {12514, 49470}, {13161, 34379}, {13725, 14552}, {13728, 37653}, {13741, 32911}, {14009, 24390}, {14011, 17757}, {14594, 41538}, {14996, 16454}, {15934, 19851}, {16053, 17316}, {16065, 33093}, {16726, 21896}, {16749, 30806}, {16834, 24632}, {16948, 20050}, {17002, 37149}, {17034, 17681}, {17056, 25446}, {17156, 54421}, {17162, 17164}, {17182, 21075}, {17343, 37164}, {17514, 26044}, {17528, 50133}, {17539, 20014}, {17551, 46933}, {17587, 20046}, {17676, 31303}, {17770, 24851}, {18165, 34791}, {18755, 50252}, {19280, 19684}, {19623, 52244}, {19860, 26638}, {19998, 35983}, {20009, 47512}, {20051, 35978}, {20090, 26051}, {20158, 33817}, {20536, 37159}, {20970, 26244}, {22253, 49130}, {24161, 50755}, {24556, 24982}, {24880, 41878}, {25059, 37592}, {25441, 30832}, {25645, 41806}, {25650, 35466}, {26117, 49716}, {26131, 42045}, {26300, 49592}, {26301, 49593}, {30699, 31902}, {31145, 51669}, {32852, 36568}, {34195, 39766}, {35935, 50129}, {37038, 54429}, {37092, 51223}, {37156, 45794}, {37176, 37666}, {37482, 50586}, {37516, 50619}, {39589, 49765}, {39594, 54386}, {41610, 51192}, {42025, 53620}, {43531, 46922}, {44143, 51481}, {48863, 50638}, {48875, 50577}, {50074, 54367}

X(56018) = reflection of X(i) in X(j) for these {i,j}: {1043, 58}, {1330, 1834}, {4234, 41629}
X(56018) = anticomplement of X(41014)
X(56018) = trilinear pole of line {20315, 48269}
X(56018) = X(i)-Dao conjugate of X(j) for these {i, j}: {4361, 4365}, {20315, 3120}, {41014, 41014}
X(56018) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {28, 2891}, {1126, 52364}, {1171, 4329}, {1474, 41821}, {28615, 3151}, {32676, 14779}, {40438, 1370}, {47947, 13219}, {52558, 20243}
X(56018) = intersection, other than A, B, C, of circumconics {{A, B, C, X(79), X(3879)}}, {{A, B, C, X(989), X(1126)}}, {{A, B, C, X(1000), X(1222)}}, {{A, B, C, X(1069), X(6391)}}, {{A, B, C, X(1778), X(5331)}}, {{A, B, C, X(2994), X(2996)}}, {{A, B, C, X(4600), X(8747)}}, {{A, B, C, X(5203), X(31013)}}, {{A, B, C, X(32014), X(37870)}}
X(56018) = barycentric product X(i)*X(j) for these (i, j): {1778, 75}, {1788, 333}, {14868, 92}, {14974, 310}, {17314, 86}, {17888, 4567}, {20315, 648}, {46937, 81}, {48269, 99}, {50501, 799}
X(56018) = barycentric quotient X(i)/X(j) for these (i, j): {1778, 1}, {1788, 226}, {14868, 63}, {14974, 42}, {17314, 10}, {17888, 16732}, {20315, 525}, {46937, 321}, {48269, 523}, {50501, 661}
X(56018) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 333, 11110}, {6, 10449, 13740}, {8, 81, 1010}, {10, 4658, 86}, {10, 86, 14007}, {58, 519, 1043}, {69, 387, 16062}, {145, 16704, 21}, {519, 41629, 4234}, {1043, 41629, 58}, {1150, 19767, 19270}, {1330, 1834, 17677}, {1698, 28619, 25507}, {3555, 18180, 5208}, {3617, 8025, 14005}, {3621, 11115, 4720}, {4205, 49718, 1654}, {4678, 26860, 17589}, {12649, 40571, 29}, {17731, 49488, 35916}, {20090, 26051, 49743}

X(56019) = KP2(X(2)) OF X(4) AND X(28)

Barycentrics    (a+b)*(a+c)*(a^3-2*b*c*(b+c)+a*(b+c)^2) : :

X(56019) lies on these lines: {4, 193}, {6, 44140}, {21, 192}, {27, 30699}, {58, 3729}, {69, 33736}, {75, 2303}, {81, 314}, {86, 2345}, {92, 1172}, {144, 16704}, {190, 1778}, {194, 37399}, {239, 2287}, {284, 3875}, {297, 18685}, {333, 17257}, {346, 16050}, {385, 4220}, {524, 21287}, {536, 1333}, {648, 2991}, {964, 17379}, {1010, 20009}, {1444, 19623}, {1654, 5051}, {1766, 18206}, {1817, 3210}, {2092, 26243}, {2346, 20045}, {3164, 36029}, {3663, 24632}, {3912, 17189}, {4019, 17763}, {4273, 4852}, {4452, 14953}, {4461, 11115}, {4921, 17333}, {5016, 17363}, {5235, 17248}, {5279, 19791}, {5327, 51192}, {8759, 44766}, {13588, 17759}, {14005, 28604}, {16998, 47511}, {17033, 17743}, {17147, 27174}, {17148, 54391}, {17366, 30906}, {18178, 43216}, {19645, 37683}, {25255, 39766}, {27958, 33296}, {28605, 37095}, {30939, 46738}, {32863, 50320}, {41316, 52897}, {41364, 46108}, {41610, 49496}, {41629, 42047}, {53421, 53508}

X(56019) = reflection of X(i) in X(j) for these {i,j}: {21287, 53417}
X(56019) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {1169, 4329}, {2203, 5484}, {2363, 1370}
X(56019) = intersection, other than A, B, C, of these circumconics: {{A, B, C, X(2298), X(14248)}}, {{A, B, C, X(2991), X(6391)}}, {{A, B, C, X(2996), X(2997)}}, {{A, B, C, X(4601), X(5317)}}, {{A, B, C, X(14534), X(38810)}}, {{A, B, C, X(30710), X(34208)}}
X(56019) = barycentric product X(i)*X(j) for these (i, j): {23676, 4600}
X(56019) = barycentric quotient X(i)/X(j) for these (i, j): {23676, 3120}
X(56019) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 2303, 26643}

X(56020) = KP2(X(2)) OF X(4) AND X(29)

Barycentrics    (a+b)*(a+c)*(a^3-3*a^2*(b+c)+(b-c)^2*(b+c)+a*(b+c)^2) : :

X(56020) lies on these lines: {4, 193}, {6, 37086}, {7, 2287}, {9, 86}, {21, 144}, {27, 5905}, {28, 42461}, {29, 3868}, {57, 27398}, {63, 37265}, {69, 5746}, {72, 894}, {81, 329}, {190, 22021}, {218, 27644}, {226, 333}, {284, 527}, {332, 40882}, {385, 7413}, {405, 17379}, {440, 17778}, {442, 1654}, {518, 5327}, {524, 1901}, {648, 8748}, {651, 52673}, {758, 11683}, {943, 37296}, {1014, 12848}, {1043, 3729}, {1260, 13588}, {1434, 23618}, {1708, 31631}, {1743, 17189}, {1817, 9965}, {1944, 9119}, {1992, 5802}, {1993, 37279}, {2303, 4644}, {2327, 41572}, {2328, 9440}, {2905, 14054}, {3419, 17363}, {3487, 11110}, {3879, 8804}, {3945, 37169}, {4199, 40721}, {4229, 5759}, {4273, 17276}, {4461, 4720}, {4480, 52352}, {4658, 12572}, {5208, 10025}, {5757, 13727}, {5758, 37422}, {5776, 10446}, {6356, 17950}, {7232, 30906}, {7415, 18446}, {7522, 37652}, {8232, 16713}, {10381, 17499}, {11517, 37288}, {12635, 25252}, {13442, 20077}, {14953, 20059}, {16050, 17350}, {17139, 41610}, {17169, 24557}, {17206, 27958}, {17300, 30810}, {17364, 41004}, {17532, 50074}, {18666, 30266}, {20072, 25516}, {20078, 27174}, {25255, 34195}, {26647, 40905}, {28609, 41629}

X(56020) = reflection of X(i) in X(j) for these {i,j}: {2893, 1901}, {8822, 284}
X(56020) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {40430, 1370}
X(56020) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2279), X(14248)}}, {{A, B, C, X(2996), X(39695)}}, {{A, B, C, X(4416), X(6598)}}, {{A, B, C, X(4620), X(8748)}}, {{A, B, C, X(23618), X(25568)}}
X(56020) = barycentric product X(i)*X(j) for these (i, j): {25568, 86}
X(56020) = barycentric quotient X(i)/X(j) for these (i, j): {25568, 10}
X(56020) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 2287, 16054}, {9, 86, 16053}, {69, 5746, 37445}, {284, 527, 8822}, {524, 1901, 2893}, {5905, 40571, 27}

X(56021) = KP2(X(2)) OF X(4) AND X(30)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(4*a^4+b^4+4*b^2*c^2+c^4-5*a^2*(b^2+c^2)) : :
X(56021) = -3*X[297]+2*X[340], -2*X[1494]+3*X[44578], -4*X[3163]+3*X[44576], -4*X[3284]+3*X[40884], -3*X[44650]+4*X[52951]

X(56021) lies on these lines: {2, 5702}, {4, 193}, {6, 44134}, {30, 39358}, {69, 11331}, {232, 50251}, {264, 3629}, {297, 340}, {317, 6144}, {323, 15262}, {325, 6103}, {385, 468}, {393, 11008}, {427, 7837}, {441, 39352}, {445, 50256}, {458, 1992}, {460, 38294}, {470, 3180}, {471, 3181}, {532, 6110}, {533, 6111}, {550, 3164}, {1249, 20080}, {1494, 44578}, {1897, 20072}, {2322, 20090}, {3163, 44576}, {3186, 46444}, {3284, 40884}, {3292, 47204}, {3580, 14920}, {3589, 53025}, {3793, 37934}, {3850, 17035}, {5032, 52288}, {5059, 17037}, {5094, 7774}, {5095, 39931}, {5965, 6530}, {7777, 52293}, {7779, 16318}, {7877, 27376}, {8057, 33294}, {9870, 52301}, {10151, 19570}, {10295, 41676}, {11064, 16080}, {11160, 52283}, {11898, 41371}, {15534, 52281}, {15712, 43980}, {16264, 37517}, {17008, 52292}, {17555, 50074}, {17907, 40341}, {20065, 37196}, {25045, 46818}, {25986, 42045}, {31859, 35485}, {32000, 51170}, {32455, 36794}, {34380, 41204}, {34507, 42873}, {37448, 50133}, {37667, 52290}, {38664, 53778}, {40890, 52229}, {41617, 52418}, {41628, 52280}, {44650, 52951}

X(56021) = reflection of X(i) in X(j) for these {i,j}: {297, 648}, {340, 1990}, {39352, 441}
X(56021) = anticomplement of X(40996)
X(56021) = X(i)-Dao conjugate of X(j) for these {i, j}: {40996, 40996}
X(56021) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {34570, 4329}
X(56021) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2996), X(5641)}}, {{A, B, C, X(44877), X(51228)}}
X(56021) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 44134, 52289}, {69, 40138, 11331}, {193, 9308, 27377}, {340, 1990, 297}, {340, 648, 1990}, {524, 1990, 340}

X(56022) = KP2(X(2)) OF X(4) AND X(140)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(-b^4+4*b^2*c^2-c^4+a^2*(b^2+c^2)) : :

X(56022) lies on these lines: {2, 42459}, {4, 193}, {5, 3164}, {6, 52281}, {25, 17008}, {53, 141}, {69, 52282}, {194, 1907}, {273, 48627}, {317, 40341}, {318, 48628}, {324, 3580}, {385, 428}, {393, 458}, {427, 7777}, {468, 17006}, {524, 32002}, {546, 17035}, {547, 43982}, {550, 43980}, {623, 52670}, {624, 52671}, {625, 27371}, {648, 6748}, {1990, 6329}, {2052, 37648}, {3260, 53481}, {3575, 14712}, {3589, 37765}, {3793, 6756}, {5064, 7774}, {5241, 31623}, {6530, 19130}, {6656, 44142}, {6820, 8796}, {7714, 37667}, {7790, 21447}, {8744, 53489}, {8754, 39931}, {10549, 46104}, {10985, 22329}, {11547, 41244}, {14129, 37636}, {14767, 52945}, {14893, 39358}, {15466, 37873}, {16264, 48884}, {17037, 50689}, {17907, 47355}, {32000, 37174}, {32085, 52979}, {33630, 51171}, {33971, 46264}, {36412, 45198}, {36430, 44576}, {39284, 54911}, {40853, 41008}, {40896, 41005}, {42400, 51360}, {53416, 53477}

X(56022) = reflection of X(i) in X(j) for these {i,j}: {45198, 36412}
X(56022) = polar conjugate of X(45857)
X(56022) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 45857}
X(56022) = intersection, other than A, B, C, of circumconics {{A, B, C, X(327), X(2996)}}, {{A, B, C, X(5943), X(6391)}}, {{A, B, C, X(27377), X(40413)}}
X(56022) = barycentric product X(i)*X(j) for these (i, j): {264, 5943}, {17868, 92}
X(56022) = barycentric quotient X(i)/X(j) for these (i, j): {4, 45857}, {5943, 3}, {17868, 63}
X(56022) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 43981, 9308}, {4, 9308, 27377}, {53, 264, 297}

X(56023) = KP2(X(2)) OF X(6) AND X(81)

Barycentrics    (a+b)*(a+c)*(-(b*c*(b+c))+a*(b^2+b*c+c^2)) : :

X(56023) lies on these lines: {2, 39983}, {6, 194}, {21, 16684}, {37, 274}, {45, 32107}, {58, 32921}, {75, 27164}, {76, 4261}, {81, 4360}, {86, 192}, {99, 713}, {148, 53421}, {190, 27644}, {310, 2276}, {314, 536}, {325, 53417}, {330, 16884}, {333, 3210}, {344, 16752}, {346, 18600}, {385, 1030}, {538, 2092}, {583, 17034}, {594, 17759}, {668, 21858}, {714, 1045}, {726, 3736}, {740, 24437}, {1014, 4552}, {1043, 3242}, {1107, 20174}, {1108, 16728}, {1172, 41676}, {1213, 1655}, {1278, 16738}, {1444, 19623}, {1575, 31008}, {1778, 17489}, {2220, 7760}, {2277, 28660}, {2321, 16887}, {2345, 16705}, {3175, 16700}, {3247, 17175}, {3286, 49453}, {3644, 30939}, {3693, 16750}, {3703, 33730}, {3729, 54308}, {3760, 25505}, {3786, 49447}, {3875, 18206}, {3891, 4184}, {3943, 33947}, {3948, 24530}, {3950, 17205}, {3995, 5333}, {4254, 22253}, {4272, 17499}, {4277, 34283}, {4452, 16713}, {4658, 50281}, {4659, 10455}, {4664, 16709}, {4718, 16726}, {4788, 17178}, {5019, 7781}, {5069, 7757}, {5124, 7783}, {5235, 17495}, {5276, 8267}, {6144, 50577}, {6385, 40874}, {7754, 36744}, {7798, 16946}, {8680, 39774}, {10458, 17155}, {13588, 20990}, {14570, 32029}, {15668, 24621}, {16589, 25457}, {16685, 34063}, {16712, 17281}, {16722, 16885}, {16736, 35652}, {16749, 27396}, {17150, 39673}, {17160, 29767}, {17189, 25536}, {17233, 30965}, {17262, 52897}, {17277, 31036}, {17299, 33297}, {17314, 30941}, {17318, 18166}, {17362, 21226}, {18140, 46838}, {18147, 24598}, {18196, 23886}, {18601, 42044}, {18792, 49445}, {20168, 32005}, {21065, 30170}, {24557, 25243}, {25426, 42328}, {25507, 41839}, {25534, 27633}, {26110, 40908}, {28606, 30599}, {30940, 32453}, {30984, 32848}, {31089, 53486}, {31859, 36743}, {32934, 38832}, {39747, 42025}, {41629, 50120}, {47286, 50036}

X(56023) = reflection of X(i) in X(j) for these {i,j}: {314, 16696}, {3770, 2092}
X(56023) = anticomplement of X(53478)
X(56023) = trilinear pole of line {20983, 21260}
X(56023) = X(i)-Dao conjugate of X(j) for these {i, j}: {21260, 3121}, {53478, 53478}
X(56023) = X(i)-Ceva conjugate of X(j) for these {i, j}: {40408, 2}
X(56023) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {40408, 6327}, {40433, 21287}, {40439, 315}, {50520, 21294}
X(56023) = intersection, other than A, B, C, of circumconics {{A, B, C, X(713), X(3224)}}, {{A, B, C, X(2998), X(18825)}}, {{A, B, C, X(25264), X(25426)}}
X(56023) = barycentric product X(i)*X(j) for these (i, j): {17458, 799}, {20909, 662}, {20983, 670}, {21055, 4610}, {21142, 4600}, {21260, 99}, {22095, 6331}, {30473, 81}, {32925, 86}
X(56023) = barycentric quotient X(i)/X(j) for these (i, j): {17458, 661}, {20909, 1577}, {20983, 512}, {21055, 4024}, {21142, 3120}, {21260, 523}, {22095, 647}, {30473, 321}, {32925, 10}
X(56023) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {37, 274, 25508}, {75, 40773, 27164}, {330, 20170, 16884}, {536, 16696, 314}, {538, 2092, 3770}, {3948, 24530, 27111}, {17147, 17148, 4360}

X(56024) = KP2(X(2)) OF X(8) AND X(42)

Barycentrics    2*b^2*c^2+a^3*(b+c)-a^2*(b^2+c^2) : :
X(56024) = -3*X[2]+2*X[24214]

X(56024) lies on these lines: {2, 24214}, {7, 27523}, {8, 144}, {9, 34284}, {31, 7754}, {37, 4754}, {39, 4721}, {41, 1975}, {42, 17499}, {57, 28809}, {71, 3770}, {72, 50156}, {75, 3691}, {76, 672}, {190, 1334}, {194, 1193}, {213, 538}, {321, 25735}, {330, 1149}, {346, 36854}, {350, 1475}, {519, 20109}, {527, 17137}, {536, 3780}, {726, 17489}, {894, 1655}, {1107, 24330}, {1400, 28660}, {2251, 7816}, {2269, 34283}, {2275, 4713}, {2292, 49514}, {2295, 17351}, {2340, 25242}, {3161, 27253}, {3214, 17759}, {3663, 26965}, {3730, 3761}, {3760, 4253}, {3765, 25733}, {3933, 4766}, {3952, 25244}, {3967, 4447}, {3971, 25263}, {3975, 32939}, {3978, 53129}, {4044, 18206}, {4357, 26035}, {4396, 33863}, {4400, 17735}, {4441, 21384}, {4465, 16604}, {4805, 7748}, {4968, 49516}, {5230, 6392}, {5254, 24995}, {5308, 30568}, {6381, 16549}, {7760, 21764}, {7881, 30816}, {16466, 22253}, {16552, 20888}, {16827, 40908}, {17001, 37603}, {17002, 54354}, {17033, 17350}, {17140, 25261}, {17165, 25237}, {17257, 31339}, {17353, 26978}, {17738, 33950}, {17753, 30036}, {17754, 18135}, {17755, 20880}, {17781, 50154}, {19582, 27340}, {20244, 49774}, {20335, 27109}, {20347, 26770}, {21024, 24690}, {21071, 30941}, {21422, 30807}, {21935, 47286}, {23649, 26959}, {24215, 27097}, {24443, 25994}, {25591, 25918}, {27318, 28257}, {50093, 50155}

X(56024) = anticomplement of X(24214)
X(56024) = X(i)-Dao conjugate of X(j) for these {i, j}: {24214, 24214}
X(56024) = barycentric product X(i)*X(j) for these (i, j): {17066, 190}
X(56024) = barycentric quotient X(i)/X(j) for these (i, j): {17066, 514}
X(56024) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 27523, 29966}, {190, 1909, 1334}, {194, 24514, 1193}, {16552, 20888, 24592}, {17350, 20081, 17033}, {17499, 25264, 42}, {20347, 26770, 29960}

X(56025) = KP2(X(2)) OF X(8) AND X(43)

Barycentrics    2*b^2*c^2+a^3*(b+c)-a*b*c*(b+c)-a^2*(b^2-b*c+c^2) : :

X(56025) lies on these lines: {1, 1655}, {2, 23649}, {7, 30030}, {8, 144}, {9, 1909}, {43, 194}, {45, 24656}, {57, 3975}, {63, 3765}, {76, 17026}, {85, 17755}, {190, 3208}, {239, 20081}, {304, 35102}, {330, 21214}, {527, 21281}, {668, 3501}, {726, 21216}, {799, 24615}, {894, 41838}, {982, 25994}, {1086, 24735}, {1334, 25728}, {1423, 27424}, {1475, 18135}, {1707, 4039}, {1743, 17033}, {1757, 9902}, {1975, 3684}, {2082, 17738}, {2295, 50127}, {3177, 17760}, {3596, 44421}, {3691, 4384}, {3760, 45751}, {3761, 16552}, {3780, 3875}, {3912, 27523}, {3985, 18156}, {4253, 6381}, {4554, 34497}, {4713, 17448}, {4721, 16975}, {4754, 10436}, {5247, 7754}, {5814, 50153}, {5905, 30059}, {6376, 17754}, {6392, 33137}, {9369, 10025}, {16779, 16916}, {16997, 37608}, {17298, 29966}, {17304, 26965}, {17308, 26035}, {17316, 30568}, {17350, 17752}, {17753, 49774}, {18206, 28660}, {19565, 53676}, {20347, 30036}, {20436, 30807}, {20943, 37686}, {21025, 24691}, {24214, 27299}, {24349, 27288}, {24351, 24708}, {25101, 27253}, {25264, 50581}, {25298, 32933}, {25350, 25610}, {26102, 27269}, {27340, 27538}, {27626, 44139}, {28809, 30567}, {30038, 30946}, {33888, 33890}, {37598, 49514}, {41015, 49518}, {46196, 52716}, {50029, 54406}

X(56025) = anticomplement of X(24215)
X(56025) = X(i)-Dao conjugate of X(j) for these {i, j}: {24215, 24215}
X(56025) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2665), X(3062)}}, {{A, B, C, X(10405), X(39925)}}
X(56025) = barycentric product X(i)*X(j) for these (i, j): {22222, 799}, {24666, 668}
X(56025) = barycentric quotient X(i)/X(j) for these (i, j): {22222, 661}, {24666, 513}
X(56025) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {76, 21384, 17026}, {190, 24524, 3208}, {3177, 32937, 17760}, {17350, 21219, 17752}, {21226, 24514, 1}, {27523, 36854, 3912}

X(56026) = KP2(X(2)) OF X(8) AND X(86)

Barycentrics    (a^3+(b-c)^2*c-a^2*(2*b+c)+a*(b^2+4*b*c-c^2))*(a^3+b*(b-c)^2-a^2*(b+2*c)+a*(-b^2+4*b*c+c^2)) : :

X(56026) lies on these lines: {2, 4513}, {7, 480}, {8, 36620}, {75, 8580}, {86, 13405}, {144, 11051}, {200, 1088}, {658, 17658}, {673, 3452}, {2319, 27498}, {3729, 19605}, {5437, 27475}, {5836, 7249}, {6745, 21453}, {14828, 30712}, {35983, 39734}

X(56026) = isogonal conjugate of X(20978)
X(56026) = isotomic conjugate of X(11019)
X(56026) = trilinear pole of line {40872, 514}
X(56026) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 20978}, {6, 40133}, {19, 22088}, {25, 10167}, {31, 11019}, {32, 20905}, {56, 14100}, {57, 1200}, {213, 26818}, {604, 41006}, {1333, 21049}, {1420, 45229}
X(56026) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 14100}, {2, 11019}, {3, 20978}, {6, 22088}, {9, 40133}, {37, 21049}, {3161, 41006}, {5452, 1200}, {6376, 20905}, {6505, 10167}, {6626, 26818}
X(56026) = X(i)-cross conjugate of X(j) for these {i, j}: {3900, 190}, {20103, 2}, {46402, 668}
X(56026) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(8580)}}, {{A, B, C, X(2), X(7)}}, {{A, B, C, X(8), X(16284)}}, {{A, B, C, X(10), X(13405)}}, {{A, B, C, X(69), X(52406)}}, {{A, B, C, X(76), X(52156)}}, {{A, B, C, X(144), X(4461)}}, {{A, B, C, X(200), X(480)}}, {{A, B, C, X(312), X(8817)}}, {{A, B, C, X(333), X(4998)}}, {{A, B, C, X(664), X(31628)}}, {{A, B, C, X(765), X(6605)}}, {{A, B, C, X(1043), X(1257)}}, {{A, B, C, X(1222), X(1376)}}, {{A, B, C, X(1280), X(55997)}}, {{A, B, C, X(1909), X(5836)}}, {{A, B, C, X(2481), X(40420)}}, {{A, B, C, X(3452), X(7018)}}, {{A, B, C, X(4102), X(34409)}}, {{A, B, C, X(4416), X(4431)}}, {{A, B, C, X(4847), X(6745)}}, {{A, B, C, X(4997), X(6063)}}, {{A, B, C, X(5437), X(40719)}}, {{A, B, C, X(5850), X(51090)}}, {{A, B, C, X(6557), X(44186)}}, {{A, B, C, X(7045), X(40399)}}, {{A, B, C, X(11019), X(20103)}}, {{A, B, C, X(14004), X(35983)}}, {{A, B, C, X(26981), X(27024)}}, {{A, B, C, X(32008), X(40419)}}, {{A, B, C, X(32023), X(35160)}}, {{A, B, C, X(40417), X(40422)}}
X(56026) = barycentric product X(i)*X(j) for these (i, j): {14493, 304}, {23618, 8}
X(56026) = barycentric quotient X(i)/X(j) for these (i, j): {1, 40133}, {2, 11019}, {3, 22088}, {6, 20978}, {8, 41006}, {9, 14100}, {10, 21049}, {55, 1200}, {63, 10167}, {75, 20905}, {86, 26818}, {144, 43182}, {3680, 45202}, {14493, 19}, {23618, 7}

X(56027) = KP3(X(1)) OF X(1) AND X(4)

Barycentrics    a*(2*a^3+2*b^3-b^2*c-2*b*c^2+c^3-a^2*(2*b+c)-2*a*(b^2+c^2))*(2*a^3+b^3-2*b^2*c-b*c^2+2*c^3-a^2*(b+2*c)-2*a*(b^2+c^2)) : :

X(56027) lies on the Feuerbach hyperbola and on these lines: {1, 6875}, {3, 17097}, {4, 2646}, {7, 1385}, {8, 5791}, {9, 22836}, {21, 5730}, {36, 15173}, {55, 1389}, {79, 3485}, {80, 498}, {84, 13384}, {90, 45230}, {104, 34471}, {411, 37606}, {1000, 37080}, {1056, 24299}, {1058, 43740}, {1156, 3560}, {1319, 3296}, {1320, 3295}, {1388, 15179}, {1392, 9957}, {1476, 10246}, {2320, 3869}, {2476, 10609}, {3057, 14497}, {3062, 6261}, {3255, 5698}, {3488, 6598}, {3576, 5665}, {3577, 3601}, {3612, 6876}, {3616, 11604}, {3746, 21398}, {4313, 37820}, {5426, 15910}, {5557, 21842}, {5558, 24928}, {5560, 6873}, {5561, 12047}, {5703, 10526}, {6597, 30144}, {6855, 7319}, {6869, 30275}, {10266, 11415}, {10393, 38271}, {18490, 20323}, {23838, 48340}, {34918, 45701}

X(56027) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 31266}
X(56027) = X(i)-vertex conjugate of X(j) for these {i, j}: {56, 3296}
X(56027) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 31266}
X(56027) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(2), X(22836)}}, {{A, B, C, X(3), X(2646)}}, {{A, B, C, X(28), X(6857)}}, {{A, B, C, X(29), X(6875)}}, {{A, B, C, X(35), X(37525)}}, {{A, B, C, X(36), X(37571)}}, {{A, B, C, X(37), X(5730)}}, {{A, B, C, X(40), X(13384)}}, {{A, B, C, X(55), X(945)}}, {{A, B, C, X(56), X(1175)}}, {{A, B, C, X(77), X(4305)}}, {{A, B, C, X(78), X(21165)}}, {{A, B, C, X(284), X(3417)}}, {{A, B, C, X(498), X(4511)}}, {{A, B, C, X(517), X(34471)}}, {{A, B, C, X(759), X(959)}}, {{A, B, C, X(951), X(10623)}}, {{A, B, C, X(953), X(1036)}}, {{A, B, C, X(957), X(2218)}}, {{A, B, C, X(999), X(37080)}}, {{A, B, C, X(1057), X(3445)}}, {{A, B, C, X(1068), X(45230)}}, {{A, B, C, X(1319), X(3295)}}, {{A, B, C, X(1388), X(9957)}}, {{A, B, C, X(1411), X(37739)}}, {{A, B, C, X(1442), X(4299)}}, {{A, B, C, X(1807), X(11375)}}, {{A, B, C, X(1870), X(3486)}}, {{A, B, C, X(2098), X(15178)}}, {{A, B, C, X(2167), X(55963)}}, {{A, B, C, X(2217), X(5791)}}, {{A, B, C, X(2339), X(45098)}}, {{A, B, C, X(3057), X(10246)}}, {{A, B, C, X(3303), X(24928)}}, {{A, B, C, X(3316), X(30557)}}, {{A, B, C, X(3317), X(30556)}}, {{A, B, C, X(3345), X(3576)}}, {{A, B, C, X(3431), X(52185)}}, {{A, B, C, X(3477), X(28219)}}, {{A, B, C, X(3560), X(52891)}}, {{A, B, C, X(3746), X(21842)}}, {{A, B, C, X(3748), X(7373)}}, {{A, B, C, X(3869), X(4653)}}, {{A, B, C, X(5048), X(37624)}}, {{A, B, C, X(5397), X(10570)}}, {{A, B, C, X(5426), X(46441)}}, {{A, B, C, X(5697), X(24926)}}, {{A, B, C, X(6767), X(20323)}}, {{A, B, C, X(6852), X(17515)}}, {{A, B, C, X(7040), X(7098)}}, {{A, B, C, X(7952), X(21740)}}, {{A, B, C, X(7987), X(53054)}}, {{A, B, C, X(10013), X(37142)}}, {{A, B, C, X(11270), X(37741)}}, {{A, B, C, X(13390), X(38234)}}, {{A, B, C, X(13472), X(36052)}}, {{A, B, C, X(24299), X(26357)}}, {{A, B, C, X(24624), X(25417)}}, {{A, B, C, X(24927), X(26358)}}, {{A, B, C, X(25430), X(36100)}}, {{A, B, C, X(26363), X(34772)}}, {{A, B, C, X(30392), X(53053)}}, {{A, B, C, X(37600), X(37606)}}, {{A, B, C, X(37837), X(39167)}}, {{A, B, C, X(39392), X(41442)}}, {{A, B, C, X(40437), X(43531)}}
X(56027) = barycentric quotient X(i)/X(j) for these (i, j): {1, 31266}

X(56028) = KP3(X(1)) OF X(1) AND X(7)

Barycentrics    a*(2*a^2-4*a*b+2*b^2-3*a*c-3*b*c+c^2)*(2*a^2-3*a*b+b^2-4*a*c-3*b*c+2*c^2) : :

X(56028) lies on the Feuerbach hyperbola and on these lines: {4, 8236}, {7, 3748}, {8, 17240}, {9, 3957}, {21, 42871}, {79, 390}, {294, 16777}, {516, 43732}, {885, 4802}, {1000, 15933}, {1001, 32635}, {1100, 40779}, {1320, 8162}, {2550, 43741}, {3254, 20095}, {3255, 20059}, {3551, 4343}, {3616, 43745}, {4326, 31507}, {4900, 54318}, {5557, 11038}, {5558, 37080}, {5560, 43179}, {5561, 30331}, {6598, 10587}, {7284, 30284}, {10389, 10390}, {14189, 30494}, {17570, 38316}, {18490, 24929}, {30318, 43730}, {30332, 43733}

X(56028) = trilinear pole of line {650, 42325}
X(56028) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 20195}, {1212, 39669}
X(56028) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 20195}
X(56028) = X(i)-cross conjugate of X(j) for these {i, j}: {11025, 7}
X(56028) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(2), X(3957)}}, {{A, B, C, X(6), X(42819)}}, {{A, B, C, X(37), X(42871)}}, {{A, B, C, X(55), X(3748)}}, {{A, B, C, X(59), X(3477)}}, {{A, B, C, X(77), X(8236)}}, {{A, B, C, X(81), X(42318)}}, {{A, B, C, X(390), X(1442)}}, {{A, B, C, X(518), X(4802)}}, {{A, B, C, X(673), X(25417)}}, {{A, B, C, X(765), X(30712)}}, {{A, B, C, X(1001), X(1100)}}, {{A, B, C, X(1002), X(2160)}}, {{A, B, C, X(1255), X(39273)}}, {{A, B, C, X(1280), X(5936)}}, {{A, B, C, X(1319), X(8162)}}, {{A, B, C, X(1445), X(27818)}}, {{A, B, C, X(2646), X(33963)}}, {{A, B, C, X(3243), X(16673)}}, {{A, B, C, X(3303), X(37080)}}, {{A, B, C, X(3750), X(17715)}}, {{A, B, C, X(3872), X(15933)}}, {{A, B, C, X(4661), X(17240)}}, {{A, B, C, X(5220), X(46845)}}, {{A, B, C, X(5572), X(34522)}}, {{A, B, C, X(6553), X(40430)}}, {{A, B, C, X(6767), X(24929)}}, {{A, B, C, X(7269), X(11038)}}, {{A, B, C, X(10385), X(28071)}}, {{A, B, C, X(10587), X(34772)}}, {{A, B, C, X(13384), X(51779)}}, {{A, B, C, X(15570), X(16675)}}, {{A, B, C, X(16667), X(38316)}}, {{A, B, C, X(20059), X(29007)}}, {{A, B, C, X(29815), X(32858)}}, {{A, B, C, X(39704), X(55989)}}
X(56028) = barycentric quotient X(i)/X(j) for these (i, j): {1, 20195}

X(56029) = KP3(X(1)) OF X(1) AND X(8)

Barycentrics    a*(2*a^3+2*b^3-b^2*c-2*b*c^2+c^3-a^2*(2*b+c)-2*a*(b^2-5*b*c+c^2))*(2*a^3+b^3-2*b^2*c-b*c^2+2*c^3-a^2*(b+2*c)-2*a*(b^2-5*b*c+c^2)) : :

X(56029) lies on the Feuerbach hyperbola and on these lines: {4, 51788}, {8, 17728}, {80, 14986}, {354, 1392}, {1000, 24928}, {1210, 43731}, {1319, 7320}, {1320, 3304}, {1388, 2346}, {1389, 7373}, {3255, 11038}, {3296, 5734}, {4308, 5555}, {4866, 19861}, {4900, 17572}, {5045, 14497}, {5553, 11037}, {6598, 11240}, {13602, 21842}, {13606, 15717}, {18398, 24302}, {21398, 37602}, {26129, 30513}

X(56029) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 20196}
X(56029) = X(i)-vertex conjugate of X(j) for these {i, j}: {56, 7320}
X(56029) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 20196}
X(56029) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(3), X(51788)}}, {{A, B, C, X(56), X(20323)}}, {{A, B, C, X(145), X(55991)}}, {{A, B, C, X(354), X(1388)}}, {{A, B, C, X(936), X(38314)}}, {{A, B, C, X(945), X(41431)}}, {{A, B, C, X(963), X(41432)}}, {{A, B, C, X(999), X(24928)}}, {{A, B, C, X(1002), X(17728)}}, {{A, B, C, X(1319), X(2334)}}, {{A, B, C, X(1385), X(7373)}}, {{A, B, C, X(3241), X(36846)}}, {{A, B, C, X(3616), X(19861)}}, {{A, B, C, X(4511), X(14986)}}, {{A, B, C, X(5045), X(10246)}}, {{A, B, C, X(5734), X(7190)}}, {{A, B, C, X(7131), X(44559)}}, {{A, B, C, X(11240), X(34772)}}, {{A, B, C, X(12629), X(20057)}}, {{A, B, C, X(15178), X(15934)}}, {{A, B, C, X(17609), X(34471)}}, {{A, B, C, X(21842), X(37602)}}, {{A, B, C, X(25417), X(34234)}}
X(56029) = barycentric quotient X(i)/X(j) for these (i, j): {1, 20196}

X(56030) = KP3(X(1)) OF X(1) AND X(21)

Barycentrics    a*(3*a^3+4*b^3-3*b^2*c-4*b*c^2+3*c^3-a^2*(4*b+3*c)-3*a*(b^2+c^2))*(3*a^3+3*b^3-4*b^2*c-3*b*c^2+4*c^3-a^2*(3*b+4*c)-3*a*(b^2+c^2)) : :

X(56030) lies on the Feuerbach hyperbola and on these lines: {8, 31245}, {21, 44663}, {79, 28164}, {943, 50194}, {1389, 33597}, {1476, 44840}, {2346, 11011}, {3485, 7319}, {3486, 5556}, {3984, 4866}, {4311, 5557}, {5045, 37518}, {5559, 13405}, {5844, 7317}, {10592, 43734}, {12047, 17501}, {15910, 34195}, {16615, 21740}, {17098, 36002}

X(56030) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(81), X(6336)}}, {{A, B, C, X(105), X(31245)}}, {{A, B, C, X(354), X(11011)}}, {{A, B, C, X(523), X(31503)}}, {{A, B, C, X(942), X(50194)}}, {{A, B, C, X(1482), X(15934)}}, {{A, B, C, X(2099), X(2218)}}, {{A, B, C, X(3057), X(44840)}}, {{A, B, C, X(3984), X(4652)}}, {{A, B, C, X(4311), X(7269)}}, {{A, B, C, X(4861), X(13405)}}, {{A, B, C, X(5045), X(10222)}}, {{A, B, C, X(5048), X(17609)}}, {{A, B, C, X(7373), X(10247)}}, {{A, B, C, X(25417), X(36100)}}, {{A, B, C, X(28164), X(35057)}}, {{A, B, C, X(33179), X(51788)}}, {{A, B, C, X(34195), X(46441)}}, {{A, B, C, X(37741), X(43719)}}

X(56031) = KP3(X(1)) OF X(1) AND X(56)

Barycentrics    a*(2*b*c*(b+c)+a^2*(2*b+c)+a*(2*b^2-5*b*c+c^2))*(2*b*c*(b+c)+a^2*(b+2*c)+a*(b^2-5*b*c+2*c^2)) : :

X(56031) lies on these lines: {58, 37542}, {106, 474}, {977, 38460}, {1222, 5192}, {2163, 5255}, {3623, 5331}, {10459, 41436}, {11354, 39748}, {20057, 40433}, {23345, 48342}

X(56031) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(6)}}, {{A, B, C, X(29), X(33963)}}, {{A, B, C, X(65), X(6553)}}, {{A, B, C, X(280), X(3057)}}, {{A, B, C, X(474), X(37168)}}, {{A, B, C, X(519), X(15315)}}, {{A, B, C, X(976), X(38460)}}, {{A, B, C, X(2099), X(5255)}}, {{A, B, C, X(3241), X(10459)}}, {{A, B, C, X(3666), X(42360)}}, {{A, B, C, X(3720), X(20057)}}, {{A, B, C, X(3938), X(4861)}}, {{A, B, C, X(4186), X(11115)}}, {{A, B, C, X(4492), X(5559)}}, {{A, B, C, X(11011), X(37540)}}, {{A, B, C, X(15179), X(40401)}}

X(56032) = KP3(X(1)) OF X(1) AND X(58)

Barycentrics    a*(2*b*c*(b+c)+a^2*(2*b+c)+a*(2*b^2+c^2))*(2*b*c*(b+c)+a^2*(b+2*c)+a*(b^2+2*c^2)) : :

X(56032) lies on these lines: {1, 31264}, {56, 16374}, {58, 5258}, {519, 5331}, {977, 30147}, {2163, 2975}, {2334, 50637}, {3244, 40433}, {4653, 52150}, {8672, 23345}, {30145, 40436}

X(56032) = isogonal conjugate of X(50604)
X(56032) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(6)}}, {{A, B, C, X(8), X(30116)}}, {{A, B, C, X(10), X(10459)}}, {{A, B, C, X(29), X(16374)}}, {{A, B, C, X(37), X(5258)}}, {{A, B, C, X(98), X(1389)}}, {{A, B, C, X(291), X(31264)}}, {{A, B, C, X(502), X(2292)}}, {{A, B, C, X(519), X(8672)}}, {{A, B, C, X(943), X(2975)}}, {{A, B, C, X(975), X(3872)}}, {{A, B, C, X(976), X(30147)}}, {{A, B, C, X(1000), X(55036)}}, {{A, B, C, X(1224), X(34434)}}, {{A, B, C, X(1255), X(2985)}}, {{A, B, C, X(3244), X(3720)}}, {{A, B, C, X(3616), X(50637)}}, {{A, B, C, X(3924), X(30145)}}, {{A, B, C, X(3938), X(30143)}}, {{A, B, C, X(4492), X(5560)}}, {{A, B, C, X(5053), X(40450)}}, {{A, B, C, X(12629), X(17022)}}, {{A, B, C, X(15446), X(40401)}}, {{A, B, C, X(17098), X(23051)}}, {{A, B, C, X(25430), X(34234)}}, {{A, B, C, X(30142), X(49487)}}, {{A, B, C, X(31359), X(40039)}}
X(56032) = barycentric quotient X(i)/X(j) for these (i, j): {6, 50604}

X(56033) = KP3(X(1)) OF X(1) AND X(63)

Barycentrics    a*(a^4+3*b^4-4*b^2*c^2+c^4-2*a^2*(2*b^2+c^2))*(a^4+b^4-4*b^2*c^2+3*c^4-2*a^2*(b^2+2*c^2)) : :

X(56033) lies on these lines: {1, 2181}, {19, 2167}, {63, 1953}, {72, 1482}, {226, 8796}, {304, 14213}, {306, 8797}, {1214, 3306}, {2184, 45224}, {13464, 39130}

X(56033) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 11402}, {3, 3087}, {4, 36748}, {6, 631}, {32, 44149}, {97, 6755}, {110, 47122}, {275, 26907}
X(56033) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 631}, {244, 47122}, {6376, 44149}, {32664, 11402}, {36033, 36748}, {36103, 3087}
X(56033) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(63)}}, {{A, B, C, X(2), X(1320)}}, {{A, B, C, X(7), X(34408)}}, {{A, B, C, X(19), X(1953)}}, {{A, B, C, X(27), X(3577)}}, {{A, B, C, X(57), X(1482)}}, {{A, B, C, X(81), X(11682)}}, {{A, B, C, X(82), X(18713)}}, {{A, B, C, X(189), X(1255)}}, {{A, B, C, X(223), X(13464)}}, {{A, B, C, X(278), X(1389)}}, {{A, B, C, X(329), X(5558)}}, {{A, B, C, X(908), X(44733)}}, {{A, B, C, X(945), X(1790)}}, {{A, B, C, X(969), X(54121)}}, {{A, B, C, X(1096), X(2186)}}, {{A, B, C, X(1392), X(40399)}}, {{A, B, C, X(1821), X(23051)}}, {{A, B, C, X(2339), X(18359)}}, {{A, B, C, X(2982), X(14497)}}, {{A, B, C, X(3305), X(43745)}}, {{A, B, C, X(3680), X(40435)}}, {{A, B, C, X(5665), X(40444)}}, {{A, B, C, X(7131), X(30690)}}, {{A, B, C, X(10405), X(27789)}}, {{A, B, C, X(17097), X(55963)}}, {{A, B, C, X(17098), X(37203)}}, {{A, B, C, X(19611), X(40440)}}, {{A, B, C, X(21398), X(37887)}}, {{A, B, C, X(25417), X(36100)}}, {{A, B, C, X(25430), X(34234)}}, {{A, B, C, X(34051), X(45098)}}
X(56033) = barycentric product X(i)*X(j) for these (i, j): {1, 8797}, {63, 8796}, {304, 34818}, {3527, 75}
X(56033) = barycentric quotient X(i)/X(j) for these (i, j): {1, 631}, {19, 3087}, {31, 11402}, {48, 36748}, {75, 44149}, {661, 47122}, {2181, 6755}, {3527, 1}, {8796, 92}, {8797, 75}, {34818, 19}

X(56034) = KP3(X(1)) OF X(1) AND X(75)

Barycentrics    a*(2*a^2+2*b^2+c^2)*(2*a^2+b^2+2*c^2) : :

X(56034) lies on these lines: {10, 17352}, {37, 5332}, {75, 17469}, {759, 7954}, {1581, 17467}, {1964, 51844}, {2186, 17438}, {2962, 4008}, {5263, 39708}, {17370, 17716}, {17393, 39714}, {17394, 39712}, {17400, 29648}, {18058, 18832}, {18833, 52138}, {32922, 39711}

X(56034) = trilinear pole of line {661, 48065}
X(56034) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 7772}, {3, 5064}, {6, 3763}, {39, 39668}, {99, 8665}, {101, 47923}, {110, 7950}, {3108, 39784}
X(56034) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 3763}, {244, 7950}, {1015, 47923}, {32664, 7772}, {36103, 5064}, {38986, 8665}
X(56034) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}}, {{A, B, C, X(2), X(17371)}}, {{A, B, C, X(6), X(5332)}}, {{A, B, C, X(31), X(17469)}}, {{A, B, C, X(81), X(17352)}}, {{A, B, C, X(92), X(39727)}}, {{A, B, C, X(105), X(30598)}}, {{A, B, C, X(673), X(25417)}}, {{A, B, C, X(749), X(985)}}, {{A, B, C, X(751), X(983)}}, {{A, B, C, X(757), X(39958)}}, {{A, B, C, X(765), X(9452)}}, {{A, B, C, X(977), X(36125)}}, {{A, B, C, X(1100), X(15485)}}, {{A, B, C, X(1390), X(28650)}}, {{A, B, C, X(1449), X(3246)}}, {{A, B, C, X(1964), X(34248)}}, {{A, B, C, X(2298), X(39704)}}, {{A, B, C, X(3920), X(29648)}}, {{A, B, C, X(3938), X(29852)}}, {{A, B, C, X(5263), X(17394)}}, {{A, B, C, X(7194), X(40401)}}, {{A, B, C, X(16706), X(17342)}}, {{A, B, C, X(17149), X(18058)}}, {{A, B, C, X(17289), X(17400)}}, {{A, B, C, X(17358), X(17370)}}, {{A, B, C, X(17393), X(32922)}}, {{A, B, C, X(27475), X(40044)}}, {{A, B, C, X(28395), X(29423)}}, {{A, B, C, X(30597), X(51838)}}, {{A, B, C, X(38831), X(39973)}}
X(56034) = barycentric product X(i)*X(j) for these (i, j): {1, 43527}, {1577, 7954}, {39955, 75}
X(56034) = barycentric quotient X(i)/X(j) for these (i, j): {1, 3763}, {19, 5064}, {31, 7772}, {82, 39668}, {513, 47923}, {661, 7950}, {798, 8665}, {7954, 662}, {17469, 39784}, {39955, 1}, {43527, 75}

X(56035) = KP3(X(1)) OF X(1) AND X(79)

Barycentrics    a*(2*a^3+2*b^3-b^2*c-2*b*c^2+c^3-a^2*(2*b+c)-a*(2*b^2+5*b*c+2*c^2))*(2*a^3+b^3-2*b^2*c-b*c^2+2*c^3-a^2*(b+2*c)-a*(2*b^2+5*b*c+2*c^2)) : :

X(56035) lies on the Feuerbach hyperbola and on these lines: {4, 11218}, {79, 4330}, {2320, 3881}, {3295, 15173}, {3296, 37571}, {3612, 10390}, {3748, 5559}, {5557, 24929}, {5558, 37525}, {5560, 37719}, {5561, 6284}, {6147, 43732}, {6767, 21398}, {10389, 17098}, {18490, 21842}, {41862, 43740}

X(56035) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(35), X(37080)}}, {{A, B, C, X(1442), X(4330)}}, {{A, B, C, X(3295), X(37571)}}, {{A, B, C, X(3303), X(37525)}}, {{A, B, C, X(3612), X(10389)}}, {{A, B, C, X(3746), X(24929)}}, {{A, B, C, X(3748), X(5563)}}, {{A, B, C, X(3881), X(4653)}}, {{A, B, C, X(5919), X(24926)}}, {{A, B, C, X(6767), X(21842)}}, {{A, B, C, X(25417), X(43758)}}, {{A, B, C, X(28146), X(35057)}}

X(56036) = KP3(X(1)) OF X(1) AND X(80)

Barycentrics    a*(2*a^3+2*b^3-b^2*c-2*b*c^2+c^3-a^2*(2*b+c)+a*(-2*b^2+5*b*c-2*c^2))*(2*a^3+b^3-2*b^2*c-b*c^2+2*c^3-a^2*(b+2*c)+a*(-2*b^2+5*b*c-2*c^2)) : :

X(56036) lies on the Feuerbach hyperbola and on these lines: {1, 12515}, {4, 11715}, {8, 214}, {9, 17455}, {11, 5560}, {21, 10074}, {36, 1320}, {56, 21398}, {79, 24928}, {80, 1319}, {515, 23959}, {517, 24302}, {549, 1317}, {943, 24926}, {952, 43731}, {1000, 37525}, {1385, 5559}, {1387, 5561}, {1388, 15446}, {1389, 5563}, {1392, 5903}, {1476, 10058}, {1807, 46821}, {2320, 3898}, {2646, 13606}, {2802, 37307}, {3036, 13747}, {3065, 12740}, {3255, 42819}, {3304, 15173}, {3467, 6265}, {3680, 5541}, {4867, 45393}, {5258, 32635}, {5533, 37406}, {5557, 20323}, {5902, 14497}, {6598, 12750}, {7161, 12739}, {7320, 37571}, {7705, 37710}, {10090, 24297}, {10246, 15175}, {10308, 46816}, {10698, 37518}, {11256, 15015}, {12737, 13143}, {12749, 34918}, {13602, 24929}, {23838, 53314}, {33709, 45287}, {36004, 50891}, {37719, 38032}

X(56036) = reflection of X(i) in X(j) for these {i,j}: {5560, 11}
X(56036) = trilinear pole of line {650, 16669}
X(56036) = X(i)-vertex conjugate of X(j) for these {i, j}: {56, 80}, {34442, 55929}
X(56036) = X(i)-cross conjugate of X(j) for these {i, j}: {25405, 1}
X(56036) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(35), X(24928)}}, {{A, B, C, X(36), X(106)}}, {{A, B, C, X(56), X(21842)}}, {{A, B, C, X(59), X(28219)}}, {{A, B, C, X(74), X(1318)}}, {{A, B, C, X(765), X(6095)}}, {{A, B, C, X(942), X(24926)}}, {{A, B, C, X(999), X(37525)}}, {{A, B, C, X(1100), X(5258)}}, {{A, B, C, X(1385), X(5563)}}, {{A, B, C, X(1388), X(5903)}}, {{A, B, C, X(1411), X(2718)}}, {{A, B, C, X(1420), X(37618)}}, {{A, B, C, X(1795), X(11715)}}, {{A, B, C, X(1807), X(16173)}}, {{A, B, C, X(2006), X(3218)}}, {{A, B, C, X(2160), X(5445)}}, {{A, B, C, X(2164), X(41436)}}, {{A, B, C, X(3304), X(37571)}}, {{A, B, C, X(3445), X(7163)}}, {{A, B, C, X(3582), X(4511)}}, {{A, B, C, X(3738), X(28204)}}, {{A, B, C, X(3746), X(20323)}}, {{A, B, C, X(3898), X(4653)}}, {{A, B, C, X(4564), X(34578)}}, {{A, B, C, X(4867), X(8609)}}, {{A, B, C, X(5902), X(10246)}}, {{A, B, C, X(7052), X(41225)}}, {{A, B, C, X(8756), X(41529)}}, {{A, B, C, X(10013), X(40110)}}, {{A, B, C, X(12515), X(44693)}}, {{A, B, C, X(13384), X(51816)}}, {{A, B, C, X(15227), X(28193)}}, {{A, B, C, X(15337), X(28211)}}, {{A, B, C, X(16669), X(39781)}}, {{A, B, C, X(18398), X(34471)}}, {{A, B, C, X(24929), X(37602)}}, {{A, B, C, X(25417), X(43757)}}, {{A, B, C, X(26745), X(31231)}}, {{A, B, C, X(28233), X(36052)}}, {{A, B, C, X(30282), X(53058)}}, {{A, B, C, X(38602), X(51565)}}, {{A, B, C, X(43655), X(46819)}}

X(56037) = KP3(X(1)) OF X(1) AND X(81)

Barycentrics    a*(3*a+4*b+3*c)*(3*a+3*b+4*c) : :

X(56037) lies on these lines: {1, 3988}, {2, 4399}, {81, 3723}, {88, 17019}, {105, 28214}, {274, 4980}, {551, 1224}, {1022, 15309}, {1255, 35595}, {1929, 3722}, {5287, 39963}, {16777, 25417}, {17011, 40434}, {19738, 38247}, {24857, 51107}, {24858, 51104}, {25430, 37680}, {26745, 37633}, {27789, 32911}, {28606, 39980}, {29570, 39736}, {29584, 32009}, {31332, 50277}, {33761, 39260}, {36871, 42044}, {39747, 42025}

X(56037) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 19862}, {55, 4114}, {101, 28213}, {1213, 39670}
X(56037) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 19862}, {223, 4114}, {1015, 28213}
X(56037) = X(i)-cross conjugate of X(j) for these {i, j}: {4813, 100}, {48074, 4606}, {50191, 7}
X(56037) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(21), X(4102)}}, {{A, B, C, X(27), X(16861)}}, {{A, B, C, X(37), X(3723)}}, {{A, B, C, X(42), X(29580)}}, {{A, B, C, X(226), X(3988)}}, {{A, B, C, X(335), X(42041)}}, {{A, B, C, X(519), X(15309)}}, {{A, B, C, X(551), X(17011)}}, {{A, B, C, X(553), X(35595)}}, {{A, B, C, X(739), X(39967)}}, {{A, B, C, X(989), X(41895)}}, {{A, B, C, X(1029), X(5559)}}, {{A, B, C, X(1100), X(46845)}}, {{A, B, C, X(1171), X(41434)}}, {{A, B, C, X(1320), X(42030)}}, {{A, B, C, X(1962), X(52208)}}, {{A, B, C, X(2051), X(37518)}}, {{A, B, C, X(2214), X(16777)}}, {{A, B, C, X(3187), X(48855)}}, {{A, B, C, X(3241), X(5287)}}, {{A, B, C, X(3720), X(29584)}}, {{A, B, C, X(3920), X(29574)}}, {{A, B, C, X(4664), X(42044)}}, {{A, B, C, X(4921), X(37633)}}, {{A, B, C, X(5256), X(38314)}}, {{A, B, C, X(5311), X(17389)}}, {{A, B, C, X(5557), X(55027)}}, {{A, B, C, X(6605), X(7073)}}, {{A, B, C, X(10013), X(20332)}}, {{A, B, C, X(16834), X(29814)}}, {{A, B, C, X(17012), X(51103)}}, {{A, B, C, X(17013), X(51105)}}, {{A, B, C, X(17018), X(29597)}}, {{A, B, C, X(17021), X(51071)}}, {{A, B, C, X(17310), X(29816)}}, {{A, B, C, X(17388), X(23617)}}, {{A, B, C, X(28606), X(42034)}}, {{A, B, C, X(29570), X(42042)}}, {{A, B, C, X(29573), X(29815)}}, {{A, B, C, X(29817), X(50114)}}, {{A, B, C, X(32008), X(52393)}}, {{A, B, C, X(32089), X(40438)}}, {{A, B, C, X(32911), X(42025)}}, {{A, B, C, X(37680), X(42028)}}, {{A, B, C, X(39284), X(40396)}}, {{A, B, C, X(40433), X(55971)}}, {{A, B, C, X(40439), X(55997)}}
X(56037) = barycentric product X(i)*X(j) for these (i, j): {28214, 693}
X(56037) = barycentric quotient X(i)/X(j) for these (i, j): {1, 19862}, {57, 4114}, {513, 28213}, {28214, 100}

X(56038) = KP3(X(1)) OF X(1) AND X(84)

Barycentrics    a*(a^3+3*b^3-b^2*c-3*b*c^2+c^3-a^2*(3*b+c)-a*(b^2-10*b*c+c^2))*(a^3+b^3-3*b^2*c-b*c^2+3*c^3-a^2*(b+3*c)-a*(b^2-10*b*c+c^2)) : :

X(56038) lies on the Feuerbach hyperbola and on these lines: {4, 7962}, {7, 7982}, {9, 9957}, {21, 31393}, {40, 1476}, {46, 15180}, {57, 15179}, {79, 30323}, {80, 51785}, {84, 3057}, {104, 1697}, {517, 7091}, {936, 3680}, {943, 37556}, {944, 10307}, {1000, 1210}, {1320, 19861}, {1387, 11530}, {1482, 5665}, {2098, 3577}, {3062, 12672}, {3243, 3255}, {3244, 34919}, {3296, 3340}, {5258, 30337}, {5445, 13602}, {5557, 25415}, {5558, 11529}, {5697, 7284}, {5777, 33576}, {5919, 7160}, {7320, 14986}, {7971, 10309}, {10912, 42470}, {11518, 18490}, {12641, 17527}, {13384, 37518}, {15829, 34918}, {16005, 37738}, {16200, 17097}, {25097, 34894}

X(56038) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(2), X(12629)}}, {{A, B, C, X(3), X(7962)}}, {{A, B, C, X(10), X(36846)}}, {{A, B, C, X(35), X(30323)}}, {{A, B, C, X(40), X(3057)}}, {{A, B, C, X(55), X(7982)}}, {{A, B, C, X(57), X(9957)}}, {{A, B, C, X(65), X(31393)}}, {{A, B, C, X(145), X(936)}}, {{A, B, C, X(517), X(1697)}}, {{A, B, C, X(519), X(19861)}}, {{A, B, C, X(909), X(2334)}}, {{A, B, C, X(942), X(37556)}}, {{A, B, C, X(947), X(53089)}}, {{A, B, C, X(996), X(1067)}}, {{A, B, C, X(1057), X(1126)}}, {{A, B, C, X(1167), X(3478)}}, {{A, B, C, X(1210), X(3872)}}, {{A, B, C, X(1482), X(3601)}}, {{A, B, C, X(1807), X(37709)}}, {{A, B, C, X(1870), X(51785)}}, {{A, B, C, X(2098), X(3576)}}, {{A, B, C, X(2646), X(16200)}}, {{A, B, C, X(3247), X(5258)}}, {{A, B, C, X(3295), X(3340)}}, {{A, B, C, X(3303), X(11529)}}, {{A, B, C, X(3333), X(5919)}}, {{A, B, C, X(3445), X(45818)}}, {{A, B, C, X(3554), X(31435)}}, {{A, B, C, X(3746), X(25415)}}, {{A, B, C, X(4853), X(14986)}}, {{A, B, C, X(5045), X(51779)}}, {{A, B, C, X(5119), X(5697)}}, {{A, B, C, X(6336), X(39963)}}, {{A, B, C, X(6767), X(11518)}}, {{A, B, C, X(7991), X(9819)}}, {{A, B, C, X(8602), X(34434)}}, {{A, B, C, X(10222), X(13384)}}, {{A, B, C, X(11531), X(53053)}}, {{A, B, C, X(16189), X(53054)}}, {{A, B, C, X(25430), X(34234)}}

X(56039) = KP3(X(1)) OF X(1) AND X(89)

Barycentrics    a*(4*a+7*b+4*c)*(4*a+4*b+7*c) : :

X(56039) lies on these lines: {2, 4727}, {44, 25417}, {81, 16672}, {88, 16777}, {1022, 4813}, {1224, 46934}, {5287, 36603}, {8056, 17021}, {16676, 39948}, {17013, 25430}, {17019, 39980}, {29570, 36871}, {29585, 34914}, {29624, 34578}, {30589, 40833}, {37682, 39962}

X(56039) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(6), X(39260)}}, {{A, B, C, X(37), X(16672)}}, {{A, B, C, X(44), X(941)}}, {{A, B, C, X(145), X(17021)}}, {{A, B, C, X(679), X(30712)}}, {{A, B, C, X(1029), X(43734)}}, {{A, B, C, X(3240), X(29570)}}, {{A, B, C, X(3247), X(16676)}}, {{A, B, C, X(3616), X(17013)}}, {{A, B, C, X(3617), X(17019)}}, {{A, B, C, X(3621), X(5287)}}, {{A, B, C, X(3622), X(17012)}}, {{A, B, C, X(3920), X(29583)}}, {{A, B, C, X(3935), X(29624)}}, {{A, B, C, X(4792), X(30590)}}, {{A, B, C, X(5297), X(29585)}}, {{A, B, C, X(7320), X(21739)}}, {{A, B, C, X(16666), X(39960)}}, {{A, B, C, X(16816), X(29814)}}, {{A, B, C, X(17011), X(46934)}}, {{A, B, C, X(17018), X(29595)}}, {{A, B, C, X(17025), X(29586)}}, {{A, B, C, X(29579), X(29815)}}, {{A, B, C, X(43733), X(55027)}}

X(56040) = KP3(X(1)) OF X(1) AND X(104)

Barycentrics    a*(3*a^3+4*b^3-3*b^2*c-4*b*c^2+3*c^3-a^2*(4*b+3*c)+a*(-3*b^2+10*b*c-3*c^2))*(3*a^3+3*b^3-4*b^2*c-3*b*c^2+4*c^3-a^2*(3*b+4*c)+a*(-3*b^2+10*b*c-3*c^2)) : :

X(56040) lies on the Feuerbach hyperbola and on these lines: {1, 34474}, {4, 1317}, {7, 10247}, {8, 1387}, {84, 10698}, {100, 1392}, {104, 5048}, {952, 7319}, {1000, 5432}, {1156, 12737}, {1320, 5440}, {1389, 33176}, {1476, 10222}, {3057, 37518}, {3062, 25485}, {3255, 30331}, {3680, 45391}, {5553, 30305}, {5556, 5734}, {5603, 38307}, {6264, 33576}, {7972, 17501}, {10090, 24302}, {10308, 20586}, {11011, 15179}, {12531, 17533}, {12739, 16615}, {12740, 24297}, {17097, 33179}, {23838, 53532}

X(56040) = reflection of X(i) in X(j) for these {i,j}: {100, 51577}, {43734, 11}
X(56040) = isogonal conjugate of X(25405)
X(56040) = trilinear pole of line {650, 16885}
X(56040) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(3), X(33963)}}, {{A, B, C, X(55), X(10247)}}, {{A, B, C, X(59), X(28203)}}, {{A, B, C, X(102), X(1391)}}, {{A, B, C, X(105), X(31272)}}, {{A, B, C, X(106), X(18771)}}, {{A, B, C, X(517), X(5048)}}, {{A, B, C, X(999), X(54446)}}, {{A, B, C, X(1057), X(34442)}}, {{A, B, C, X(1120), X(40437)}}, {{A, B, C, X(1168), X(8686)}}, {{A, B, C, X(1280), X(6095)}}, {{A, B, C, X(1317), X(1807)}}, {{A, B, C, X(1318), X(36052)}}, {{A, B, C, X(1385), X(33176)}}, {{A, B, C, X(1387), X(1411)}}, {{A, B, C, X(1482), X(2098)}}, {{A, B, C, X(2316), X(28219)}}, {{A, B, C, X(2646), X(33179)}}, {{A, B, C, X(2802), X(4962)}}, {{A, B, C, X(3057), X(10222)}}, {{A, B, C, X(5919), X(50194)}}, {{A, B, C, X(6553), X(7040)}}, {{A, B, C, X(7962), X(16200)}}, {{A, B, C, X(7982), X(54197)}}, {{A, B, C, X(9957), X(11011)}}, {{A, B, C, X(10698), X(15501)}}, {{A, B, C, X(12740), X(34232)}}, {{A, B, C, X(15337), X(28197)}}, {{A, B, C, X(25416), X(36125)}}, {{A, B, C, X(34474), X(51565)}}
X(56040) = barycentric quotient X(i)/X(j) for these (i, j): {6, 25405}

X(56041) = KP3(X(1)) OF X(2) AND X(4)

Barycentrics    a*(a^4-2*a*b^2*c+(b^2-c^2)^2-2*a^2*(b^2+c^2))*(a^4-2*a*b*c^2+(b^2-c^2)^2-2*a^2*(b^2+c^2)) : :

X(56041) lies on these lines: {1, 1993}, {2, 44179}, {28, 37615}, {57, 2337}, {278, 31019}, {279, 26842}, {1224, 19860}, {2006, 31266}, {2990, 28606}, {3083, 3302}, {3084, 3300}

X(56041) = trilinear pole of line {39212, 513}
X(56041) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 498}, {9, 1454}, {19, 26921}, {71, 14016}
X(56041) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 26921}, {9, 498}, {478, 1454}
X(56041) = X(i)-cross conjugate of X(j) for these {i, j}: {13401, 100}
X(56041) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(7), X(6504)}}, {{A, B, C, X(9), X(26842)}}, {{A, B, C, X(21), X(2994)}}, {{A, B, C, X(34), X(593)}}, {{A, B, C, X(60), X(56002)}}, {{A, B, C, X(63), X(30690)}}, {{A, B, C, X(77), X(97)}}, {{A, B, C, X(78), X(31626)}}, {{A, B, C, X(79), X(13579)}}, {{A, B, C, X(84), X(1029)}}, {{A, B, C, X(85), X(2167)}}, {{A, B, C, X(86), X(1993)}}, {{A, B, C, X(92), X(2185)}}, {{A, B, C, X(189), X(2320)}}, {{A, B, C, X(257), X(5392)}}, {{A, B, C, X(275), X(1063)}}, {{A, B, C, X(394), X(7100)}}, {{A, B, C, X(612), X(26639)}}, {{A, B, C, X(1039), X(8796)}}, {{A, B, C, X(1061), X(2052)}}, {{A, B, C, X(1096), X(30650)}}, {{A, B, C, X(1214), X(37615)}}, {{A, B, C, X(1411), X(2221)}}, {{A, B, C, X(1870), X(45126)}}, {{A, B, C, X(2339), X(18359)}}, {{A, B, C, X(3218), X(31266)}}, {{A, B, C, X(3577), X(55027)}}, {{A, B, C, X(3615), X(6513)}}, {{A, B, C, X(5560), X(11538)}}, {{A, B, C, X(5561), X(13585)}}, {{A, B, C, X(5712), X(26637)}}, {{A, B, C, X(13582), X(43732)}}, {{A, B, C, X(14621), X(40393)}}, {{A, B, C, X(14919), X(41081)}}, {{A, B, C, X(17011), X(19860)}}, {{A, B, C, X(17019), X(19861)}}, {{A, B, C, X(25930), X(29817)}}, {{A, B, C, X(28606), X(48380)}}
X(56041) = barycentric product X(i)*X(j) for these (i, j): {2337, 85}
X(56041) = barycentric quotient X(i)/X(j) for these (i, j): {1, 498}, {3, 26921}, {28, 14016}, {56, 1454}, {2337, 9}, {3338, 10044}

X(56042) = KP3(X(1)) OF X(2) AND X(6)

Barycentrics    (a^2+3*a*b+b^2)*(a^2+3*a*c+c^2) : :

X(56042) lies on these lines: {1, 7783}, {238, 1468}, {239, 940}, {330, 4038}, {1016, 17750}, {1429, 21454}, {1434, 17396}, {2275, 39971}, {6625, 24217}, {7785, 48825}, {7793, 37607}, {9345, 21226}, {17319, 34860}, {17743, 24512}, {27145, 27156}, {40432, 51356}

X(56042) = isotomic conjugate of X(48628)
X(56042) = trilinear pole of line {659, 4778}
X(56042) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 48628}, {55, 7201}, {100, 4502}, {101, 4490}, {190, 4507}, {292, 4489}, {692, 4500}, {1333, 48644}, {2176, 7275}
X(56042) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 48628}, {37, 48644}, {223, 7201}, {1015, 4490}, {1086, 4500}, {8054, 4502}, {19557, 4489}, {55053, 4507}
X(56042) = X(i)-cross conjugate of X(j) for these {i, j}: {48016, 190}
X(56042) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(83)}}, {{A, B, C, X(2), X(1434)}}, {{A, B, C, X(7), X(257)}}, {{A, B, C, X(8), X(18845)}}, {{A, B, C, X(56), X(81)}}, {{A, B, C, X(76), X(5557)}}, {{A, B, C, X(79), X(53105)}}, {{A, B, C, X(80), X(53107)}}, {{A, B, C, X(86), X(330)}}, {{A, B, C, X(321), X(35576)}}, {{A, B, C, X(335), X(3296)}}, {{A, B, C, X(385), X(17103)}}, {{A, B, C, X(514), X(17771)}}, {{A, B, C, X(596), X(44572)}}, {{A, B, C, X(598), X(5559)}}, {{A, B, C, X(671), X(43732)}}, {{A, B, C, X(673), X(39738)}}, {{A, B, C, X(904), X(2162)}}, {{A, B, C, X(1000), X(18843)}}, {{A, B, C, X(1015), X(17750)}}, {{A, B, C, X(1125), X(29612)}}, {{A, B, C, X(1220), X(38247)}}, {{A, B, C, X(1258), X(3445)}}, {{A, B, C, X(2163), X(40408)}}, {{A, B, C, X(2214), X(17962)}}, {{A, B, C, X(2275), X(24512)}}, {{A, B, C, X(2296), X(39925)}}, {{A, B, C, X(2321), X(17396)}}, {{A, B, C, X(2334), X(20332)}}, {{A, B, C, X(3227), X(43531)}}, {{A, B, C, X(3247), X(17117)}}, {{A, B, C, X(3304), X(5228)}}, {{A, B, C, X(3750), X(8616)}}, {{A, B, C, X(3875), X(17319)}}, {{A, B, C, X(3946), X(17242)}}, {{A, B, C, X(4038), X(7304)}}, {{A, B, C, X(5331), X(25417)}}, {{A, B, C, X(5395), X(7320)}}, {{A, B, C, X(6625), X(9311)}}, {{A, B, C, X(6650), X(31359)}}, {{A, B, C, X(8025), X(35058)}}, {{A, B, C, X(14377), X(32009)}}, {{A, B, C, X(14534), X(39948)}}, {{A, B, C, X(14623), X(24037)}}, {{A, B, C, X(17109), X(37633)}}, {{A, B, C, X(17367), X(49768)}}, {{A, B, C, X(18166), X(34444)}}, {{A, B, C, X(18490), X(30701)}}, {{A, B, C, X(19722), X(42025)}}, {{A, B, C, X(27475), X(39724)}}, {{A, B, C, X(31999), X(40720)}}, {{A, B, C, X(32014), X(36871)}}, {{A, B, C, X(34892), X(43527)}}, {{A, B, C, X(36807), X(39730)}}, {{A, B, C, X(39702), X(39722)}}, {{A, B, C, X(39716), X(54123)}}, {{A, B, C, X(39736), X(42335)}}, {{A, B, C, X(43731), X(53109)}}
X(56042) = barycentric quotient X(i)/X(j) for these (i, j): {2, 48628}, {10, 48644}, {57, 7201}, {87, 7275}, {238, 4489}, {513, 4490}, {514, 4500}, {649, 4502}, {667, 4507}, {39914, 27450}

X(56043) = KP3(X(1)) OF X(2) AND X(9)

Barycentrics    (a^2-2*a*(b-3*c)+(b-c)^2)*(a^2+a*(6*b-2*c)+(b-c)^2) : :

X(56043) lies on these lines: {1, 144}, {2, 4875}, {57, 3160}, {88, 23587}, {105, 3304}, {145, 39959}, {192, 6553}, {241, 44794}, {274, 26818}, {279, 50561}, {291, 14759}, {330, 4452}, {1002, 3057}, {1219, 4461}, {1280, 3623}, {1422, 7955}, {5222, 8056}, {10405, 11019}, {18228, 25430}, {21105, 35348}, {21226, 39703}, {25242, 50122}, {28610, 39948}, {28809, 32017}, {30330, 42483}, {31793, 51223}, {34018, 43983}, {36603, 50114}, {37685, 40399}

X(56043) = isotomic conjugate of X(4461)
X(56043) = trilinear pole of line {2473, 2487}
X(56043) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 8580}, {31, 4461}, {41, 31994}, {42, 24557}
X(56043) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 4461}, {9, 8580}, {3160, 31994}, {40592, 24557}
X(56043) = X(i)-cross conjugate of X(j) for these {i, j}: {3672, 2}, {10980, 7}, {17410, 100}
X(56043) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(4), X(36605)}}, {{A, B, C, X(6), X(20978)}}, {{A, B, C, X(7), X(144)}}, {{A, B, C, X(8), X(1434)}}, {{A, B, C, X(27), X(11106)}}, {{A, B, C, X(85), X(5558)}}, {{A, B, C, X(145), X(5222)}}, {{A, B, C, X(192), X(4452)}}, {{A, B, C, X(241), X(3304)}}, {{A, B, C, X(257), X(4373)}}, {{A, B, C, X(346), X(42317)}}, {{A, B, C, X(514), X(3296)}}, {{A, B, C, X(673), X(7320)}}, {{A, B, C, X(1000), X(9328)}}, {{A, B, C, X(1121), X(5556)}}, {{A, B, C, X(1222), X(39716)}}, {{A, B, C, X(1476), X(39273)}}, {{A, B, C, X(2214), X(52223)}}, {{A, B, C, X(2334), X(3669)}}, {{A, B, C, X(2994), X(10429)}}, {{A, B, C, X(2996), X(36606)}}, {{A, B, C, X(3008), X(3623)}}, {{A, B, C, X(3057), X(5228)}}, {{A, B, C, X(3420), X(38811)}}, {{A, B, C, X(3445), X(42290)}}, {{A, B, C, X(3616), X(29624)}}, {{A, B, C, X(3621), X(50114)}}, {{A, B, C, X(3622), X(5308)}}, {{A, B, C, X(3672), X(4461)}}, {{A, B, C, X(4673), X(18228)}}, {{A, B, C, X(4875), X(17474)}}, {{A, B, C, X(5395), X(6185)}}, {{A, B, C, X(6625), X(52803)}}, {{A, B, C, X(7091), X(36101)}}, {{A, B, C, X(7100), X(8813)}}, {{A, B, C, X(7153), X(9309)}}, {{A, B, C, X(7955), X(42872)}}, {{A, B, C, X(9533), X(11019)}}, {{A, B, C, X(15179), X(44178)}}, {{A, B, C, X(16020), X(29585)}}, {{A, B, C, X(17018), X(27304)}}, {{A, B, C, X(17113), X(30330)}}, {{A, B, C, X(17758), X(18490)}}, {{A, B, C, X(18840), X(39697)}}, {{A, B, C, X(26626), X(39587)}}, {{A, B, C, X(26805), X(41276)}}, {{A, B, C, X(27475), X(27818)}}, {{A, B, C, X(31793), X(37543)}}, {{A, B, C, X(38259), X(39720)}}, {{A, B, C, X(39702), X(39749)}}
X(56043) = barycentric quotient X(i)/X(j) for these (i, j): {1, 8580}, {2, 4461}, {7, 31994}, {81, 24557}

X(56044) = KP3(X(1)) OF X(2) AND X(19)

Barycentrics    (a^2+b^2+2*a*c+2*b*c-c^2)*(a^2+2*a*b-b^2+2*b*c+c^2) : :

X(56044) lies on these lines: {1, 6392}, {2, 7176}, {7, 257}, {8, 193}, {312, 1909}, {333, 17103}, {388, 17257}, {2996, 24210}, {3486, 14942}, {4102, 50079}, {4518, 27340}, {5308, 6557}, {5749, 17743}, {5942, 55036}, {19797, 42030}, {26065, 40435}, {26685, 32008}, {26965, 41791}, {27424, 27443}, {39581, 40745}, {39721, 41015}

X(56044) = isotomic conjugate of X(17257)
X(56044) = trilinear pole of line {3798, 4369}
X(56044) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 17594}, {31, 17257}, {101, 48136}, {1333, 4104}
X(56044) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 17257}, {9, 17594}, {37, 4104}, {1015, 48136}
X(56044) = X(i)-cross conjugate of X(j) for these {i, j}: {10436, 2}, {26098, 7}
X(56044) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2991)}}, {{A, B, C, X(2), X(8)}}, {{A, B, C, X(4), X(274)}}, {{A, B, C, X(7), X(330)}}, {{A, B, C, X(27), X(50408)}}, {{A, B, C, X(34), X(81)}}, {{A, B, C, X(75), X(2996)}}, {{A, B, C, X(79), X(36871)}}, {{A, B, C, X(80), X(32022)}}, {{A, B, C, X(83), X(277)}}, {{A, B, C, X(86), X(193)}}, {{A, B, C, X(87), X(1432)}}, {{A, B, C, X(142), X(26685)}}, {{A, B, C, X(145), X(5308)}}, {{A, B, C, X(256), X(27443)}}, {{A, B, C, X(278), X(14534)}}, {{A, B, C, X(279), X(4307)}}, {{A, B, C, X(287), X(348)}}, {{A, B, C, X(334), X(5936)}}, {{A, B, C, X(335), X(1219)}}, {{A, B, C, X(388), X(5307)}}, {{A, B, C, X(514), X(5847)}}, {{A, B, C, X(673), X(5395)}}, {{A, B, C, X(948), X(40950)}}, {{A, B, C, X(959), X(37128)}}, {{A, B, C, X(977), X(25417)}}, {{A, B, C, X(996), X(17758)}}, {{A, B, C, X(1000), X(32009)}}, {{A, B, C, X(1222), X(27475)}}, {{A, B, C, X(1255), X(42360)}}, {{A, B, C, X(1258), X(42290)}}, {{A, B, C, X(2297), X(4876)}}, {{A, B, C, X(3227), X(3296)}}, {{A, B, C, X(3241), X(29569)}}, {{A, B, C, X(3486), X(5236)}}, {{A, B, C, X(3616), X(6542)}}, {{A, B, C, X(3661), X(39581)}}, {{A, B, C, X(3662), X(5749)}}, {{A, B, C, X(3765), X(52082)}}, {{A, B, C, X(4373), X(7229)}}, {{A, B, C, X(5249), X(26065)}}, {{A, B, C, X(5275), X(41015)}}, {{A, B, C, X(5485), X(32018)}}, {{A, B, C, X(5550), X(20055)}}, {{A, B, C, X(5556), X(6650)}}, {{A, B, C, X(5558), X(38247)}}, {{A, B, C, X(6630), X(7320)}}, {{A, B, C, X(7319), X(39736)}}, {{A, B, C, X(9309), X(40432)}}, {{A, B, C, X(9776), X(27064)}}, {{A, B, C, X(10327), X(26965)}}, {{A, B, C, X(10436), X(17257)}}, {{A, B, C, X(15315), X(47947)}}, {{A, B, C, X(17077), X(27254)}}, {{A, B, C, X(17292), X(48849)}}, {{A, B, C, X(17350), X(26806)}}, {{A, B, C, X(17363), X(28626)}}, {{A, B, C, X(17493), X(41838)}}, {{A, B, C, X(18230), X(27147)}}, {{A, B, C, X(18840), X(20568)}}, {{A, B, C, X(19797), X(28605)}}, {{A, B, C, X(23617), X(40779)}}, {{A, B, C, X(26125), X(27334)}}, {{A, B, C, X(26627), X(31018)}}, {{A, B, C, X(26735), X(31643)}}, {{A, B, C, X(27253), X(36845)}}, {{A, B, C, X(27340), X(39914)}}, {{A, B, C, X(27483), X(43533)}}, {{A, B, C, X(27818), X(39716)}}, {{A, B, C, X(29579), X(36479)}}, {{A, B, C, X(34434), X(39981)}}, {{A, B, C, X(35578), X(50128)}}, {{A, B, C, X(39713), X(39732)}}, {{A, B, C, X(39722), X(39749)}}, {{A, B, C, X(40023), X(43681)}}, {{A, B, C, X(40720), X(41771)}}
X(56044) = barycentric quotient X(i)/X(j) for these (i, j): {1, 17594}, {2, 17257}, {10, 4104}, {513, 48136}

X(56045) = KP3(X(1)) OF X(2) AND X(28)

Barycentrics    a*(a+b)*(a+c)*(a^3+b^3+a^2*(b-c)+b^2*c+b*c^2+c^3+a*(b^2-c^2))*(a^3+b^3+b^2*c+b*c^2+c^3+a^2*(-b+c)+a*(-b^2+c^2)) : :

X(56045) lies on these lines: {2, 1396}, {58, 78}, {63, 1412}, {81, 345}, {280, 11115}, {593, 1812}, {1171, 41610}, {1172, 17587}, {1791, 3219}, {2303, 26223}, {2339, 27174}, {4357, 52381}, {31623, 36419}

X(56045) = trilinear pole of line {3733, 48387}
X(56045) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 41340}, {42, 19785}, {1400, 2478}
X(56045) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 41340}, {40582, 2478}, {40592, 19785}
X(56045) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(40406)}}, {{A, B, C, X(2), X(21)}}, {{A, B, C, X(3), X(37095)}}, {{A, B, C, X(58), X(81)}}, {{A, B, C, X(86), X(40571)}}, {{A, B, C, X(275), X(1172)}}, {{A, B, C, X(314), X(2994)}}, {{A, B, C, X(333), X(26637)}}, {{A, B, C, X(394), X(2193)}}, {{A, B, C, X(404), X(17587)}}, {{A, B, C, X(1010), X(27174)}}, {{A, B, C, X(1220), X(2167)}}, {{A, B, C, X(1257), X(39700)}}, {{A, B, C, X(1476), X(35058)}}, {{A, B, C, X(1790), X(1801)}}, {{A, B, C, X(1817), X(11115)}}, {{A, B, C, X(1931), X(35623)}}, {{A, B, C, X(2194), X(7123)}}, {{A, B, C, X(2215), X(2298)}}, {{A, B, C, X(2982), X(39945)}}, {{A, B, C, X(2991), X(25417)}}, {{A, B, C, X(3219), X(4357)}}, {{A, B, C, X(4184), X(26643)}}, {{A, B, C, X(4195), X(27651)}}, {{A, B, C, X(4228), X(16050)}}, {{A, B, C, X(4567), X(37870)}}, {{A, B, C, X(5333), X(37783)}}, {{A, B, C, X(8025), X(41610)}}, {{A, B, C, X(16046), X(35983)}}, {{A, B, C, X(38813), X(40142)}}, {{A, B, C, X(40435), X(55991)}}
X(56045) = barycentric quotient X(i)/X(j) for these (i, j): {3, 41340}, {21, 2478}, {81, 19785}

X(56046) = KP3(X(1)) OF X(2) AND X(56)

Barycentrics    (a^3+a^2*c+a*b*c+b^2*(b+c))*(a^3+a^2*b+a*b*c+c^2*(b+c)) : :

X(56046) lies on these lines: {2, 604}, {6, 312}, {8, 31}, {29, 2203}, {63, 257}, {81, 3765}, {85, 1407}, {92, 608}, {239, 2221}, {333, 1333}, {384, 54373}, {612, 1911}, {958, 31359}, {1462, 18031}, {1943, 41247}, {2162, 27424}, {2214, 17790}, {4102, 17281}, {4181, 52865}, {4997, 9456}, {5294, 17743}, {5737, 28607}, {6557, 38266}, {7020, 7151}, {17961, 28606}, {18359, 26223}, {25898, 27184}, {26081, 27319}, {27130, 42339}, {34819, 42030}

X(56046) = isotomic conjugate of X(27184)
X(56046) = trilinear pole of line {667, 8045}
X(56046) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 2277}, {6, 986}, {31, 27184}
X(56046) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 27184}, {3, 2277}, {9, 986}
X(56046) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1999)}}, {{A, B, C, X(2), X(8)}}, {{A, B, C, X(6), X(31)}}, {{A, B, C, X(7), X(26065)}}, {{A, B, C, X(9), X(7058)}}, {{A, B, C, X(27), X(330)}}, {{A, B, C, X(57), X(83)}}, {{A, B, C, X(63), X(287)}}, {{A, B, C, X(75), X(7224)}}, {{A, B, C, X(80), X(34258)}}, {{A, B, C, X(86), X(37652)}}, {{A, B, C, X(89), X(42338)}}, {{A, B, C, X(171), X(3223)}}, {{A, B, C, X(226), X(34895)}}, {{A, B, C, X(239), X(612)}}, {{A, B, C, X(274), X(1751)}}, {{A, B, C, X(279), X(4339)}}, {{A, B, C, X(321), X(5130)}}, {{A, B, C, X(335), X(33163)}}, {{A, B, C, X(870), X(40415)}}, {{A, B, C, X(940), X(2334)}}, {{A, B, C, X(967), X(1258)}}, {{A, B, C, X(996), X(13478)}}, {{A, B, C, X(1016), X(25430)}}, {{A, B, C, X(1029), X(39700)}}, {{A, B, C, X(1107), X(4426)}}, {{A, B, C, X(1222), X(39694)}}, {{A, B, C, X(1509), X(39948)}}, {{A, B, C, X(1824), X(3765)}}, {{A, B, C, X(2185), X(55991)}}, {{A, B, C, X(2296), X(4600)}}, {{A, B, C, X(2982), X(40403)}}, {{A, B, C, X(3218), X(26223)}}, {{A, B, C, X(3662), X(5294)}}, {{A, B, C, X(4359), X(17281)}}, {{A, B, C, X(5235), X(5737)}}, {{A, B, C, X(5256), X(41261)}}, {{A, B, C, X(5278), X(27164)}}, {{A, B, C, X(5331), X(25417)}}, {{A, B, C, X(6542), X(29837)}}, {{A, B, C, X(6692), X(27130)}}, {{A, B, C, X(8033), X(41534)}}, {{A, B, C, X(9776), X(26685)}}, {{A, B, C, X(11323), X(26643)}}, {{A, B, C, X(16826), X(17156)}}, {{A, B, C, X(17790), X(28606)}}, {{A, B, C, X(21384), X(41239)}}, {{A, B, C, X(26627), X(27065)}}, {{A, B, C, X(30513), X(34277)}}, {{A, B, C, X(33162), X(40013)}}, {{A, B, C, X(34409), X(39712)}}, {{A, B, C, X(37870), X(43531)}}, {{A, B, C, X(39701), X(41629)}}, {{A, B, C, X(39748), X(53083)}}, {{A, B, C, X(39979), X(46331)}}, {{A, B, C, X(41258), X(52136)}}
X(56046) = barycentric product X(i)*X(j) for these (i, j): {75, 987}
X(56046) = barycentric quotient X(i)/X(j) for these (i, j): {1, 986}, {2, 27184}, {6, 2277}, {987, 1}

X(56047) = KP3(X(1)) OF X(2) AND X(58)

Barycentrics    (a+b)*(a+c)*(a^2+a*(b+c)+b*(b+c))*(a^2+a*(b+c)+c*(b+c)) : :

X(56047) lies on cubic K1285 and on these lines: {1, 15376}, {2, 58}, {7, 1412}, {27, 29833}, {75, 81}, {86, 593}, {226, 16947}, {272, 5249}, {273, 1396}, {284, 19717}, {310, 1509}, {333, 1171}, {335, 741}, {903, 42028}, {1240, 14534}, {1246, 7560}, {1333, 19684}, {1790, 20028}, {2206, 33682}, {2303, 26223}, {3285, 19722}, {3286, 19719}, {4273, 19738}, {4373, 26860}, {5235, 28650}, {5323, 27174}, {5333, 30598}, {5936, 16704}, {6548, 48580}, {8049, 18656}, {17169, 39732}, {17185, 53081}, {18739, 37633}, {19741, 33628}, {26626, 26830}, {27475, 51443}, {27494, 51449}, {29766, 30593}, {37218, 40039}, {39704, 42025}, {43926, 43927}

X(56047) = trilinear pole of line {3733, 21121}
X(56047) = X(i)-isoconjugate-of-X(j) for these {i, j}: {32, 42714}, {37, 386}, {42, 28606}, {72, 44103}, {100, 42664}, {101, 47842}, {163, 23282}, {190, 50488}, {213, 5224}, {228, 469}, {692, 23879}, {798, 33948}, {834, 1018}, {1400, 3876}, {1918, 33935}, {4033, 8637}, {4557, 14349}, {17038, 28622}, {22276, 53082}, {40521, 52615}
X(56047) = X(i)-Dao conjugate of X(j) for these {i, j}: {115, 23282}, {1015, 47842}, {1086, 23879}, {6376, 42714}, {6626, 5224}, {8054, 42664}, {31998, 33948}, {34021, 33935}, {40582, 3876}, {40589, 386}, {40592, 28606}, {40620, 45746}, {55053, 50488}
X(56047) = X(i)-cross conjugate of X(j) for these {i, j}: {86, 28621}, {940, 81}, {4657, 274}, {4840, 99}, {4932, 4610}, {54311, 39747}
X(56047) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1724)}}, {{A, B, C, X(2), X(7)}}, {{A, B, C, X(21), X(46103)}}, {{A, B, C, X(28), X(37095)}}, {{A, B, C, X(57), X(37522)}}, {{A, B, C, X(58), X(81)}}, {{A, B, C, X(79), X(321)}}, {{A, B, C, X(83), X(1255)}}, {{A, B, C, X(97), X(1790)}}, {{A, B, C, X(226), X(3454)}}, {{A, B, C, X(239), X(17019)}}, {{A, B, C, X(251), X(1474)}}, {{A, B, C, X(257), X(1029)}}, {{A, B, C, X(274), X(25526)}}, {{A, B, C, X(279), X(4340)}}, {{A, B, C, X(306), X(29833)}}, {{A, B, C, X(324), X(17167)}}, {{A, B, C, X(333), X(8025)}}, {{A, B, C, X(940), X(2221)}}, {{A, B, C, X(996), X(48867)}}, {{A, B, C, X(1220), X(35058)}}, {{A, B, C, X(1231), X(52381)}}, {{A, B, C, X(1330), X(6625)}}, {{A, B, C, X(1434), X(39747)}}, {{A, B, C, X(1999), X(17011)}}, {{A, B, C, X(2006), X(37693)}}, {{A, B, C, X(2162), X(2206)}}, {{A, B, C, X(2185), X(19607)}}, {{A, B, C, X(3615), X(27412)}}, {{A, B, C, X(3666), X(28273)}}, {{A, B, C, X(5235), X(42025)}}, {{A, B, C, X(5331), X(25417)}}, {{A, B, C, X(6186), X(40747)}}, {{A, B, C, X(6693), X(55090)}}, {{A, B, C, X(6994), X(11110)}}, {{A, B, C, X(7108), X(10266)}}, {{A, B, C, X(8024), X(17171)}}, {{A, B, C, X(13486), X(43190)}}, {{A, B, C, X(14014), X(26643)}}, {{A, B, C, X(15315), X(28606)}}, {{A, B, C, X(16704), X(42028)}}, {{A, B, C, X(17206), X(30679)}}, {{A, B, C, X(17743), X(27789)}}, {{A, B, C, X(18653), X(46809)}}, {{A, B, C, X(19717), X(29766)}}, {{A, B, C, X(20569), X(48868)}}, {{A, B, C, X(21907), X(26131)}}, {{A, B, C, X(24624), X(37870)}}, {{A, B, C, X(26860), X(41629)}}, {{A, B, C, X(27174), X(44734)}}, {{A, B, C, X(27660), X(40432)}}, {{A, B, C, X(27946), X(40725)}}, {{A, B, C, X(28621), X(43531)}}, {{A, B, C, X(28654), X(34920)}}, {{A, B, C, X(29841), X(33077)}}, {{A, B, C, X(30588), X(37887)}}, {{A, B, C, X(34914), X(49723)}}, {{A, B, C, X(36011), X(51354)}}, {{A, B, C, X(40409), X(55971)}}, {{A, B, C, X(40415), X(40439)}}, {{A, B, C, X(44572), X(49729)}}, {{A, B, C, X(49744), X(52374)}}, {{A, B, C, X(50226), X(55949)}}
X(56047) = barycentric product X(i)*X(j) for these (i, j): {1019, 37218}, {2214, 274}, {7192, 835}, {17379, 28621}, {43531, 86}, {43927, 99}
X(56047) = barycentric quotient X(i)/X(j) for these (i, j): {21, 3876}, {27, 469}, {58, 386}, {75, 42714}, {81, 28606}, {86, 5224}, {99, 33948}, {274, 33935}, {513, 47842}, {514, 23879}, {523, 23282}, {649, 42664}, {667, 50488}, {835, 3952}, {1019, 14349}, {1434, 33949}, {1474, 44103}, {2214, 37}, {3733, 834}, {4184, 26911}, {7192, 45746}, {37218, 4033}, {43531, 10}, {43927, 523}, {53081, 21078}
X(56047) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {81, 37095, 3187}

X(56048) = KP3(X(1)) OF X(2) AND X(81)

Barycentrics    a*(a+b)*(a+c)*(a+3*b+c)*(a+b+3*c) : :

X(56048) lies on the Feuerbach hyperbola and on these lines: {1, 1014}, {4, 3945}, {7, 4854}, {8, 86}, {9, 81}, {21, 757}, {77, 5665}, {79, 3664}, {104, 5545}, {256, 4038}, {284, 42317}, {294, 2303}, {314, 873}, {347, 51512}, {885, 47844}, {940, 941}, {943, 37594}, {1039, 54407}, {1172, 14014}, {1320, 4614}, {1434, 5558}, {1442, 17097}, {1444, 2320}, {1449, 24557}, {1476, 7269}, {1963, 2344}, {2298, 37595}, {2346, 3745}, {3296, 3672}, {3663, 5557}, {3680, 54308}, {4346, 5551}, {4606, 4876}, {4633, 36798}, {4658, 4866}, {4663, 32635}, {4888, 43732}, {4909, 5559}, {7091, 7190}, {7155, 51356}, {9345, 22174}, {10455, 45032}, {18166, 34820}, {30479, 30941}, {30939, 40023}, {42025, 50292}, {42028, 42032}

X(56048) = isogonal conjugate of X(37593)
X(56048) = trilinear pole of line {650, 1019}
X(56048) = perspector of circumconic {{A, B, C, X(4614), X(4633)}}
X(56048) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 37593}, {6, 5257}, {19, 4047}, {25, 4101}, {37, 1449}, {42, 3616}, {55, 3671}, {56, 4061}, {65, 4512}, {72, 5338}, {73, 461}, {100, 4822}, {101, 4841}, {106, 4819}, {109, 4843}, {190, 4832}, {210, 3361}, {213, 19804}, {226, 4258}, {228, 5342}, {292, 4771}, {307, 44100}, {391, 1400}, {604, 42712}, {664, 8653}, {672, 14625}, {692, 4815}, {741, 4829}, {813, 4839}, {1018, 4790}, {1020, 4827}, {1334, 21454}, {1402, 4673}, {1500, 42028}, {1824, 4652}, {3690, 31903}, {4557, 4778}, {4559, 4765}, {4734, 23493}, {4835, 20964}, {7180, 30728}
X(56048) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 4061}, {3, 37593}, {6, 4047}, {9, 5257}, {11, 4843}, {214, 4819}, {223, 3671}, {1015, 4841}, {1086, 4815}, {3161, 42712}, {6505, 4101}, {6626, 19804}, {8054, 4822}, {8299, 4829}, {19557, 4771}, {39025, 8653}, {40582, 391}, {40589, 1449}, {40592, 3616}, {40602, 4512}, {40605, 4673}, {40620, 4801}, {40623, 4839}, {40625, 4811}, {55053, 4832}, {55067, 4765}
X(56048) = X(i)-cross conjugate of X(j) for these {i, j}: {1697, 333}, {4658, 81}, {6005, 100}, {6051, 2}, {17418, 651}
X(56048) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(2), X(969)}}, {{A, B, C, X(6), X(51443)}}, {{A, B, C, X(28), X(14005)}}, {{A, B, C, X(29), X(37402)}}, {{A, B, C, X(37), X(4733)}}, {{A, B, C, X(57), X(28626)}}, {{A, B, C, X(75), X(1255)}}, {{A, B, C, X(77), X(1812)}}, {{A, B, C, X(81), X(86)}}, {{A, B, C, X(88), X(30598)}}, {{A, B, C, X(105), X(2214)}}, {{A, B, C, X(171), X(4038)}}, {{A, B, C, X(269), X(39948)}}, {{A, B, C, X(286), X(39734)}}, {{A, B, C, X(354), X(3745)}}, {{A, B, C, X(513), X(46971)}}, {{A, B, C, X(942), X(37594)}}, {{A, B, C, X(1100), X(4663)}}, {{A, B, C, X(1178), X(51449)}}, {{A, B, C, X(1268), X(40434)}}, {{A, B, C, X(1280), X(39739)}}, {{A, B, C, X(1390), X(13476)}}, {{A, B, C, X(1442), X(3664)}}, {{A, B, C, X(1509), X(38810)}}, {{A, B, C, X(1963), X(30966)}}, {{A, B, C, X(2160), X(34585)}}, {{A, B, C, X(2194), X(10579)}}, {{A, B, C, X(2991), X(25417)}}, {{A, B, C, X(2995), X(55987)}}, {{A, B, C, X(3477), X(7050)}}, {{A, B, C, X(3663), X(7269)}}, {{A, B, C, X(3666), X(37595)}}, {{A, B, C, X(3672), X(7190)}}, {{A, B, C, X(3702), X(3931)}}, {{A, B, C, X(3744), X(4883)}}, {{A, B, C, X(4373), X(27789)}}, {{A, B, C, X(4854), X(7073)}}, {{A, B, C, X(5936), X(25430)}}, {{A, B, C, X(7100), X(49743)}}, {{A, B, C, X(8049), X(40422)}}, {{A, B, C, X(13610), X(30571)}}, {{A, B, C, X(17011), X(50292)}}, {{A, B, C, X(17377), X(39704)}}, {{A, B, C, X(23617), X(40433)}}, {{A, B, C, X(27644), X(51356)}}, {{A, B, C, X(30576), X(30939)}}, {{A, B, C, X(30941), X(47844)}}, {{A, B, C, X(39972), X(40400)}}, {{A, B, C, X(40401), X(49680)}}
X(56048) = barycentric product X(i)*X(j) for these (i, j): {1019, 53658}, {1434, 4866}, {2334, 274}, {3737, 4624}, {4391, 5545}, {4606, 7192}, {4614, 514}, {4627, 693}, {4633, 513}, {5936, 81}, {7199, 8694}, {25430, 86}, {34074, 52619}, {40023, 58}, {47915, 99}
X(56048) = barycentric quotient X(i)/X(j) for these (i, j): {1, 5257}, {3, 4047}, {6, 37593}, {8, 42712}, {9, 4061}, {21, 391}, {27, 5342}, {44, 4819}, {57, 3671}, {58, 1449}, {63, 4101}, {81, 3616}, {86, 19804}, {105, 14625}, {238, 4771}, {284, 4512}, {333, 4673}, {513, 4841}, {514, 4815}, {643, 30728}, {649, 4822}, {650, 4843}, {659, 4839}, {667, 4832}, {757, 42028}, {1014, 21454}, {1019, 4778}, {1172, 461}, {1412, 3361}, {1474, 5338}, {1790, 4652}, {2194, 4258}, {2204, 44100}, {2238, 4829}, {2334, 37}, {3063, 8653}, {3733, 4790}, {3737, 4765}, {4481, 4818}, {4560, 4811}, {4606, 3952}, {4614, 190}, {4627, 100}, {4633, 668}, {4866, 2321}, {5545, 651}, {5936, 321}, {7192, 4801}, {7203, 30723}, {8694, 1018}, {14626, 3930}, {16702, 4831}, {16704, 4742}, {18206, 4684}, {21789, 4827}, {25430, 10}, {27644, 4734}, {34074, 4557}, {34820, 210}, {35339, 4115}, {40023, 313}, {40153, 4719}, {40432, 4835}, {47915, 523}, {50456, 4830}, {52680, 4700}, {52897, 4706}, {53658, 4033}

X(56049) = KP3(X(1)) OF X(2) AND X(88)

Barycentrics    a*(a+b-2*c)*(a+b-c)*(a-2*b+c)*(a-b+c) : :

X(56049) lies on these lines: {7, 528}, {57, 88}, {77, 19604}, {106, 269}, {226, 4945}, {241, 51908}, {279, 14260}, {347, 52803}, {479, 4626}, {679, 1318}, {901, 15728}, {1014, 1122}, {1022, 34056}, {1119, 36118}, {1156, 3675}, {1168, 6549}, {1447, 52761}, {1462, 6610}, {1465, 2226}, {2161, 53546}, {3160, 45247}, {3257, 37787}, {3911, 36592}, {4674, 7271}, {4792, 18421}, {4896, 5425}, {4997, 5226}, {6336, 55110}, {8051, 31227}, {8545, 21446}, {8686, 39414}, {16610, 40400}, {16944, 38859}, {17074, 47056}, {20568, 31643}, {21454, 42026}, {23345, 43930}, {23838, 43736}, {28997, 42304}, {30379, 46790}, {36048, 36058}, {36918, 40615}, {37771, 40617}, {38459, 52478}, {40862, 46795}

X(56049) = isogonal conjugate of X(3689)
X(56049) = isotomic conjugate of X(4723)
X(56049) = trilinear pole of line {57, 1022}
X(56049) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 3689}, {6, 2325}, {8, 902}, {9, 44}, {19, 52978}, {21, 21805}, {31, 4723}, {33, 5440}, {41, 4358}, {55, 519}, {100, 4895}, {101, 1639}, {106, 4152}, {109, 4528}, {200, 1319}, {210, 52680}, {212, 38462}, {214, 52371}, {219, 8756}, {220, 3911}, {281, 22356}, {284, 3943}, {294, 14439}, {312, 2251}, {318, 23202}, {333, 52963}, {346, 1404}, {522, 23344}, {607, 3977}, {643, 4730}, {644, 1635}, {645, 14407}, {649, 30731}, {650, 1023}, {651, 14427}, {663, 17780}, {678, 1320}, {692, 4768}, {900, 3939}, {901, 4543}, {1017, 4997}, {1145, 2342}, {1252, 4530}, {1260, 1877}, {1318, 8028}, {1334, 16704}, {1500, 30606}, {1647, 6065}, {1783, 14418}, {1802, 37790}, {1960, 3699}, {2175, 3264}, {2194, 3992}, {2316, 4370}, {2318, 37168}, {2319, 52964}, {2321, 3285}, {2328, 40663}, {2338, 51406}, {2341, 40988}, {2361, 51975}, {2364, 4908}, {2429, 4521}, {3063, 24004}, {3596, 9459}, {3900, 23703}, {4120, 5546}, {4169, 7252}, {4432, 7077}, {4511, 40172}, {4542, 9268}, {4578, 53528}, {4700, 34820}, {4814, 52924}, {4845, 6174}, {4969, 33635}, {5548, 6544}, {10482, 51463}, {17455, 36910}, {28071, 53531}, {40869, 45144}, {41553, 42064}, {46109, 52425}, {46791, 52969}
X(56049) = X(i)-vertex conjugate of X(j) for these {i, j}: {1156, 3446}
X(56049) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 4723}, {3, 3689}, {6, 52978}, {9, 2325}, {11, 4528}, {214, 4152}, {223, 519}, {478, 44}, {661, 4530}, {1015, 1639}, {1086, 4768}, {1214, 3992}, {3160, 4358}, {5375, 30731}, {6609, 1319}, {8054, 4895}, {9460, 312}, {10001, 24004}, {16591, 4783}, {16594, 52871}, {36908, 40663}, {38979, 4543}, {38991, 14427}, {39006, 14418}, {40590, 3943}, {40593, 3264}, {40594, 8}, {40595, 9}, {40611, 21805}, {40615, 3762}, {40617, 900}, {40837, 38462}, {45247, 51380}, {52659, 4738}, {52879, 6174}, {55060, 4730}
X(56049) = X(i)-cross conjugate of X(j) for these {i, j}: {106, 88}, {1319, 57}, {1411, 34051}, {1443, 1014}, {1465, 279}, {14260, 2226}, {30117, 81}, {53528, 651}
X(56049) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3241)}}, {{A, B, C, X(2), X(50101)}}, {{A, B, C, X(6), X(42871)}}, {{A, B, C, X(7), X(57)}}, {{A, B, C, X(8), X(45818)}}, {{A, B, C, X(9), X(16487)}}, {{A, B, C, X(19), X(41439)}}, {{A, B, C, X(21), X(37817)}}, {{A, B, C, X(28), X(17579)}}, {{A, B, C, X(34), X(1476)}}, {{A, B, C, X(56), X(1405)}}, {{A, B, C, X(59), X(1477)}}, {{A, B, C, X(75), X(4398)}}, {{A, B, C, X(80), X(9802)}}, {{A, B, C, X(81), X(17378)}}, {{A, B, C, X(86), X(1255)}}, {{A, B, C, X(88), X(679)}}, {{A, B, C, X(104), X(6224)}}, {{A, B, C, X(105), X(513)}}, {{A, B, C, X(106), X(1168)}}, {{A, B, C, X(244), X(14193)}}, {{A, B, C, X(279), X(17079)}}, {{A, B, C, X(291), X(7312)}}, {{A, B, C, X(651), X(664)}}, {{A, B, C, X(738), X(27818)}}, {{A, B, C, X(739), X(9319)}}, {{A, B, C, X(759), X(9963)}}, {{A, B, C, X(840), X(909)}}, {{A, B, C, X(915), X(34256)}}, {{A, B, C, X(937), X(5558)}}, {{A, B, C, X(957), X(55924)}}, {{A, B, C, X(961), X(5434)}}, {{A, B, C, X(1002), X(51099)}}, {{A, B, C, X(1022), X(36887)}}, {{A, B, C, X(1122), X(1441)}}, {{A, B, C, X(1280), X(37129)}}, {{A, B, C, X(1317), X(1319)}}, {{A, B, C, X(1358), X(7233)}}, {{A, B, C, X(1390), X(55919)}}, {{A, B, C, X(1416), X(7316)}}, {{A, B, C, X(1438), X(10699)}}, {{A, B, C, X(1443), X(34051)}}, {{A, B, C, X(1447), X(52896)}}, {{A, B, C, X(2006), X(41803)}}, {{A, B, C, X(2191), X(2346)}}, {{A, B, C, X(2298), X(7194)}}, {{A, B, C, X(2481), X(53391)}}, {{A, B, C, X(2718), X(10031)}}, {{A, B, C, X(2991), X(25417)}}, {{A, B, C, X(3418), X(41442)}}, {{A, B, C, X(3451), X(41431)}}, {{A, B, C, X(3598), X(8545)}}, {{A, B, C, X(3660), X(18801)}}, {{A, B, C, X(3669), X(43038)}}, {{A, B, C, X(3676), X(18815)}}, {{A, B, C, X(4555), X(39414)}}, {{A, B, C, X(6548), X(52031)}}, {{A, B, C, X(6610), X(34855)}}, {{A, B, C, X(7023), X(16079)}}, {{A, B, C, X(7192), X(18816)}}, {{A, B, C, X(7313), X(55022)}}, {{A, B, C, X(8056), X(36588)}}, {{A, B, C, X(9083), X(15742)}}, {{A, B, C, X(9456), X(23345)}}, {{A, B, C, X(16099), X(36100)}}, {{A, B, C, X(17096), X(34018)}}, {{A, B, C, X(19302), X(28535)}}, {{A, B, C, X(36124), X(40450)}}, {{A, B, C, X(39982), X(55935)}}, {{A, B, C, X(40215), X(52553)}}, {{A, B, C, X(50839), X(55920)}}, {{A, B, C, X(51643), X(51654)}}
X(56049) = barycentric product X(i)*X(j) for these (i, j): {7, 88}, {57, 903}, {106, 85}, {269, 4997}, {331, 36058}, {348, 36125}, {651, 6548}, {1014, 4080}, {1022, 664}, {1088, 2316}, {1168, 17078}, {1170, 53240}, {1319, 54974}, {1320, 279}, {1358, 5376}, {1414, 4049}, {1417, 76}, {1434, 4674}, {1797, 273}, {2006, 52553}, {2099, 40833}, {3257, 3676}, {3669, 4555}, {3911, 679}, {4017, 4615}, {4077, 4591}, {4564, 6549}, {4573, 55244}, {4622, 7178}, {4625, 55263}, {4634, 7180}, {6063, 9456}, {6336, 77}, {7182, 8752}, {18815, 40215}, {19604, 31227}, {20568, 56}, {23345, 4554}, {23838, 658}, {24002, 901}, {30725, 4618}, {32665, 52621}, {34018, 34230}, {34056, 36887}, {43932, 4582}, {52574, 8686}
X(56049) = barycentric quotient X(i)/X(j) for these (i, j): {1, 2325}, {2, 4723}, {3, 52978}, {6, 3689}, {7, 4358}, {34, 8756}, {44, 4152}, {56, 44}, {57, 519}, {65, 3943}, {77, 3977}, {85, 3264}, {88, 8}, {100, 30731}, {106, 9}, {109, 1023}, {222, 5440}, {226, 3992}, {244, 4530}, {269, 3911}, {273, 46109}, {278, 38462}, {513, 1639}, {514, 4768}, {553, 4975}, {603, 22356}, {604, 902}, {649, 4895}, {650, 4528}, {651, 17780}, {663, 14427}, {664, 24004}, {679, 4997}, {757, 30606}, {764, 52338}, {901, 644}, {903, 312}, {1014, 16704}, {1022, 522}, {1106, 1404}, {1119, 37790}, {1122, 51415}, {1168, 36910}, {1319, 4370}, {1320, 346}, {1357, 2087}, {1396, 37168}, {1397, 2251}, {1400, 21805}, {1402, 52963}, {1403, 52964}, {1404, 678}, {1407, 1319}, {1408, 3285}, {1412, 52680}, {1415, 23344}, {1417, 6}, {1418, 51463}, {1427, 40663}, {1429, 4432}, {1434, 30939}, {1435, 1877}, {1443, 51583}, {1456, 51406}, {1458, 14439}, {1459, 14418}, {1461, 23703}, {1464, 40988}, {1465, 1145}, {1635, 4543}, {1797, 78}, {2006, 51975}, {2087, 4542}, {2099, 4908}, {2226, 1320}, {2316, 200}, {2441, 4162}, {3257, 3699}, {3361, 4700}, {3669, 900}, {3676, 3762}, {3911, 4738}, {4017, 4120}, {4049, 4086}, {4080, 3701}, {4510, 4494}, {4551, 4169}, {4555, 646}, {4573, 55243}, {4591, 643}, {4615, 7257}, {4618, 4582}, {4622, 645}, {4625, 55262}, {4674, 2321}, {4792, 4873}, {4997, 341}, {5221, 4727}, {5228, 4702}, {5376, 4076}, {5435, 4487}, {5548, 4578}, {6336, 318}, {6548, 4391}, {6549, 4858}, {6610, 6174}, {7146, 4439}, {7175, 4434}, {7180, 4730}, {7216, 30572}, {7223, 4506}, {7341, 30576}, {8686, 52556}, {8752, 33}, {9456, 55}, {10428, 52663}, {16609, 4783}, {16610, 52871}, {16944, 2323}, {17078, 1227}, {20568, 3596}, {21454, 4742}, {23345, 650}, {23352, 4944}, {23703, 53582}, {23838, 3239}, {27922, 3975}, {31227, 44720}, {32636, 4969}, {32659, 212}, {32665, 3939}, {34051, 36944}, {34056, 52746}, {34230, 3693}, {36058, 219}, {36125, 281}, {40215, 4511}, {42026, 3902}, {43922, 2170}, {43924, 1635}, {43932, 30725}, {46150, 33299}, {47056, 36926}, {51641, 14407}, {51656, 14425}, {51664, 14429}, {52031, 6735}, {52206, 3880}, {52411, 23202}, {52440, 17455}, {52553, 32851}, {52900, 4009}, {53240, 1229}, {53528, 6544}, {53538, 1647}, {53546, 51402}, {55244, 3700}, {55263, 4041}

X(56050) = KP3(X(1)) OF X(2) AND X(90)

Barycentrics    (a^3-a^2*(b-3*c)+(b-c)^2*(b+c)-a*(b^2-3*c^2))*(a^3+a^2*(3*b-c)+(b-c)^2*(b+c)+a*(3*b^2-c^2)) : :

X(56050) lies on these lines: {1, 5905}, {2, 20930}, {81, 26830}, {88, 37642}, {279, 33150}, {330, 19789}, {347, 2982}, {908, 25430}, {1219, 28605}, {1255, 5712}, {1257, 20013}, {1993, 40399}, {2401, 4801}, {2994, 53596}, {3086, 30690}, {3672, 25417}, {3995, 54123}, {8056, 26723}, {17147, 39696}, {21454, 34051}, {30699, 35058}

X(56050) = trilinear pole of line {21188, 513}
X(56050) = X(i)-isoconjugate-of-X(j) for these {i, j}: {9, 11509}
X(56050) = X(i)-Dao conjugate of X(j) for these {i, j}: {478, 11509}
X(56050) = X(i)-cross conjugate of X(j) for these {i, j}: {3338, 7}, {19785, 2}
X(56050) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(4), X(26830)}}, {{A, B, C, X(7), X(5905)}}, {{A, B, C, X(27), X(2994)}}, {{A, B, C, X(92), X(1434)}}, {{A, B, C, X(145), X(26723)}}, {{A, B, C, X(189), X(44559)}}, {{A, B, C, X(192), X(19789)}}, {{A, B, C, X(346), X(33150)}}, {{A, B, C, X(552), X(32023)}}, {{A, B, C, X(757), X(7318)}}, {{A, B, C, X(908), X(4801)}}, {{A, B, C, X(1029), X(10405)}}, {{A, B, C, X(1797), X(30679)}}, {{A, B, C, X(2221), X(3669)}}, {{A, B, C, X(3668), X(43675)}}, {{A, B, C, X(3672), X(28605)}}, {{A, B, C, X(5712), X(8025)}}, {{A, B, C, X(6336), X(44733)}}, {{A, B, C, X(16704), X(37642)}}, {{A, B, C, X(17014), X(25006)}}, {{A, B, C, X(17147), X(30699)}}, {{A, B, C, X(20013), X(40940)}}, {{A, B, C, X(33099), X(39720)}}, {{A, B, C, X(55027), X(55937)}}
X(56050) = barycentric quotient X(i)/X(j) for these (i, j): {56, 11509}

X(56051) = KP3(X(2)) OF X(1) AND X(2)

Barycentrics    (2*b*c+a*(2*b+c))*(2*b*c+a*(b+2*c)) : :

X(56051) lies on these lines: {1, 3696}, {2, 3760}, {9, 39797}, {10, 1002}, {57, 4059}, {75, 4099}, {81, 4384}, {89, 16815}, {105, 5248}, {142, 51223}, {194, 39736}, {239, 25417}, {274, 4751}, {277, 24778}, {278, 17911}, {279, 17077}, {291, 1698}, {330, 16819}, {957, 17050}, {959, 3671}, {1107, 36871}, {1219, 19853}, {1224, 25499}, {1255, 16831}, {1258, 54981}, {1390, 39586}, {2282, 20367}, {3227, 31997}, {3294, 25590}, {3624, 30571}, {3644, 32090}, {3934, 19872}, {4000, 25512}, {4668, 24656}, {4687, 32102}, {4699, 31996}, {4932, 43928}, {5283, 31238}, {8056, 24774}, {10471, 19804}, {16826, 27789}, {16833, 39948}, {17030, 39925}, {17066, 47683}, {17289, 32019}, {17758, 26037}, {20269, 37887}, {21264, 34595}, {21384, 39950}, {25430, 31993}, {27248, 54123}

X(56051) = isotomic conjugate of X(4687)
X(56051) = trilinear pole of line {4382, 4804}
X(56051) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 17018}, {9, 16878}, {31, 4687}, {37, 39673}, {101, 6005}, {163, 48407}, {190, 8655}, {662, 50483}, {692, 47666}
X(56051) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 4687}, {9, 17018}, {115, 48407}, {478, 16878}, {1015, 6005}, {1084, 50483}, {1086, 47666}, {40589, 39673}, {55053, 8655}
X(56051) = X(i)-cross conjugate of X(j) for these {i, j}: {2258, 10435}, {5283, 1}, {29198, 668}, {31238, 2}, {37593, 7}, {47926, 190}
X(56051) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(8), X(16832)}}, {{A, B, C, X(9), X(16552)}}, {{A, B, C, X(10), X(85)}}, {{A, B, C, X(27), X(16458)}}, {{A, B, C, X(29), X(37075)}}, {{A, B, C, X(37), X(4751)}}, {{A, B, C, X(43), X(16819)}}, {{A, B, C, X(58), X(39981)}}, {{A, B, C, X(75), X(3739)}}, {{A, B, C, X(76), X(27483)}}, {{A, B, C, X(79), X(39721)}}, {{A, B, C, X(80), X(32022)}}, {{A, B, C, X(86), X(14377)}}, {{A, B, C, X(87), X(25264)}}, {{A, B, C, X(239), X(1698)}}, {{A, B, C, X(257), X(20569)}}, {{A, B, C, X(292), X(34819)}}, {{A, B, C, X(333), X(19732)}}, {{A, B, C, X(335), X(39711)}}, {{A, B, C, X(514), X(28581)}}, {{A, B, C, X(596), X(27475)}}, {{A, B, C, X(612), X(16818)}}, {{A, B, C, X(673), X(43531)}}, {{A, B, C, X(756), X(4099)}}, {{A, B, C, X(870), X(1268)}}, {{A, B, C, X(996), X(32008)}}, {{A, B, C, X(1107), X(54981)}}, {{A, B, C, X(1125), X(16831)}}, {{A, B, C, X(1218), X(2665)}}, {{A, B, C, X(1247), X(7096)}}, {{A, B, C, X(1400), X(45820)}}, {{A, B, C, X(1434), X(42335)}}, {{A, B, C, X(2163), X(40432)}}, {{A, B, C, X(2191), X(24790)}}, {{A, B, C, X(2218), X(40398)}}, {{A, B, C, X(2258), X(5283)}}, {{A, B, C, X(2279), X(25092)}}, {{A, B, C, X(2481), X(5936)}}, {{A, B, C, X(2664), X(17030)}}, {{A, B, C, X(2999), X(19853)}}, {{A, B, C, X(3226), X(34816)}}, {{A, B, C, X(3294), X(21384)}}, {{A, B, C, X(3500), X(39949)}}, {{A, B, C, X(3624), X(16826)}}, {{A, B, C, X(3634), X(16834)}}, {{A, B, C, X(3671), X(19804)}}, {{A, B, C, X(3679), X(16815)}}, {{A, B, C, X(4359), X(39700)}}, {{A, B, C, X(4657), X(28653)}}, {{A, B, C, X(4687), X(31238)}}, {{A, B, C, X(4852), X(28650)}}, {{A, B, C, X(4866), X(36796)}}, {{A, B, C, X(4932), X(31997)}}, {{A, B, C, X(5219), X(26627)}}, {{A, B, C, X(5248), X(18206)}}, {{A, B, C, X(5256), X(16828)}}, {{A, B, C, X(5272), X(27248)}}, {{A, B, C, X(5287), X(25512)}}, {{A, B, C, X(5561), X(6625)}}, {{A, B, C, X(6650), X(43732)}}, {{A, B, C, X(7110), X(41791)}}, {{A, B, C, X(8580), X(27304)}}, {{A, B, C, X(9311), X(42285)}}, {{A, B, C, X(9780), X(16833)}}, {{A, B, C, X(10435), X(10436)}}, {{A, B, C, X(14621), X(32014)}}, {{A, B, C, X(15175), X(40403)}}, {{A, B, C, X(16706), X(17303)}}, {{A, B, C, X(16816), X(19875)}}, {{A, B, C, X(16823), X(17284)}}, {{A, B, C, X(16825), X(17308)}}, {{A, B, C, X(16830), X(29598)}}, {{A, B, C, X(17012), X(19871)}}, {{A, B, C, X(17023), X(39586)}}, {{A, B, C, X(17278), X(17289)}}, {{A, B, C, X(17356), X(17371)}}, {{A, B, C, X(17367), X(36531)}}, {{A, B, C, X(17370), X(17385)}}, {{A, B, C, X(18152), X(26037)}}, {{A, B, C, X(18822), X(36957)}}, {{A, B, C, X(18827), X(28639)}}, {{A, B, C, X(18841), X(42318)}}, {{A, B, C, X(19808), X(24789)}}, {{A, B, C, X(19862), X(29597)}}, {{A, B, C, X(19872), X(29584)}}, {{A, B, C, X(20367), X(37523)}}, {{A, B, C, X(24778), X(27819)}}, {{A, B, C, X(25055), X(29578)}}, {{A, B, C, X(25130), X(40027)}}, {{A, B, C, X(25426), X(39983)}}, {{A, B, C, X(26102), X(31996)}}, {{A, B, C, X(27351), X(41531)}}, {{A, B, C, X(28660), X(45032)}}, {{A, B, C, X(29570), X(34595)}}, {{A, B, C, X(30712), X(31312)}}, {{A, B, C, X(31211), X(49451)}}, {{A, B, C, X(31327), X(34258)}}, {{A, B, C, X(33296), X(52716)}}, {{A, B, C, X(35167), X(36954)}}, {{A, B, C, X(36956), X(53209)}}, {{A, B, C, X(40509), X(52209)}}, {{A, B, C, X(43731), X(54120)}}
X(56051) = barycentric product X(i)*X(j) for these (i, j): {6013, 693}, {10013, 75}, {17110, 34258}, {46772, 86}
X(56051) = barycentric quotient X(i)/X(j) for these (i, j): {1, 17018}, {2, 4687}, {56, 16878}, {58, 39673}, {512, 50483}, {513, 6005}, {514, 47666}, {523, 48407}, {667, 8655}, {6013, 100}, {10013, 1}, {17110, 940}, {46772, 10}

X(56052) = KP3(X(2)) OF X(1) AND X(86)

Barycentrics    (a+b)*(a+c)*(a*(b+c)+b*(2*b+c))*(a*(b+c)+c*(b+2*c)) : :

X(56052) lies on these lines: {2, 21024}, {7, 30966}, {10, 40418}, {27, 6626}, {75, 17038}, {86, 3741}, {274, 6384}, {310, 30970}, {333, 14621}, {335, 31993}, {675, 43359}, {871, 40072}, {1246, 5224}, {2296, 31330}, {3666, 27483}, {16609, 44733}, {16738, 53677}, {17206, 40164}, {18091, 52394}, {25507, 31028}, {26102, 30598}, {27447, 32010}, {29827, 40027}, {30712, 30941}, {31002, 31241}

X(56052) = isotomic conjugate of X(43223)
X(56052) = trilinear pole of line {17217, 514}
X(56052) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 43223}, {213, 17379}, {1918, 31997}, {2214, 28622}
X(56052) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 43223}, {86, 17689}, {6626, 17379}, {34021, 31997}, {40620, 4932}
X(56052) = X(i)-Ceva conjugate of X(j) for these {i, j}: {28621, 86}
X(56052) = X(i)-cross conjugate of X(j) for these {i, j}: {784, 190}, {4699, 274}, {17591, 81}
X(56052) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(7)}}, {{A, B, C, X(10), X(3741)}}, {{A, B, C, X(42), X(30970)}}, {{A, B, C, X(58), X(28513)}}, {{A, B, C, X(65), X(4038)}}, {{A, B, C, X(256), X(16606)}}, {{A, B, C, X(257), X(51865)}}, {{A, B, C, X(274), X(7304)}}, {{A, B, C, X(291), X(5331)}}, {{A, B, C, X(333), X(30966)}}, {{A, B, C, X(350), X(16609)}}, {{A, B, C, X(693), X(41851)}}, {{A, B, C, X(893), X(40775)}}, {{A, B, C, X(899), X(31241)}}, {{A, B, C, X(1698), X(26102)}}, {{A, B, C, X(3223), X(4492)}}, {{A, B, C, X(3634), X(25501)}}, {{A, B, C, X(4212), X(11110)}}, {{A, B, C, X(6626), X(7019)}}, {{A, B, C, X(16569), X(29827)}}, {{A, B, C, X(16832), X(30822)}}, {{A, B, C, X(17026), X(17308)}}, {{A, B, C, X(17038), X(39967)}}, {{A, B, C, X(18827), X(37870)}}, {{A, B, C, X(19875), X(31137)}}, {{A, B, C, X(26037), X(30942)}}, {{A, B, C, X(29576), X(31028)}}, {{A, B, C, X(29828), X(30752)}}, {{A, B, C, X(30710), X(39717)}}, {{A, B, C, X(32783), X(33138)}}
X(56052) = barycentric product X(i)*X(j) for these (i, j): {310, 39967}, {3261, 43359}, {17038, 274}, {28621, 5224}
X(56052) = barycentric quotient X(i)/X(j) for these (i, j): {2, 43223}, {86, 17379}, {274, 31997}, {386, 28622}, {6626, 17689}, {7192, 4932}, {17038, 37}, {28621, 43531}, {39967, 42}, {43359, 101}

X(56053) = KP3(X(2)) OF X(1) AND X(99)

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a*(b-c)-b*c)*(a*(b-c)+b*c) : :

X(56053) lies on these lines: {87, 261}, {99, 932}, {645, 4584}, {662, 4598}, {670, 3733}, {1509, 7121}, {2106, 51864}, {4565, 17941}, {6383, 23086}, {17103, 17105}, {17929, 43931}, {19623, 40881}, {34594, 35572}, {40753, 51356}

X(56053) = isogonal conjugate of X(50491)
X(56053) = isotomic conjugate of X(21051)
X(56053) = trilinear pole of line {81, 330}
X(56053) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 50491}, {6, 21834}, {10, 8640}, {31, 21051}, {37, 20979}, {42, 4083}, {43, 512}, {190, 21835}, {192, 798}, {213, 3835}, {523, 2209}, {649, 20691}, {661, 2176}, {667, 3971}, {669, 6376}, {756, 16695}, {872, 17217}, {1018, 6377}, {1084, 36860}, {1334, 43051}, {1402, 4147}, {1403, 4041}, {1423, 3709}, {1500, 18197}, {1824, 22090}, {1918, 20906}, {1924, 6382}, {2333, 25098}, {2489, 22370}, {3121, 4595}, {3122, 52923}, {3123, 4557}, {3208, 7180}, {3700, 41526}, {3952, 38986}, {4033, 21762}, {4079, 27644}, {4455, 41531}, {4705, 38832}, {18107, 21814}, {21759, 23886}, {21832, 51973}, {23493, 25142}, {27538, 51641}, {31008, 53581}, {33296, 50487}, {52964, 55263}
X(56053) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 21051}, {3, 50491}, {9, 21834}, {5375, 20691}, {6626, 3835}, {6631, 3971}, {9428, 6382}, {16606, 21056}, {17755, 21959}, {31998, 192}, {34021, 20906}, {36830, 2176}, {39054, 43}, {40589, 20979}, {40592, 4083}, {40605, 4147}, {40620, 21138}, {55053, 21835}
X(56053) = X(i)-cross conjugate of X(j) for these {i, j}: {87, 5383}, {748, 1016}, {799, 99}, {4594, 53655}, {16695, 81}, {23467, 6}, {25537, 1}
X(56053) = intersection, other than A, B, C, of these circumconics: {{A, B, C, X(86), X(670)}}, {{A, B, C, X(99), X(662)}}, {{A, B, C, X(190), X(8709)}}, {{A, B, C, X(261), X(645)}}, {{A, B, C, X(648), X(17930)}}, {{A, B, C, X(651), X(789)}}, {{A, B, C, X(692), X(898)}}, {{A, B, C, X(799), X(3222)}}, {{A, B, C, X(932), X(34071)}}, {{A, B, C, X(1492), X(8707)}}, {{A, B, C, X(3737), X(21388)}}, {{A, B, C, X(4033), X(30598)}}, {{A, B, C, X(4565), X(36066)}}, {{A, B, C, X(4573), X(53631)}}, {{A, B, C, X(4583), X(54458)}}, {{A, B, C, X(4589), X(4625)}}, {{A, B, C, X(4598), X(18830)}}, {{A, B, C, X(8706), X(36086)}}, {{A, B, C, X(9067), X(27834)}}, {{A, B, C, X(15455), X(35147)}}, {{A, B, C, X(18829), X(40834)}}, {{A, B, C, X(25537), X(50491)}}, {{A, B, C, X(35008), X(37218)}}
X(56053) = barycentric product X(i)*X(j) for these (i, j): {110, 6383}, {274, 932}, {310, 34071}, {330, 99}, {643, 7209}, {799, 87}, {1414, 27424}, {2162, 670}, {2319, 4625}, {4573, 7155}, {4598, 86}, {4602, 7121}, {5383, 7192}, {6384, 662}, {7153, 7257}, {16606, 4623}, {16710, 35572}, {18830, 81}, {23086, 6331}, {23493, 52612}, {32039, 33296}, {34252, 4639}, {36860, 53678}, {39914, 4589}, {42027, 4610}, {43931, 4601}
X(56053) = barycentric quotient X(i)/X(j) for these (i, j): {1, 21834}, {2, 21051}, {6, 50491}, {58, 20979}, {81, 4083}, {86, 3835}, {87, 661}, {99, 192}, {100, 20691}, {110, 2176}, {163, 2209}, {190, 3971}, {261, 27527}, {274, 20906}, {330, 523}, {333, 4147}, {593, 16695}, {643, 3208}, {645, 27538}, {662, 43}, {667, 21835}, {670, 6382}, {757, 18197}, {799, 6376}, {932, 37}, {1014, 43051}, {1019, 3123}, {1333, 8640}, {1414, 1423}, {1444, 25098}, {1509, 17217}, {1790, 22090}, {2053, 3709}, {2162, 512}, {2319, 4041}, {3733, 6377}, {3912, 21959}, {4556, 38832}, {4558, 20760}, {4565, 1403}, {4567, 52923}, {4573, 3212}, {4584, 41531}, {4589, 40848}, {4592, 22370}, {4598, 10}, {4600, 4595}, {4601, 36863}, {4609, 40367}, {4610, 33296}, {4623, 31008}, {4625, 30545}, {5383, 3952}, {6383, 850}, {6384, 1577}, {7121, 798}, {7153, 4017}, {7155, 3700}, {7192, 21138}, {7209, 4077}, {7257, 4110}, {8025, 4992}, {15373, 810}, {16606, 4705}, {16695, 40610}, {16710, 21128}, {18830, 321}, {21759, 50487}, {23086, 647}, {23493, 4079}, {23829, 23773}, {24037, 36860}, {27424, 4086}, {27455, 50330}, {27496, 4404}, {27644, 25142}, {27958, 30584}, {32039, 42027}, {33296, 23886}, {34071, 42}, {34252, 21832}, {36860, 8026}, {39914, 4010}, {40720, 4806}, {42027, 4024}, {43931, 3125}, {45218, 42661}, {51321, 4455}, {51837, 4122}, {52394, 18107}, {52680, 14408}, {52897, 14426}, {52935, 27644}

X(56054) = KP3(X(2)) OF X(2) AND X(8)

Barycentrics    (a^2+3*b^2-4*b*c+c^2-2*a*(2*b+c))*(a^2+b^2-4*b*c+3*c^2-2*a*(b+2*c)) : :

X(56054) lies on these lines: {2, 10481}, {7, 32008}, {8, 142}, {29, 53238}, {85, 34019}, {92, 53237}, {277, 10578}, {312, 20880}, {333, 17169}, {962, 20328}, {1121, 31994}, {1220, 34821}, {3616, 14942}, {4384, 30711}, {4518, 53239}, {4997, 53240}, {6557, 25525}, {6706, 9780}, {9776, 40435}, {9778, 14377}, {9779, 34847}, {10405, 52715}, {18230, 32100}, {21258, 53620}, {28660, 53236}, {38093, 41006}, {52156, 52422}

X(56054) = isotomic conjugate of X(18230)
X(56054) = trilinear pole of line {21104, 48125}
X(56054) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 10389}, {31, 18230}
X(56054) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 18230}, {9, 10389}
X(56054) = X(i)-cross conjugate of X(j) for these {i, j}: {3475, 7}, {20195, 2}
X(56054) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3243)}}, {{A, B, C, X(2), X(8)}}, {{A, B, C, X(4), X(38200)}}, {{A, B, C, X(7), X(142)}}, {{A, B, C, X(21), X(21446)}}, {{A, B, C, X(27), X(37436)}}, {{A, B, C, X(57), X(11518)}}, {{A, B, C, X(75), X(32086)}}, {{A, B, C, X(86), X(4869)}}, {{A, B, C, X(274), X(39749)}}, {{A, B, C, X(279), X(5558)}}, {{A, B, C, X(514), X(7320)}}, {{A, B, C, X(673), X(5556)}}, {{A, B, C, X(1219), X(36807)}}, {{A, B, C, X(2320), X(7131)}}, {{A, B, C, X(2346), X(41790)}}, {{A, B, C, X(2481), X(5936)}}, {{A, B, C, X(3296), X(34578)}}, {{A, B, C, X(3616), X(3912)}}, {{A, B, C, X(3748), X(41711)}}, {{A, B, C, X(4384), X(9780)}}, {{A, B, C, X(5226), X(5437)}}, {{A, B, C, X(5249), X(9776)}}, {{A, B, C, X(5273), X(41867)}}, {{A, B, C, X(5435), X(25525)}}, {{A, B, C, X(5550), X(29616)}}, {{A, B, C, X(5665), X(8056)}}, {{A, B, C, X(5749), X(17282)}}, {{A, B, C, X(6172), X(38093)}}, {{A, B, C, X(8797), X(46137)}}, {{A, B, C, X(10266), X(34401)}}, {{A, B, C, X(10578), X(17093)}}, {{A, B, C, X(16284), X(52715)}}, {{A, B, C, X(16823), X(29611)}}, {{A, B, C, X(17077), X(25521)}}, {{A, B, C, X(17257), X(27147)}}, {{A, B, C, X(17296), X(28626)}}, {{A, B, C, X(18025), X(30598)}}, {{A, B, C, X(18221), X(44794)}}, {{A, B, C, X(18230), X(20195)}}, {{A, B, C, X(18810), X(38254)}}, {{A, B, C, X(18821), X(36956)}}, {{A, B, C, X(20568), X(32022)}}, {{A, B, C, X(20569), X(30701)}}, {{A, B, C, X(25935), X(27383)}}, {{A, B, C, X(27827), X(56003)}}, {{A, B, C, X(30625), X(31618)}}, {{A, B, C, X(30712), X(35160)}}, {{A, B, C, X(30806), X(31994)}}, {{A, B, C, X(30807), X(52422)}}, {{A, B, C, X(32014), X(37202)}}, {{A, B, C, X(32021), X(36620)}}, {{A, B, C, X(35158), X(43527)}}, {{A, B, C, X(35167), X(39738)}}, {{A, B, C, X(39963), X(55924)}}, {{A, B, C, X(40014), X(43533)}}, {{A, B, C, X(40509), X(43531)}}
X(56054) = barycentric product X(i)*X(j) for these (i, j): {10390, 75}, {34821, 3596}
X(56054) = barycentric quotient X(i)/X(j) for these (i, j): {1, 10389}, {2, 18230}, {10390, 1}, {34821, 56}

X(56055) = KP3(X(2)) OF X(2) AND X(13)

Barycentrics    -11*a^4+31*a^2*(b^2+c^2)-8*(b^4-5*b^2*c^2+c^4)+10*sqrt(3)*(a^2+2*(b^2+c^2))*S : :

X(56055) lies on the Kiepert hyperbola and on these lines: {4, 618}, {13, 40334}, {14, 620}, {98, 12213}, {141, 43544}, {530, 33602}, {616, 38412}, {623, 54562}, {629, 54937}, {3424, 9749}, {3642, 54848}, {5459, 33604}, {5463, 12816}, {6669, 43542}, {10188, 44382}, {14971, 42036}, {21156, 54850}, {22489, 33607}, {22687, 54673}, {36767, 54480}, {38743, 54570}, {41042, 54939}

X(56055) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(618), X(40709)}}

X(56056) = KP3(X(2)) OF X(2) AND X(14)

Barycentrics    -11*a^4+31*a^2*(b^2+c^2)-8*(b^4-5*b^2*c^2+c^4)-10*sqrt(3)*(a^2+2*(b^2+c^2))*S : :

X(56056) lies on the Kiepert hyperbola and on these lines: {4, 619}, {13, 620}, {14, 40335}, {98, 12214}, {141, 43545}, {531, 33603}, {617, 43541}, {624, 54561}, {630, 54938}, {3424, 9750}, {3643, 54847}, {5460, 33605}, {5464, 12817}, {6670, 43543}, {10187, 44383}, {14971, 42035}, {21157, 54849}, {22490, 33606}, {22689, 54672}, {38743, 54569}, {41043, 54940}

X(56056) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(619), X(40710)}}

X(56057) = KP3(X(2)) OF X(2) AND X(67)

Barycentrics    (a^4+3*b^4-2*b^2*c^2+c^4-a^2*(2*b^2+c^2))*(a^4+b^4-2*b^2*c^2+3*c^4-a^2*(b^2+2*c^2)) : :

X(56057) lies on these lines: {67, 625}, {126, 136}, {599, 626}, {7761, 30542}, {9132, 25328}, {9133, 41133}, {9464, 44166}, {10130, 16890}, {32961, 45809}, {36792, 43620}

X(56057) = X(i)-isoconjugate-of-X(j) for these {i, j}: {163, 9131}, {923, 10552}
X(56057) = X(i)-Dao conjugate of X(j) for these {i, j}: {115, 9131}, {2482, 10552}
X(56057) = X(i)-cross conjugate of X(j) for these {i, j}: {31275, 2}
X(56057) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(67)}}, {{A, B, C, X(4), X(11318)}}, {{A, B, C, X(83), X(626)}}, {{A, B, C, X(98), X(40511)}}, {{A, B, C, X(126), X(30786)}}, {{A, B, C, X(136), X(338)}}, {{A, B, C, X(141), X(37688)}}, {{A, B, C, X(264), X(9516)}}, {{A, B, C, X(290), X(8797)}}, {{A, B, C, X(316), X(625)}}, {{A, B, C, X(325), X(44380)}}, {{A, B, C, X(328), X(51454)}}, {{A, B, C, X(523), X(8781)}}, {{A, B, C, X(524), X(41133)}}, {{A, B, C, X(671), X(5461)}}, {{A, B, C, X(1494), X(36953)}}, {{A, B, C, X(1502), X(2963)}}, {{A, B, C, X(1916), X(1989)}}, {{A, B, C, X(2165), X(2996)}}, {{A, B, C, X(2980), X(53105)}}, {{A, B, C, X(3228), X(35005)}}, {{A, B, C, X(5475), X(7934)}}, {{A, B, C, X(5503), X(6094)}}, {{A, B, C, X(7603), X(7831)}}, {{A, B, C, X(7608), X(42286)}}, {{A, B, C, X(9227), X(34898)}}, {{A, B, C, X(9462), X(40824)}}, {{A, B, C, X(13481), X(42407)}}, {{A, B, C, X(39446), X(40513)}}, {{A, B, C, X(40347), X(44182)}}, {{A, B, C, X(40826), X(43529)}}, {{A, B, C, X(40832), X(51480)}}, {{A, B, C, X(44369), X(44377)}}, {{A, B, C, X(46154), X(46316)}}, {{A, B, C, X(52154), X(54122)}}
X(56057) = barycentric product X(i)*X(j) for these (i, j): {523, 9133}, {850, 9132}
X(56057) = barycentric quotient X(i)/X(j) for these (i, j): {523, 9131}, {524, 10552}, {9132, 110}, {9133, 99}

X(56058) = KP3(X(2)) OF X(2) AND X(81)

Barycentrics    (2*b*c*(b+c)+a^2*(2*b+c)+a*(2*b^2+c^2))*(2*b*c*(b+c)+a^2*(b+2*c)+a*(b^2+2*c^2)) : :

X(56058) lies on these lines: {1, 31264}, {81, 44417}, {88, 31993}, {89, 14829}, {291, 31241}, {957, 3820}, {959, 40663}, {1022, 50457}, {1255, 30818}, {3739, 39962}, {4358, 37870}, {5235, 53083}, {17946, 27076}

X(56058) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 50604}
X(56058) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 50604}
X(56058) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(239), X(31241)}}, {{A, B, C, X(321), X(44417)}}, {{A, B, C, X(335), X(31264)}}, {{A, B, C, X(4358), X(31993)}}, {{A, B, C, X(4359), X(30818)}}, {{A, B, C, X(5235), X(14829)}}, {{A, B, C, X(5936), X(8797)}}, {{A, B, C, X(14624), X(23617)}}, {{A, B, C, X(17289), X(33133)}}, {{A, B, C, X(18825), X(34816)}}, {{A, B, C, X(19623), X(31247)}}, {{A, B, C, X(19822), X(28808)}}, {{A, B, C, X(27163), X(37680)}}, {{A, B, C, X(35155), X(36957)}}, {{A, B, C, X(43757), X(56046)}}
X(56058) = barycentric product X(i)*X(j) for these (i, j): {56032, 75}
X(56058) = barycentric quotient X(i)/X(j) for these (i, j): {1, 50604}, {56032, 1}

X(56059) = KP3(X(2)) OF X(2) AND X(83)

Barycentrics    (3*a^2+4*b^2+3*c^2)*(3*a^2+3*b^2+4*c^2) : :

X(56059) lies on the Kiepert hyperbola and on these lines: {2, 5368}, {4, 48879}, {5, 54890}, {83, 34573}, {98, 632}, {140, 54857}, {262, 5070}, {547, 14492}, {549, 54852}, {598, 7784}, {620, 11606}, {1916, 14047}, {3096, 5395}, {3407, 14067}, {3530, 8725}, {3763, 43527}, {3860, 54813}, {5054, 14458}, {5079, 14488}, {6656, 53106}, {6683, 42006}, {7770, 53107}, {7812, 54639}, {7834, 54748}, {7841, 54493}, {7859, 10302}, {7883, 18842}, {7911, 45103}, {7915, 43535}, {7940, 11167}, {8362, 52886}, {8370, 54646}, {8703, 54477}, {10159, 51128}, {11289, 43550}, {11290, 43551}, {11303, 54591}, {11304, 54592}, {11540, 54608}, {14484, 46936}, {15692, 54519}, {15696, 54917}, {16045, 18844}, {18843, 32006}, {19709, 54582}, {38071, 54717}, {41984, 54644}, {43459, 54539}

X(56059) = isotomic conjugate of X(51126)
X(56059) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 51126}, {17457, 39676}
X(56059) = X(i)-cross conjugate of X(j) for these {i, j}: {7950, 99}
X(56059) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(141), X(34573)}}, {{A, B, C, X(297), X(632)}}, {{A, B, C, X(419), X(14047)}}, {{A, B, C, X(458), X(5070)}}, {{A, B, C, X(547), X(52289)}}, {{A, B, C, X(729), X(17042)}}, {{A, B, C, X(1698), X(29607)}}, {{A, B, C, X(2963), X(5368)}}, {{A, B, C, X(3114), X(24861)}}, {{A, B, C, X(3225), X(34816)}}, {{A, B, C, X(3589), X(51128)}}, {{A, B, C, X(3978), X(31239)}}, {{A, B, C, X(5054), X(11331)}}, {{A, B, C, X(5117), X(14067)}}, {{A, B, C, X(6292), X(33665)}}, {{A, B, C, X(6656), X(52297)}}, {{A, B, C, X(7770), X(52298)}}, {{A, B, C, X(7859), X(26235)}}, {{A, B, C, X(7890), X(40405)}}, {{A, B, C, X(14387), X(40410)}}, {{A, B, C, X(17265), X(17327)}}, {{A, B, C, X(17283), X(17307)}}, {{A, B, C, X(31268), X(40850)}}, {{A, B, C, X(42346), X(52660)}}, {{A, B, C, X(46936), X(52288)}}
X(56059) = barycentric quotient X(i)/X(j) for these (i, j): {2, 51126}

X(56060) = KP3(X(2)) OF X(2) AND X(85)

Barycentrics    (2*a^2-4*a*b+2*b^2-3*a*c-3*b*c+c^2)*(2*a^2-3*a*b+b^2-4*a*c-3*b*c+2*c^2) : :

X(56060) lies on these lines: {2, 32007}, {8, 17240}, {9, 32015}, {85, 6666}, {1698, 14942}, {3912, 42030}, {4102, 4384}, {17044, 31269}, {18230, 32100}, {30690, 30854}

X(56060) = isotomic conjugate of X(20195)
X(56060) = trilinear pole of line {47664, 47974}
X(56060) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 20195}, {2293, 39669}
X(56060) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(42819)}}, {{A, B, C, X(2), X(8)}}, {{A, B, C, X(9), X(6666)}}, {{A, B, C, X(75), X(17263)}}, {{A, B, C, X(79), X(27475)}}, {{A, B, C, X(673), X(3296)}}, {{A, B, C, X(1125), X(4384)}}, {{A, B, C, X(1223), X(34919)}}, {{A, B, C, X(1434), X(42318)}}, {{A, B, C, X(1698), X(3912)}}, {{A, B, C, X(2481), X(30598)}}, {{A, B, C, X(3873), X(5284)}}, {{A, B, C, X(5560), X(17758)}}, {{A, B, C, X(5745), X(51780)}}, {{A, B, C, X(5936), X(35160)}}, {{A, B, C, X(7162), X(37131)}}, {{A, B, C, X(8797), X(18025)}}, {{A, B, C, X(9311), X(13606)}}, {{A, B, C, X(16823), X(17367)}}, {{A, B, C, X(17095), X(30854)}}, {{A, B, C, X(17240), X(20565)}}, {{A, B, C, X(17260), X(17338)}}, {{A, B, C, X(17294), X(51073)}}, {{A, B, C, X(18841), X(42335)}}, {{A, B, C, X(29627), X(46933)}}, {{A, B, C, X(29827), X(30030)}}, {{A, B, C, X(29966), X(30970)}}, {{A, B, C, X(31269), X(40864)}}, {{A, B, C, X(31618), X(32088)}}, {{A, B, C, X(32022), X(36807)}}, {{A, B, C, X(34595), X(50095)}}, {{A, B, C, X(35158), X(56059)}}, {{A, B, C, X(35167), X(36954)}}
X(56060) = barycentric product X(i)*X(j) for these (i, j): {56028, 75}
X(56060) = barycentric quotient X(i)/X(j) for these (i, j): {2, 20195}, {1170, 39669}, {56028, 1}

X(56061) = KP3(X(2)) OF X(2) AND X(86)

Barycentrics    (3*a+4*b+3*c)*(3*a+3*b+4*c) : :

X(56061) lies on these lines: {2, 4399}, {86, 3634}, {335, 31238}, {675, 28214}, {903, 28653}, {1268, 51073}, {1698, 30598}, {4360, 19872}, {4389, 39709}, {4422, 6650}, {4698, 27483}, {5224, 30712}, {5257, 52885}, {5936, 17160}, {17272, 39704}, {19877, 28626}

X(56061) = isotomic conjugate of X(19862)
X(56061) = trilinear pole of line {48429, 514}
X(56061) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 19862}, {41, 4114}, {692, 28213}, {1962, 39670}
X(56061) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 19862}, {1086, 28213}, {3160, 4114}
X(56061) = X(i)-cross conjugate of X(j) for these {i, j}: {4802, 190}, {31253, 2}
X(56061) = intersection, other than A, B, C, of these circumconics: {{A, B, C, X(2), X(7)}}, {{A, B, C, X(10), X(3634)}}, {{A, B, C, X(37), X(55932)}}, {{A, B, C, X(334), X(48636)}}, {{A, B, C, X(350), X(31238)}}, {{A, B, C, X(757), X(39962)}}, {{A, B, C, X(1125), X(51073)}}, {{A, B, C, X(1220), X(43731)}}, {{A, B, C, X(1222), X(1224)}}, {{A, B, C, X(1698), X(43531)}}, {{A, B, C, X(2481), X(56059)}}, {{A, B, C, X(3226), X(34816)}}, {{A, B, C, X(3624), X(19872)}}, {{A, B, C, X(4358), X(28653)}}, {{A, B, C, X(6381), X(48551)}}, {{A, B, C, X(7317), X(31359)}}, {{A, B, C, X(8797), X(18025)}}, {{A, B, C, X(9780), X(19877)}}, {{A, B, C, X(17038), X(37129)}}, {{A, B, C, X(17160), X(32016)}}, {{A, B, C, X(17322), X(24589)}}, {{A, B, C, X(17731), X(31248)}}, {{A, B, C, X(19862), X(31253)}}, {{A, B, C, X(19875), X(19876)}}, {{A, B, C, X(32008), X(35141)}}, {{A, B, C, X(32014), X(32089)}}, {{A, B, C, X(35153), X(36954)}}, {{A, B, C, X(35166), X(36957)}}, {{A, B, C, X(39983), X(40433)}}, {{A, B, C, X(40410), X(40417)}}, {{A, B, C, X(40434), X(40438)}}, {{A, B, C, X(46930), X(46933)}}, {{A, B, C, X(46931), X(46932)}}
X(56061) = barycentric product X(i)*X(j) for these (i, j): {28214, 3261}, {56037, 75}
X(56061) = barycentric quotient X(i)/X(j) for these (i, j): {2, 19862}, {7, 4114}, {514, 28213}, {1171, 39670}, {28214, 101}, {56037, 1}
X(56061) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {19872, 28650, 4360}

X(56062) = KP3(X(2)) OF X(2) AND X(92)

Barycentrics    (2*a^3+2*b^3-b^2*c-2*b*c^2+c^3-a^2*(2*b+c)-2*a*(b^2+c^2))*(2*a^3+b^3-2*b^2*c-b*c^2+2*c^3-a^2*(b+2*c)-2*a*(b^2+c^2)) : :

X(56062) lies on these lines: {8, 5791}, {29, 5705}, {92, 5745}, {312, 54357}, {1952, 17044}, {3305, 4997}, {4417, 30608}, {5235, 19607}, {5273, 50442}, {24541, 31359}

X(56062) = isotomic conjugate of X(31266)
X(56062) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(8)}}, {{A, B, C, X(27), X(6857)}}, {{A, B, C, X(57), X(759)}}, {{A, B, C, X(63), X(5745)}}, {{A, B, C, X(75), X(33113)}}, {{A, B, C, X(273), X(40412)}}, {{A, B, C, X(306), X(5705)}}, {{A, B, C, X(1214), X(51281)}}, {{A, B, C, X(2006), X(37739)}}, {{A, B, C, X(3305), X(3911)}}, {{A, B, C, X(4417), X(5235)}}, {{A, B, C, X(5271), X(13411)}}, {{A, B, C, X(5273), X(5744)}}, {{A, B, C, X(5316), X(31224)}}, {{A, B, C, X(5791), X(13478)}}, {{A, B, C, X(5936), X(34393)}}, {{A, B, C, X(11679), X(24541)}}, {{A, B, C, X(14616), X(30598)}}, {{A, B, C, X(17338), X(27002)}}, {{A, B, C, X(19804), X(32849)}}, {{A, B, C, X(24624), X(44733)}}, {{A, B, C, X(34016), X(52412)}}, {{A, B, C, X(39962), X(43760)}}
X(56062) = barycentric product X(i)*X(j) for these (i, j): {56027, 75}
X(56062) = barycentric quotient X(i)/X(j) for these (i, j): {2, 31266}, {56027, 1}

X(56063) = KP3(X(2)) OF X(2) AND X(94)

Barycentrics    (2*a^6+2*b^6-3*b^4*c^2+c^6-a^4*(2*b^2+3*c^2)+a^2*(-2*b^4+5*b^2*c^2))*(2*a^6+b^6-3*b^2*c^4+2*c^6-a^4*(3*b^2+2*c^2)+a^2*(5*b^2*c^2-2*c^4)) : :

X(56063) lies on the Kiepert hyperbola and on these lines: {4, 1511}, {94, 11064}, {98, 30745}, {323, 16080}, {671, 46571}, {858, 54810}, {2052, 14920}, {2072, 18316}, {2394, 8552}, {3548, 54498}, {7506, 54912}, {12086, 54658}, {13371, 54486}, {13595, 14492}, {14458, 31074}, {33314, 55009}, {38253, 45794}, {38321, 54809}, {41254, 43676}, {44441, 54942}, {44555, 46201}, {52695, 54918}, {53105, 54395}

X(56063) = trilinear pole of line {550, 30511}
X(56063) = X(i)-isoconjugate-of-X(j) for these {i, j}: {661, 30510}, {1539, 2159}, {2173, 52130}
X(56063) = X(i)-Dao conjugate of X(j) for these {i, j}: {3163, 1539}, {36830, 30510}, {36896, 52130}
X(56063) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(297), X(30745)}}, {{A, B, C, X(323), X(1511)}}, {{A, B, C, X(328), X(340)}}, {{A, B, C, X(468), X(46571)}}, {{A, B, C, X(1990), X(34570)}}, {{A, B, C, X(11331), X(31074)}}, {{A, B, C, X(13485), X(30786)}}, {{A, B, C, X(13595), X(52289)}}, {{A, B, C, X(18019), X(18020)}}, {{A, B, C, X(18384), X(40347)}}, {{A, B, C, X(19778), X(40709)}}, {{A, B, C, X(19779), X(40710)}}, {{A, B, C, X(36789), X(46809)}}
X(56063) = barycentric quotient X(i)/X(j) for these (i, j): {30, 1539}, {74, 52130}, {110, 30510}, {22451, 381}

X(56064) = KP3(X(2)) OF X(2) AND X(98)

Barycentrics    (3*a^4+3*b^4-3*b^2*c^2+4*c^4-a^2*(4*b^2+3*c^2))*(3*a^4+4*b^4-3*b^2*c^2+3*c^4-a^2*(3*b^2+4*c^2)) : :

X(56064) lies on the Kiepert hyperbola and on these lines: {4, 620}, {83, 37647}, {98, 13196}, {99, 53105}, {114, 3424}, {141, 53104}, {147, 47586}, {542, 54866}, {598, 11288}, {2482, 54720}, {5395, 33203}, {5485, 14971}, {5503, 44534}, {6036, 43537}, {6721, 14484}, {7607, 7778}, {7612, 37690}, {10153, 22110}, {10754, 35005}, {11668, 15271}, {14061, 32820}, {14458, 23234}, {15300, 32532}, {17005, 43528}, {18843, 31274}, {18845, 33205}, {20094, 38259}, {33698, 41134}, {41133, 54103}, {41895, 52695}, {52886, 53106}

X(56064) = trilinear pole of line {40341, 523}
X(56064) = X(i)-vertex conjugate of X(j) for these {i, j}: {5503, 39644}
X(56064) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(95), X(44558)}}, {{A, B, C, X(141), X(37647)}}, {{A, B, C, X(297), X(40336)}}, {{A, B, C, X(325), X(44377)}}, {{A, B, C, X(620), X(30786)}}, {{A, B, C, X(1007), X(37690)}}, {{A, B, C, X(1494), X(36953)}}, {{A, B, C, X(1799), X(7862)}}, {{A, B, C, X(2987), X(5966)}}, {{A, B, C, X(5094), X(11288)}}, {{A, B, C, X(7868), X(31489)}}, {{A, B, C, X(7931), X(17005)}}, {{A, B, C, X(8889), X(33203)}}, {{A, B, C, X(9516), X(55958)}}, {{A, B, C, X(14971), X(52141)}}, {{A, B, C, X(17983), X(40511)}}, {{A, B, C, X(18023), X(42349)}}, {{A, B, C, X(22110), X(41133)}}, {{A, B, C, X(33205), X(52299)}}, {{A, B, C, X(34816), X(43664)}}, {{A, B, C, X(39644), X(39951)}}, {{A, B, C, X(40429), X(41909)}}

X(56065) = KP3(X(1)) OF X(6) AND X(75)

Barycentrics    (a^3+a^2*b+b^3+a*b*(b+c))*(a^3+a^2*c+c^3+a*c*(b+c)) : :

X(56065) lies on these lines: {2, 172}, {7, 17087}, {56, 7249}, {75, 171}, {86, 17203}, {310, 14012}, {335, 940}, {675, 29018}, {1429, 44733}, {2162, 27447}, {6384, 37100}, {6650, 19785}, {14621, 19786}, {21010, 37090}, {29636, 52394}, {29649, 40033}

X(56065) = isotomic conjugate of X(32778)
X(56065) = trilinear pole of line {20981, 514}
X(56065) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 32778}, {42, 35623}, {692, 29017}
X(56065) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 32778}, {1086, 29017}, {40592, 35623}
X(56065) = X(i)-cross conjugate of X(j) for these {i, j}: {29645, 2}
X(56065) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4362)}}, {{A, B, C, X(2), X(7)}}, {{A, B, C, X(25), X(82)}}, {{A, B, C, X(56), X(171)}}, {{A, B, C, X(83), X(7033)}}, {{A, B, C, X(89), X(6628)}}, {{A, B, C, X(238), X(39967)}}, {{A, B, C, X(278), X(51865)}}, {{A, B, C, X(757), X(967)}}, {{A, B, C, X(849), X(37522)}}, {{A, B, C, X(870), X(14534)}}, {{A, B, C, X(940), X(1429)}}, {{A, B, C, X(969), X(1435)}}, {{A, B, C, X(987), X(8852)}}, {{A, B, C, X(1010), X(31997)}}, {{A, B, C, X(1403), X(37607)}}, {{A, B, C, X(1509), X(40419)}}, {{A, B, C, X(1751), X(39717)}}, {{A, B, C, X(1929), X(3980)}}, {{A, B, C, X(1961), X(16825)}}, {{A, B, C, X(2298), X(3113)}}, {{A, B, C, X(3226), X(56046)}}, {{A, B, C, X(4600), X(25417)}}, {{A, B, C, X(5311), X(32914)}}, {{A, B, C, X(7247), X(33930)}}, {{A, B, C, X(13478), X(32010)}}, {{A, B, C, X(15523), X(29636)}}, {{A, B, C, X(17017), X(17763)}}, {{A, B, C, X(17087), X(40037)}}, {{A, B, C, X(17743), X(55997)}}, {{A, B, C, X(19785), X(20947)}}, {{A, B, C, X(19786), X(33931)}}, {{A, B, C, X(26128), X(43534)}}, {{A, B, C, X(29645), X(32778)}}, {{A, B, C, X(29649), X(29821)}}, {{A, B, C, X(29654), X(29674)}}, {{A, B, C, X(29658), X(29671)}}, {{A, B, C, X(29683), X(29849)}}, {{A, B, C, X(29687), X(29852)}}
X(56065) = barycentric product X(i)*X(j) for these (i, j): {29018, 3261}
X(56065) = barycentric quotient X(i)/X(j) for these (i, j): {2, 32778}, {81, 35623}, {514, 29017}, {29018, 101}

X(56066) = KP3(X(1)) OF X(6) AND X(81)

Barycentrics    a*(a+b)*(a+c)*(a*(b+c)+b*(2*b+c))*(a*(b+c)+c*(b+2*c)) : :

X(56066) lies on these lines: {1, 3728}, {2, 21024}, {6, 19232}, {21, 985}, {28, 38814}, {37, 1258}, {57, 40773}, {81, 1107}, {86, 330}, {105, 43359}, {239, 37870}, {274, 20891}, {278, 17084}, {959, 1284}, {1193, 30571}, {1929, 37442}, {2282, 28606}, {5333, 28621}, {16777, 39738}, {16826, 30710}, {16827, 32009}, {17175, 36871}, {18169, 53678}, {18206, 39980}, {25508, 34063}, {27643, 27789}, {29570, 39694}, {30562, 35058}, {31313, 38247}

X(56066) = trilinear pole of line {18197, 29807}
X(56066) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 43223}, {42, 17379}, {213, 31997}, {4557, 4932}, {28622, 43531}
X(56066) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 43223}, {6626, 31997}, {40592, 17379}
X(56066) = X(i)-cross conjugate of X(j) for these {i, j}: {17038, 56052}, {26102, 86}
X(56066) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(21), X(3786)}}, {{A, B, C, X(37), X(257)}}, {{A, B, C, X(58), X(32014)}}, {{A, B, C, X(65), X(27483)}}, {{A, B, C, X(79), X(13584)}}, {{A, B, C, X(86), X(27644)}}, {{A, B, C, X(239), X(48144)}}, {{A, B, C, X(256), X(6625)}}, {{A, B, C, X(286), X(41527)}}, {{A, B, C, X(423), X(37442)}}, {{A, B, C, X(893), X(23493)}}, {{A, B, C, X(932), X(7260)}}, {{A, B, C, X(978), X(29570)}}, {{A, B, C, X(1016), X(56032)}}, {{A, B, C, X(1193), X(16826)}}, {{A, B, C, X(1220), X(39971)}}, {{A, B, C, X(1400), X(25426)}}, {{A, B, C, X(1444), X(17084)}}, {{A, B, C, X(3720), X(16827)}}, {{A, B, C, X(3920), X(29960)}}, {{A, B, C, X(5331), X(37128)}}, {{A, B, C, X(9311), X(39737)}}, {{A, B, C, X(16703), X(17442)}}, {{A, B, C, X(17022), X(20036)}}, {{A, B, C, X(18169), X(31008)}}, {{A, B, C, X(18827), X(56048)}}, {{A, B, C, X(20332), X(43531)}}, {{A, B, C, X(21352), X(41240)}}, {{A, B, C, X(27627), X(29580)}}, {{A, B, C, X(27643), X(42025)}}, {{A, B, C, X(30598), X(31997)}}, {{A, B, C, X(43073), X(54120)}}
X(56066) = barycentric product X(i)*X(j) for these (i, j): {1, 56052}, {274, 39967}, {17038, 86}, {28606, 28621}, {43359, 693}
X(56066) = barycentric quotient X(i)/X(j) for these (i, j): {1, 43223}, {81, 17379}, {86, 31997}, {1019, 4932}, {17038, 10}, {38814, 17689}, {39967, 37}, {43359, 100}, {56052, 75}

X(56067) = KP3(X(2)) OF X(4) AND X(76)

Barycentrics    b^2*c^2*(3*a^2+3*b^2-c^2)*(3*a^2-b^2+3*c^2) : :

X(56067) lies on these lines: {76, 193}, {264, 6353}, {308, 8667}, {311, 40819}, {313, 4028}, {327, 14615}, {1502, 3815}, {1975, 45857}, {8940, 34392}, {8944, 34391}, {15480, 40074}, {18027, 21447}, {32832, 43981}, {44144, 52581}

X(56067) = isotomic conjugate of X(5013)
X(56067) = trilinear pole of line {850, 3566}
X(56067) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 5013}, {48, 12167}, {560, 3620}, {8889, 9247}
X(56067) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 5013}, {1249, 12167}, {6374, 3620}
X(56067) = X(i)-cross conjugate of X(j) for these {i, j}: {40022, 76}, {47122, 99}
X(56067) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(193)}}, {{A, B, C, X(4), X(32971)}}, {{A, B, C, X(6), X(3815)}}, {{A, B, C, X(69), X(34229)}}, {{A, B, C, X(76), X(264)}}, {{A, B, C, X(83), X(393)}}, {{A, B, C, X(141), X(8667)}}, {{A, B, C, X(262), X(2998)}}, {{A, B, C, X(523), X(31360)}}, {{A, B, C, X(598), X(32085)}}, {{A, B, C, X(671), X(8801)}}, {{A, B, C, X(1031), X(14458)}}, {{A, B, C, X(1221), X(32023)}}, {{A, B, C, X(1239), X(40831)}}, {{A, B, C, X(2052), X(42354)}}, {{A, B, C, X(2963), X(9516)}}, {{A, B, C, X(3613), X(9462)}}, {{A, B, C, X(3763), X(15480)}}, {{A, B, C, X(6339), X(14494)}}, {{A, B, C, X(6664), X(18575)}}, {{A, B, C, X(7789), X(13881)}}, {{A, B, C, X(8781), X(8797)}}, {{A, B, C, X(9230), X(43976)}}, {{A, B, C, X(14615), X(44144)}}, {{A, B, C, X(16081), X(37874)}}, {{A, B, C, X(17039), X(36212)}}, {{A, B, C, X(17983), X(43527)}}, {{A, B, C, X(18841), X(36611)}}, {{A, B, C, X(24861), X(42286)}}, {{A, B, C, X(25322), X(45090)}}, {{A, B, C, X(40073), X(52570)}}, {{A, B, C, X(40410), X(42407)}}, {{A, B, C, X(52395), X(53102)}}
X(56067) = barycentric product X(i)*X(j) for these (i, j): {5395, 76}, {31506, 40016}
X(56067) = barycentric quotient X(i)/X(j) for these (i, j): {2, 5013}, {4, 12167}, {76, 3620}, {264, 8889}, {5395, 6}, {31506, 3051}

X(56068) = KP3(X(3)) OF X(3) AND X(4)

Barycentrics    a^2*(a^2-b^2-c^2)*(2*a^6+2*b^6-3*b^4*c^2+c^6-a^4*(2*b^2+3*c^2)-2*a^2*(b^4-5*b^2*c^2))*(2*a^6+b^6-3*b^2*c^4+2*c^6-a^4*(3*b^2+2*c^2)+2*a^2*(5*b^2*c^2-c^4)) : :

X(56068) lies on the Jerabek hyperbola and on these lines: {74, 43652}, {265, 3546}, {376, 43695}, {631, 14457}, {1942, 22085}, {3426, 11413}, {3522, 10293}, {3527, 17928}, {3531, 6642}, {3917, 11270}, {5486, 10299}, {7464, 22334}, {10519, 13622}, {11585, 21400}, {15740, 51394}, {16051, 32533}

X(56068) = intersection, other than A, B, C, of these circumconics: {{A, B, C, X(3), X(4)}}, {{A, B, C, X(186), X(3546)}}, {{A, B, C, X(376), X(11413)}}, {{A, B, C, X(631), X(17928)}}, {{A, B, C, X(1995), X(10299)}}, {{A, B, C, X(3522), X(7464)}}, {{A, B, C, X(3524), X(6642)}}, {{A, B, C, X(3528), X(12085)}}, {{A, B, C, X(5879), X(18851)}}, {{A, B, C, X(5897), X(18849)}}, {{A, B, C, X(11585), X(21844)}}, {{A, B, C, X(13599), X(51967)}}, {{A, B, C, X(16051), X(32534)}}, {{A, B, C, X(18853), X(45301)}}, {{A, B, C, X(19708), X(47527)}}, {{A, B, C, X(43652), X(51394)}}

X(56069) = KP3(X(3)) OF X(3) AND X(54)

Barycentrics    a^2*(a^2-b^2-c^2)*(3*a^6-a^4*(2*b^2+3*c^2)+(b^2-c^2)^2*(4*b^2+3*c^2)-a^2*(5*b^4+3*c^4))*(3*a^6-a^4*(3*b^2+2*c^2)+(b^2-c^2)^2*(3*b^2+4*c^2)-a^2*(3*b^4+5*c^4)) : :

X(56069) lies on the Jerabek hyperbola and on these lines: {4, 35240}, {20, 44836}, {64, 8718}, {376, 38442}, {3426, 9715}, {3521, 6676}, {3527, 54994}, {3528, 16774}, {5889, 43908}, {6030, 43719}, {12161, 44731}, {14542, 43841}

X(56069) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(4)}}, {{A, B, C, X(20), X(44837)}}, {{A, B, C, X(376), X(9715)}}, {{A, B, C, X(3520), X(6676)}}, {{A, B, C, X(3528), X(9909)}}, {{A, B, C, X(6368), X(31504)}}, {{A, B, C, X(7512), X(44239)}}, {{A, B, C, X(22261), X(44684)}}

X(56070) = KP3(X(3)) OF X(3) AND X(63)

Barycentrics    a^2*(2*a+2*b+c)*(2*a+b+2*c)*(a^2-b^2-c^2) : :

X(56070) lies on these lines: {3, 23165}, {27, 19812}, {48, 1796}, {57, 1442}, {58, 5313}, {63, 22054}, {84, 37106}, {103, 8652}, {967, 28625}, {2221, 34819}, {7501, 55105}, {11340, 52423}, {34234, 37211}

X(56070) = X(i)-isoconjugate-of-X(j) for these {i, j}: {4, 16777}, {19, 1698}, {25, 28605}, {33, 4654}, {34, 4007}, {37, 31902}, {108, 4820}, {162, 4838}, {225, 4877}, {278, 3715}, {281, 5221}, {393, 3927}, {648, 48005}, {811, 4826}, {1474, 4066}, {1783, 4802}, {1824, 5333}, {1826, 4658}, {1897, 4813}, {1973, 30596}, {2355, 43260}, {4727, 36125}, {4756, 6591}, {4823, 8750}, {4834, 6335}, {4938, 36128}, {36074, 44426}
X(56070) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 1698}, {125, 4838}, {6337, 30596}, {6505, 28605}, {11517, 4007}, {17423, 4826}, {26932, 4823}, {34467, 4813}, {36033, 16777}, {38983, 4820}, {39006, 4802}, {40589, 31902}, {51574, 4066}, {55066, 48005}
X(56070) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(27)}}, {{A, B, C, X(48), X(22054)}}, {{A, B, C, X(77), X(1442)}}, {{A, B, C, X(78), X(17011)}}, {{A, B, C, X(97), X(41081)}}, {{A, B, C, X(228), X(15373)}}, {{A, B, C, X(306), X(5313)}}, {{A, B, C, X(394), X(25507)}}, {{A, B, C, X(1214), X(7280)}}, {{A, B, C, X(1444), X(40143)}}, {{A, B, C, X(1812), X(14996)}}, {{A, B, C, X(1817), X(37106)}}, {{A, B, C, X(2982), X(3431)}}, {{A, B, C, X(3998), X(19812)}}
X(56070) = barycentric product X(i)*X(j) for these (i, j): {3, 30598}, {222, 42030}, {304, 34819}, {1332, 48074}, {1459, 32042}, {4025, 8652}, {17206, 28625}, {25417, 63}, {30590, 55979}, {30597, 3927}, {37211, 905}
X(56070) = barycentric quotient X(i)/X(j) for these (i, j): {3, 1698}, {48, 16777}, {58, 31902}, {63, 28605}, {69, 30596}, {72, 4066}, {212, 3715}, {219, 4007}, {222, 4654}, {255, 3927}, {603, 5221}, {647, 4838}, {652, 4820}, {810, 48005}, {905, 4823}, {1331, 4756}, {1437, 4658}, {1459, 4802}, {1790, 5333}, {1796, 43260}, {2193, 4877}, {3049, 4826}, {3292, 4938}, {4303, 3824}, {7193, 4716}, {7254, 4960}, {8652, 1897}, {20818, 4898}, {22086, 4958}, {22356, 4727}, {22383, 4813}, {22384, 4810}, {25417, 92}, {28625, 1826}, {30598, 264}, {32660, 36074}, {34819, 19}, {37211, 6335}, {42030, 7017}, {48074, 17924}, {52407, 4880}, {55979, 30589}

X(56071) = KP3(X(3)) OF X(3) AND X(68)

Barycentrics    a^2*(a^2-b^2-c^2)*(2*a^6+b^6-2*a^2*c^4-3*b^2*c^4+2*c^6-a^4*(3*b^2+2*c^2))*(2*a^6-2*a^2*b^4+2*b^6-3*b^4*c^2+c^6-a^4*(2*b^2+3*c^2)) : :

X(56071) lies on the Jerabek hyperbola and on these lines: {2, 16000}, {4, 18475}, {5, 18434}, {6, 1658}, {54, 10298}, {64, 18570}, {68, 13367}, {69, 12038}, {70, 43608}, {184, 43689}, {265, 6639}, {631, 33565}, {2070, 3527}, {3426, 14130}, {3431, 5889}, {3529, 18363}, {3531, 18378}, {5944, 38447}, {6145, 10610}, {6391, 9932}, {10201, 22466}, {10254, 21400}, {10282, 38436}, {11270, 40647}, {11464, 43949}, {11564, 30714}, {12161, 14528}, {12289, 44516}, {18364, 43719}, {18550, 18562}, {19357, 34801}, {20421, 43604}, {37440, 52518}, {37814, 42059}, {42021, 51394}

X(56071) = isogonal conjugate of X(7547)
X(56071) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(1658)}}, {{A, B, C, X(3), X(4)}}, {{A, B, C, X(5), X(10298)}}, {{A, B, C, X(20), X(18570)}}, {{A, B, C, X(184), X(12038)}}, {{A, B, C, X(186), X(6639)}}, {{A, B, C, X(376), X(14130)}}, {{A, B, C, X(631), X(2070)}}, {{A, B, C, X(1092), X(18475)}}, {{A, B, C, X(1147), X(13367)}}, {{A, B, C, X(3523), X(37440)}}, {{A, B, C, X(3524), X(18378)}}, {{A, B, C, X(3529), X(18364)}}, {{A, B, C, X(10201), X(22467)}}, {{A, B, C, X(10254), X(21844)}}, {{A, B, C, X(18562), X(35473)}}, {{A, B, C, X(19357), X(47391)}}, {{A, B, C, X(36952), X(55999)}}
X(56071) = barycentric quotient X(i)/X(j) for these (i, j): {6, 7547}

X(56072) = KP3(X(3)) OF X(3) AND X(69)

Barycentrics    a^2*(a^2-b^2-c^2)*(2*a^2+2*b^2+c^2)*(2*a^2+b^2+2*c^2) : :

X(56072) lies on the Jerabek hyperbola and on these lines: {2, 15321}, {4, 5092}, {6, 6636}, {54, 3098}, {64, 15578}, {66, 3619}, {67, 3620}, {68, 25406}, {69, 22352}, {70, 39874}, {74, 7954}, {182, 1173}, {184, 41435}, {216, 43706}, {248, 10979}, {263, 48261}, {265, 28437}, {511, 13472}, {895, 19126}, {1177, 27866}, {1503, 38433}, {3426, 7514}, {3431, 54041}, {3519, 6776}, {3521, 33750}, {3527, 12017}, {3531, 12083}, {3618, 43726}, {3796, 34817}, {4846, 28708}, {5085, 52518}, {5157, 41464}, {5486, 11008}, {7494, 18124}, {7712, 34573}, {10519, 34483}, {11179, 45972}, {11515, 36297}, {11516, 36296}, {11574, 43697}, {13203, 31267}, {13622, 20080}, {15717, 16623}, {16835, 17508}, {22052, 43718}, {22085, 36214}, {22334, 53094}, {33878, 43908}, {34437, 52697}, {34567, 37517}, {37353, 51126}, {43720, 44573}

X(56072) = isogonal conjugate of X(5064)
X(56072) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 5064}, {19, 3763}, {92, 7772}, {162, 7950}, {811, 8665}, {1783, 47923}, {17442, 39668}
X(56072) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 5064}, {6, 3763}, {125, 7950}, {17423, 8665}, {22391, 7772}, {39006, 47923}
X(56072) = X(i)-Ceva conjugate of X(j) for these {i, j}: {43527, 39955}
X(56072) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6636)}}, {{A, B, C, X(3), X(4)}}, {{A, B, C, X(20), X(37126)}}, {{A, B, C, X(95), X(34168)}}, {{A, B, C, X(97), X(42287)}}, {{A, B, C, X(182), X(22052)}}, {{A, B, C, X(184), X(22352)}}, {{A, B, C, X(187), X(19126)}}, {{A, B, C, X(216), X(3098)}}, {{A, B, C, X(263), X(51477)}}, {{A, B, C, X(315), X(46448)}}, {{A, B, C, X(328), X(14388)}}, {{A, B, C, X(376), X(7514)}}, {{A, B, C, X(511), X(10979)}}, {{A, B, C, X(520), X(29323)}}, {{A, B, C, X(574), X(11574)}}, {{A, B, C, X(577), X(5092)}}, {{A, B, C, X(1265), X(41432)}}, {{A, B, C, X(1297), X(8797)}}, {{A, B, C, X(1383), X(1799)}}, {{A, B, C, X(1485), X(7612)}}, {{A, B, C, X(1791), X(2163)}}, {{A, B, C, X(3425), X(33631)}}, {{A, B, C, X(3524), X(12083)}}, {{A, B, C, X(3619), X(20806)}}, {{A, B, C, X(3620), X(22151)}}, {{A, B, C, X(3926), X(7859)}}, {{A, B, C, X(5481), X(36948)}}, {{A, B, C, X(6337), X(33632)}}, {{A, B, C, X(6340), X(39389)}}, {{A, B, C, X(6776), X(44180)}}, {{A, B, C, X(7056), X(41431)}}, {{A, B, C, X(7494), X(21213)}}, {{A, B, C, X(8589), X(11511)}}, {{A, B, C, X(8746), X(39874)}}, {{A, B, C, X(8801), X(29011)}}, {{A, B, C, X(9723), X(25406)}}, {{A, B, C, X(9967), X(14806)}}, {{A, B, C, X(10641), X(54849)}}, {{A, B, C, X(10642), X(54850)}}, {{A, B, C, X(11008), X(41614)}}, {{A, B, C, X(11140), X(42313)}}, {{A, B, C, X(11430), X(26899)}}, {{A, B, C, X(12017), X(36748)}}, {{A, B, C, X(12087), X(15717)}}, {{A, B, C, X(15066), X(28708)}}, {{A, B, C, X(15246), X(20062)}}, {{A, B, C, X(15389), X(20775)}}, {{A, B, C, X(15692), X(37945)}}, {{A, B, C, X(23041), X(33629)}}, {{A, B, C, X(33878), X(36751)}}, {{A, B, C, X(36889), X(41891)}}, {{A, B, C, X(38317), X(54032)}}
X(56072) = barycentric product X(i)*X(j) for these (i, j): {3, 43527}, {525, 7954}, {39955, 69}, {56034, 63}
X(56072) = barycentric quotient X(i)/X(j) for these (i, j): {3, 3763}, {6, 5064}, {184, 7772}, {647, 7950}, {1176, 39668}, {1459, 47923}, {3049, 8665}, {7954, 648}, {22352, 39784}, {39955, 4}, {43527, 264}, {56034, 92}

X(56073) = KP3(X(3)) OF X(3) AND X(74)

Barycentrics    a^2*(a^2-b^2-c^2)*(7*a^6+(b^2-c^2)^2*(6*b^2+7*c^2)-a^4*(8*b^2+7*c^2)+a^2*(-5*b^4+20*b^2*c^2-7*c^4))*(7*a^6+(b^2-c^2)^2*(7*b^2+6*c^2)-a^4*(7*b^2+8*c^2)+a^2*(-7*b^4+20*b^2*c^2-5*c^4)) : :

X(56073) lies on the Jerabek hyperbola and on these lines: {4, 15036}, {64, 15035}, {110, 43719}, {265, 16976}, {3426, 15051}, {13452, 15034}, {13622, 51737}, {14094, 43691}, {15055, 44763}, {15077, 38729}, {16163, 43699}

X(56073) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(4)}}, {{A, B, C, X(186), X(16976)}}, {{A, B, C, X(20480), X(46087)}}, {{A, B, C, X(35921), X(44268)}}, {{A, B, C, X(40082), X(48378)}}

X(56074) = KP3(X(2)) OF X(8) AND X(75)

Barycentrics    b*(a^2-2*a*(b-3*c)+(b-c)^2)*(a^2+a*(6*b-2*c)+(b-c)^2)*c : :

X(56074) lies on these lines: {2, 4875}, {7, 3742}, {75, 11019}, {85, 36620}, {673, 5437}, {3452, 27475}, {4666, 51567}, {6384, 33780}, {10582, 21453}, {17394, 40424}, {18743, 39749}, {20173, 27494}, {20905, 44186}

X(56074) = isotomic conjugate of X(8580)
X(56074) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 8580}, {32, 4461}, {213, 24557}, {2175, 31994}
X(56074) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 8580}, {6376, 4461}, {6626, 24557}, {40593, 31994}
X(56074) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(11019)}}, {{A, B, C, X(2), X(7)}}, {{A, B, C, X(85), X(16284)}}, {{A, B, C, X(3452), X(40719)}}, {{A, B, C, X(3673), X(18841)}}, {{A, B, C, X(3676), X(25430)}}, {{A, B, C, X(3680), X(3742)}}, {{A, B, C, X(4666), X(26015)}}, {{A, B, C, X(4847), X(10582)}}, {{A, B, C, X(5437), X(9436)}}, {{A, B, C, X(6376), X(33780)}}, {{A, B, C, X(6745), X(31249)}}, {{A, B, C, X(7018), X(40014)}}, {{A, B, C, X(7033), X(18743)}}, {{A, B, C, X(8580), X(31507)}}, {{A, B, C, X(11059), X(16750)}}, {{A, B, C, X(14942), X(26105)}}, {{A, B, C, X(20173), X(30963)}}, {{A, B, C, X(20905), X(50561)}}, {{A, B, C, X(31359), X(43672)}}, {{A, B, C, X(39702), X(39959)}}
X(56074) = barycentric product X(i)*X(j) for these (i, j): {56043, 75}
X(56074) = barycentric quotient X(i)/X(j) for these (i, j): {2, 8580}, {75, 4461}, {85, 31994}, {86, 24557}, {56043, 1}

X(56075) = KIMBERLING-PAVLOV X(8)-CONJUGATE OF X(2) AND X(8)

Barycentrics    (a+b-5*c)*(a-b-c)*(a-5*b+c) : :

X(56075) lies on these lines: {2, 1266}, {8, 4342}, {85, 4358}, {92, 46873}, {144, 30578}, {346, 4997}, {908, 10405}, {1121, 29616}, {1220, 3622}, {1311, 6014}, {3912, 55948}, {4767, 31145}, {4873, 5328}, {8055, 31722}, {18228, 30711}, {21454, 40420}, {26860, 55942}, {27757, 50442}, {28808, 30608}, {29569, 56044}, {31359, 46933}

X(56075) = trilinear pole of line {4528, 522}
X(56075) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 13462}, {34, 23073}, {56, 16670}, {604, 3241}, {651, 8656}, {1397, 30829}, {1408, 4029}, {1412, 21870}, {1415, 6006}, {16236, 28607}
X(56075) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 16670}, {9, 13462}, {1146, 6006}, {3161, 3241}, {11517, 23073}, {36911, 16236}, {38991, 8656}, {40599, 21870}
X(56075) = X(i)-Ceva conjugate of X(j) for these {i, j}: {40029, 36588}
X(56075) = X(i)-cross conjugate of X(j) for these {i, j}: {4873, 8}, {4900, 36588}, {5328, 2}
X(56075) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(8)}}, {{A, B, C, X(9), X(16676)}}, {{A, B, C, X(63), X(46873)}}, {{A, B, C, X(75), X(52709)}}, {{A, B, C, X(79), X(45100)}}, {{A, B, C, X(88), X(3680)}}, {{A, B, C, X(89), X(1320)}}, {{A, B, C, X(144), X(908)}}, {{A, B, C, X(278), X(51785)}}, {{A, B, C, X(279), X(4342)}}, {{A, B, C, X(346), X(2325)}}, {{A, B, C, X(522), X(28301)}}, {{A, B, C, X(693), X(1266)}}, {{A, B, C, X(885), X(24408)}}, {{A, B, C, X(2051), X(3296)}}, {{A, B, C, X(2321), X(30588)}}, {{A, B, C, X(2339), X(27789)}}, {{A, B, C, X(3306), X(45121)}}, {{A, B, C, X(3452), X(18600)}}, {{A, B, C, X(3622), X(3687)}}, {{A, B, C, X(3701), X(4080)}}, {{A, B, C, X(4009), X(28809)}}, {{A, B, C, X(4391), X(40021)}}, {{A, B, C, X(4659), X(36796)}}, {{A, B, C, X(4671), X(28808)}}, {{A, B, C, X(4873), X(4945)}}, {{A, B, C, X(4900), X(39963)}}, {{A, B, C, X(5233), X(26860)}}, {{A, B, C, X(6332), X(30680)}}, {{A, B, C, X(6601), X(17067)}}, {{A, B, C, X(6745), X(29616)}}, {{A, B, C, X(7172), X(17292)}}, {{A, B, C, X(9965), X(27131)}}, {{A, B, C, X(11679), X(46933)}}, {{A, B, C, X(27525), X(34255)}}, {{A, B, C, X(30701), X(52500)}}, {{A, B, C, X(35510), X(40424)}}, {{A, B, C, X(42032), X(46938)}}
X(56075) = barycentric product X(i)*X(j) for these (i, j): {312, 39963}, {522, 53659}, {3596, 41436}, {4900, 75}, {35519, 6014}, {36588, 8}, {36915, 4997}, {40029, 9}
X(56075) = barycentric quotient X(i)/X(j) for these (i, j): {1, 13462}, {8, 3241}, {9, 16670}, {210, 21870}, {219, 23073}, {312, 30829}, {522, 6006}, {663, 8656}, {2321, 4029}, {3679, 16236}, {3686, 4982}, {4873, 36911}, {4900, 1}, {4944, 52593}, {6014, 109}, {36588, 7}, {36915, 3911}, {36924, 1317}, {39963, 57}, {40029, 85}, {41436, 56}, {53659, 664}
X(56075) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {36588, 36915, 2}

X(56076) = KIMBERLING-PAVLOV X(8)-CONJUGATE OF X(7) AND X(7)

Barycentrics    (a-b-c)*(a^2+2*a*(b-3*c)+(b+c)^2)*(a^2+(b+c)^2+a*(-6*b+2*c)) : :

X(56076) lies on the Feuerbach hyperbola and on these lines: {1, 3161}, {7, 8051}, {9, 6555}, {104, 53630}, {346, 3680}, {1476, 44301}, {2137, 7091}, {2899, 5556}, {5558, 19582}, {7319, 32850}

X(56076) = trilinear pole of line {650, 4546}
X(56076) = X(i)-isoconjugate-of-X(j) for these {i, j}: {34, 23089}, {56, 23511}, {57, 1616}, {604, 4452}, {1106, 8055}, {1397, 33780}, {1407, 2136}, {1412, 21896}, {4564, 17071}, {6552, 7366}
X(56076) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 23511}, {3161, 4452}, {5452, 1616}, {6552, 8055}, {11517, 23089}, {24771, 2136}, {40599, 21896}
X(56076) = X(i)-Ceva conjugate of X(j) for these {i, j}: {8051, 8}
X(56076) = X(i)-cross conjugate of X(j) for these {i, j}: {5423, 8}
X(56076) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(2), X(52549)}}, {{A, B, C, X(281), X(38255)}}, {{A, B, C, X(346), X(3161)}}, {{A, B, C, X(1261), X(2297)}}, {{A, B, C, X(5296), X(50127)}}, {{A, B, C, X(5423), X(8055)}}, {{A, B, C, X(5749), X(17353)}}, {{A, B, C, X(6332), X(30681)}}, {{A, B, C, X(6556), X(8834)}}, {{A, B, C, X(21296), X(32850)}}
X(56076) = barycentric product X(i)*X(j) for these (i, j): {346, 8051}, {2137, 341}, {4391, 53630}, {6553, 8}, {44301, 6556}, {46356, 6552}
X(56076) = barycentric quotient X(i)/X(j) for these (i, j): {8, 4452}, {9, 23511}, {55, 1616}, {200, 2136}, {210, 21896}, {219, 23089}, {312, 33780}, {346, 8055}, {2137, 269}, {3271, 17071}, {3680, 47636}, {5423, 6552}, {6553, 7}, {6557, 27828}, {8051, 279}, {53630, 651}

X(56077) = KIMBERLING-PAVLOV X(8)-CONJUGATE OF X(8) AND X(9)

Barycentrics    (a-b-c)*(a*(b-2*c)-2*b*c)*(2*a*b-a*c+2*b*c) : :

X(56077) lies on the Feuerbach hyperbola and on these lines: {1, 536}, {4, 29353}, {7, 29824}, {8, 4494}, {9, 4009}, {80, 3416}, {104, 29351}, {256, 17306}, {312, 36798}, {941, 5750}, {1156, 37209}, {1320, 3886}, {2320, 3685}, {2325, 40779}, {4873, 4876}, {7319, 17751}, {23836, 47694}, {26227, 55920}, {30942, 50092}

X(56077) = trilinear pole of line {650, 4474}
X(56077) = X(i)-isoconjugate-of-X(j) for these {i, j}: {56, 3240}, {57, 54981}, {109, 29350}, {604, 4664}, {1415, 4776}
X(56077) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 3240}, {11, 29350}, {1146, 4776}, {3161, 4664}, {5452, 54981}
X(56077) = X(i)-cross conjugate of X(j) for these {i, j}: {4519, 8}
X(56077) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(29), X(16394)}}, {{A, B, C, X(75), X(49483)}}, {{A, B, C, X(200), X(7253)}}, {{A, B, C, X(312), X(522)}}, {{A, B, C, X(320), X(3416)}}, {{A, B, C, X(521), X(29353)}}, {{A, B, C, X(894), X(17306)}}, {{A, B, C, X(2297), X(2995)}}, {{A, B, C, X(2319), X(3737)}}, {{A, B, C, X(2321), X(41683)}}, {{A, B, C, X(2325), X(3886)}}, {{A, B, C, X(3596), X(49493)}}, {{A, B, C, X(3685), X(4693)}}, {{A, B, C, X(3738), X(9024)}}, {{A, B, C, X(4363), X(4494)}}, {{A, B, C, X(4451), X(49452)}}, {{A, B, C, X(4518), X(31178)}}, {{A, B, C, X(4581), X(8056)}}, {{A, B, C, X(4659), X(36796)}}, {{A, B, C, X(4670), X(30608)}}, {{A, B, C, X(5231), X(26227)}}, {{A, B, C, X(5750), X(10436)}}, {{A, B, C, X(7081), X(29827)}}, {{A, B, C, X(14942), X(48805)}}, {{A, B, C, X(17318), X(36799)}}, {{A, B, C, X(18816), X(39959)}}, {{A, B, C, X(36910), X(50126)}}, {{A, B, C, X(44040), X(50122)}}, {{A, B, C, X(50092), X(50127)}}
X(56077) = barycentric product X(i)*X(j) for these (i, j): {312, 55919}, {29351, 4391}, {36871, 8}, {37209, 522}
X(56077) = barycentric quotient X(i)/X(j) for these (i, j): {8, 4664}, {9, 3240}, {55, 54981}, {522, 4776}, {650, 29350}, {29351, 651}, {36871, 7}, {37209, 664}, {55919, 57}

X(56078) = KP2(X(8)) OF X(2) AND X(10)

Barycentrics    (a-b-c)*(2*a^2-b^2-c^2+a*(b+c)) : :

X(56078) lies on these lines: {1, 26065}, {2, 2415}, {8, 4314}, {9, 345}, {10, 846}, {21, 3710}, {31, 49476}, {37, 6703}, {55, 3717}, {57, 344}, {63, 3730}, {69, 3929}, {81, 644}, {142, 32939}, {171, 4078}, {190, 226}, {192, 40940}, {200, 27549}, {210, 3712}, {306, 2895}, {312, 2325}, {321, 54357}, {329, 25728}, {333, 2321}, {346, 5273}, {516, 29641}, {519, 8616}, {527, 18134}, {553, 17234}, {645, 40605}, {894, 26109}, {908, 33113}, {968, 33163}, {1025, 52373}, {1125, 19582}, {1211, 50093}, {1213, 50052}, {1229, 20882}, {1265, 3601}, {1266, 24789}, {1279, 4884}, {1332, 2003}, {1334, 17185}, {1621, 49466}, {1698, 2899}, {1699, 30741}, {1730, 30030}, {1738, 32934}, {1757, 4028}, {1812, 52405}, {1947, 6335}, {1997, 31231}, {1999, 3950}, {2183, 29531}, {2999, 26685}, {3008, 3210}, {3011, 32925}, {3101, 20602}, {3175, 35466}, {3305, 17740}, {3452, 32851}, {3666, 17353}, {3683, 3703}, {3685, 4847}, {3689, 4126}, {3695, 31445}, {3704, 5302}, {3705, 40998}, {3707, 4886}, {3714, 18253}, {3744, 49527}, {3750, 49529}, {3752, 4422}, {3755, 33118}, {3772, 17262}, {3817, 17777}, {3870, 4899}, {3879, 4641}, {3911, 18743}, {3914, 32936}, {3920, 35263}, {3928, 18141}, {3932, 4640}, {3936, 17781}, {3944, 50752}, {3967, 6690}, {3979, 49536}, {3995, 25268}, {3996, 24393}, {4001, 32858}, {4009, 5432}, {4011, 24239}, {4029, 34064}, {4035, 33066}, {4044, 19810}, {4082, 7081}, {4104, 33160}, {4138, 29862}, {4304, 16086}, {4312, 44446}, {4357, 32777}, {4370, 37662}, {4384, 41915}, {4388, 51090}, {4391, 40603}, {4417, 17336}, {4419, 25527}, {4428, 49688}, {4431, 5271}, {4438, 24210}, {4480, 5905}, {4545, 42030}, {4661, 50744}, {4704, 29841}, {4869, 28610}, {4936, 17316}, {4967, 19732}, {5205, 10164}, {5249, 32933}, {5257, 19808}, {5278, 50095}, {5281, 5423}, {5294, 17023}, {5712, 50127}, {5737, 17281}, {5743, 16814}, {5744, 30567}, {5847, 7262}, {6358, 28974}, {6666, 19804}, {6679, 49456}, {6684, 46937}, {6692, 30829}, {6745, 27538}, {9778, 39570}, {9965, 17298}, {10327, 35258}, {10453, 52155}, {10543, 42378}, {12437, 52352}, {13405, 32937}, {14552, 17294}, {14829, 17264}, {16704, 50292}, {17056, 17351}, {17061, 49523}, {17147, 26723}, {17182, 20258}, {17242, 37683}, {17280, 38000}, {17315, 41629}, {17338, 17490}, {17340, 44417}, {17600, 38049}, {17760, 25080}, {17862, 20881}, {17889, 28526}, {17977, 26885}, {19742, 50306}, {19822, 24603}, {20073, 26132}, {20106, 27184}, {21255, 26840}, {21454, 29627}, {21949, 28530}, {22000, 29967}, {22097, 29529}, {22464, 28776}, {24215, 27272}, {24231, 29642}, {24541, 25253}, {25006, 32929}, {25061, 25066}, {25083, 25091}, {25308, 29353}, {26792, 27757}, {27065, 33168}, {28580, 32865}, {28609, 30828}, {28661, 46934}, {29001, 34050}, {29594, 37653}, {29596, 33157}, {29639, 32930}, {29643, 41011}, {29653, 50307}, {29656, 49520}, {29873, 33100}, {30699, 55998}, {30768, 32776}, {31247, 32779}, {31424, 54433}, {32780, 50290}, {33158, 49511}, {34772, 52354}, {35652, 37646}, {37650, 42049}, {37674, 41313}, {39559, 52258}, {39595, 41839}, {39597, 50295}, {40774, 43223}, {41867, 42697}, {49774, 54373}

X(56078) = midpoint of X(i) and X(j) for these {i,j}: {7262, 33092}
X(56078) = X(i)-Dao conjugate of X(j) for these {i, j}: {3686, 1125}, {17058, 514}
X(56078) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1268, 8}
X(56078) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(27820)}}, {{A, B, C, X(1247), X(2339)}}, {{A, B, C, X(3879), X(4373)}}, {{A, B, C, X(4052), X(4102)}}, {{A, B, C, X(4859), X(42304)}}, {{A, B, C, X(9311), X(23681)}}
X(56078) = barycentric product X(i)*X(j) for these (i, j): {312, 4641}, {3699, 4897}, {3879, 8}, {11363, 3718}, {17213, 4076}, {21944, 6064}, {27820, 3161}
X(56078) = barycentric quotient X(i)/X(j) for these (i, j): {3879, 7}, {4641, 57}, {4897, 3676}, {11363, 34}, {17058, 53545}, {17213, 1358}, {17476, 53540}, {21944, 1365}, {27820, 27818}
X(56078) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 17261, 4656}, {2, 3161, 30568}, {9, 345, 3687}, {63, 17776, 3912}, {190, 33116, 226}, {306, 3219, 4416}, {333, 42033, 2321}, {346, 5273, 11679}, {846, 33164, 10}, {2321, 5325, 333}, {2325, 5745, 312}, {3219, 32849, 306}, {3683, 3703, 3883}, {5294, 28606, 17023}, {5905, 25734, 4480}, {7262, 33092, 5847}, {19732, 50048, 4967}, {29862, 33099, 4138}, {32936, 33115, 3914}, {33157, 54311, 29596}

X(56079) = KP2(X(8)) OF X(2) AND X(42)

Barycentrics    (a-b-c)*(-2*b^2*c^2+a^3*(b+c)+a^2*(b^2+c^2)) : :

X(56079) lies on these lines: {2, 2415}, {9, 28809}, {71, 17790}, {190, 1400}, {192, 1193}, {313, 29509}, {536, 992}, {644, 27644}, {894, 1655}, {978, 55998}, {1334, 17787}, {1423, 18135}, {1654, 36926}, {2269, 3596}, {2277, 17262}, {2325, 21246}, {2347, 3975}, {2899, 17257}, {3912, 20245}, {3948, 52087}, {4343, 24351}, {4416, 17751}, {17759, 28248}, {17760, 25255}, {20891, 49516}, {20923, 51052}, {24443, 25975}, {27660, 56019}, {28245, 28366}

X(56079) = X(i)-Ceva conjugate of X(j) for these {i, j}: {40418, 8}
X(56079) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(27824)}}, {{A, B, C, X(4373), X(35159)}}
X(56079) = barycentric product X(i)*X(j) for these (i, j): {27824, 3161}
X(56079) = barycentric quotient X(i)/X(j) for these (i, j): {16811, 53538}, {27824, 27818}

X(56080) = KP2(X(8)) OF X(2) AND X(43)

Barycentrics    (a-b-c)*(-2*b^2*c^2+a^3*(b+c)+a*b*c*(b+c)+a^2*(b^2-3*b*c+c^2)) : :

X(56080) lies on circumconic {{A, B, C, X(8056), X(52652)}} and on these lines: {2, 2415}, {9, 3596}, {190, 1423}, {344, 30097}, {646, 3169}, {726, 19582}, {1201, 49446}, {2325, 20258}, {2899, 24248}, {3208, 27424}, {3730, 6381}, {3912, 20348}, {4660, 36926}, {5205, 24728}, {15983, 17294}, {15985, 17281}, {17262, 28358}, {17350, 17752}, {17738, 24590}, {17776, 30076}, {18065, 29698}, {28369, 50127}, {29057, 46937}

X(56080) = X(i)-Ceva conjugate of X(j) for these {i, j}: {32011, 8}
X(56080) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3161, 56079, 30568}

X(56081) = KP2(X(8)) OF X(2) AND X(75)

Barycentrics    (2*a^2+2*b^2-b*c+c^2-a*(4*b+c))*(2*a^2+b^2-b*c+2*c^2-a*(b+4*c)) : :

X(56081) lies on these lines: {145, 344}, {3008, 17158}, {3161, 27818}, {3669, 25082}, {4595, 31638}, {4936, 36807}, {5435, 6604}, {9311, 25101}, {17107, 35160}, {29573, 41629}, {42304, 56078}

X(56081) = isotomic conjugate of X(4859)
X(56081) = trilinear pole of line {4380, 4468}
X(56081) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 4859}, {604, 24392}, {1333, 21949}
X(56081) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 4859}, {37, 21949}, {3161, 24392}
X(56081) = X(i)-cross conjugate of X(j) for these {i, j}: {3676, 190}
X(56081) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1279)}}, {{A, B, C, X(2), X(145)}}, {{A, B, C, X(8), X(10005)}}, {{A, B, C, X(10), X(29573)}}, {{A, B, C, X(75), X(344)}}, {{A, B, C, X(83), X(39704)}}, {{A, B, C, X(85), X(1016)}}, {{A, B, C, X(86), X(17158)}}, {{A, B, C, X(277), X(1120)}}, {{A, B, C, X(312), X(33116)}}, {{A, B, C, X(519), X(49703)}}, {{A, B, C, X(644), X(25082)}}, {{A, B, C, X(673), X(39702)}}, {{A, B, C, X(749), X(39970)}}, {{A, B, C, X(765), X(7131)}}, {{A, B, C, X(870), X(3759)}}, {{A, B, C, X(1121), X(40026)}}, {{A, B, C, X(3624), X(49543)}}, {{A, B, C, X(3729), X(25101)}}, {{A, B, C, X(3731), X(17355)}}, {{A, B, C, X(4595), X(6376)}}, {{A, B, C, X(6553), X(42318)}}, {{A, B, C, X(6625), X(17743)}}, {{A, B, C, X(7033), X(42310)}}, {{A, B, C, X(17261), X(17339)}}, {{A, B, C, X(17263), X(20946)}}, {{A, B, C, X(17315), X(28650)}}, {{A, B, C, X(25072), X(25590)}}, {{A, B, C, X(28978), X(29423)}}, {{A, B, C, X(30829), X(37758)}}, {{A, B, C, X(32012), X(39707)}}, {{A, B, C, X(34860), X(34892)}}, {{A, B, C, X(40012), X(42030)}}, {{A, B, C, X(41316), X(51488)}}
X(56081) = barycentric quotient X(i)/X(j) for these (i, j): {2, 4859}, {8, 24392}, {10, 21949}

X(56082) = KP2(X(8)) OF X(2) AND X(78)

Barycentrics    a^3+2*b*c*(b+c)-a*(b+c)^2 : :

X(56082) lies on these lines: {1, 3159}, {2, 2415}, {4, 3710}, {6, 3175}, {8, 3586}, {9, 321}, {19, 46738}, {31, 3994}, {37, 19701}, {40, 3701}, {44, 19750}, {45, 19744}, {55, 3967}, {57, 4358}, {63, 190}, {69, 17781}, {75, 3305}, {78, 3362}, {81, 50127}, {92, 3692}, {144, 4001}, {165, 4427}, {192, 5256}, {193, 50292}, {200, 3952}, {204, 1897}, {209, 49979}, {210, 5695}, {223, 4552}, {226, 2325}, {253, 306}, {333, 17336}, {343, 51390}, {344, 5249}, {345, 908}, {516, 4082}, {518, 4387}, {528, 30615}, {536, 4383}, {538, 28368}, {612, 3923}, {614, 726}, {728, 30807}, {756, 50314}, {846, 29828}, {894, 5287}, {940, 17351}, {968, 1215}, {988, 25591}, {1001, 4942}, {1018, 21361}, {1043, 3984}, {1089, 12514}, {1150, 3929}, {1211, 17281}, {1376, 4009}, {1697, 4696}, {1698, 32776}, {1699, 3006}, {1706, 52353}, {1707, 17763}, {1743, 3187}, {1757, 17156}, {1760, 46747}, {1766, 21376}, {1796, 55094}, {1817, 38869}, {1836, 3932}, {1965, 8026}, {1999, 17350}, {2257, 22040}, {2321, 5739}, {2324, 28950}, {2401, 6332}, {2895, 17294}, {2899, 24982}, {2999, 17147}, {3008, 19789}, {3058, 49688}, {3208, 3765}, {3218, 30567}, {3219, 4671}, {3247, 19684}, {3306, 18743}, {3403, 18152}, {3416, 6057}, {3434, 3717}, {3452, 17740}, {3501, 3948}, {3589, 50068}, {3666, 17262}, {3679, 32947}, {3681, 3886}, {3685, 3870}, {3687, 31018}, {3696, 3715}, {3703, 24703}, {3705, 17777}, {3706, 5220}, {3723, 19722}, {3730, 4044}, {3749, 32927}, {3751, 32915}, {3758, 34064}, {3760, 27661}, {3769, 36277}, {3771, 21093}, {3773, 4703}, {3782, 17279}, {3790, 4388}, {3799, 25308}, {3875, 32911}, {3891, 7290}, {3895, 4737}, {3912, 5905}, {3936, 28609}, {3944, 29857}, {3946, 50071}, {3951, 10449}, {3969, 4873}, {3973, 19742}, {3974, 5698}, {3985, 40131}, {3992, 54286}, {3998, 27413}, {4042, 15481}, {4050, 25298}, {4115, 54330}, {4135, 4362}, {4309, 50607}, {4359, 4659}, {4363, 44307}, {4384, 27065}, {4385, 5250}, {4415, 17340}, {4417, 42033}, {4418, 5268}, {4419, 54311}, {4422, 24789}, {4423, 49483}, {4432, 32920}, {4439, 4865}, {4454, 9776}, {4480, 20078}, {4488, 9965}, {4494, 29418}, {4512, 26227}, {4582, 52031}, {4654, 18139}, {4661, 49451}, {4666, 24349}, {4676, 32926}, {4681, 20182}, {4702, 41711}, {4854, 38047}, {4884, 17721}, {4901, 5014}, {4903, 5205}, {4968, 31435}, {5044, 50044}, {5057, 32862}, {5219, 33113}, {5223, 17135}, {5272, 17155}, {5294, 54389}, {5300, 41869}, {5423, 17784}, {5687, 12912}, {5741, 31142}, {5743, 50048}, {6172, 14552}, {6541, 32946}, {6542, 56025}, {6703, 49726}, {7081, 35258}, {7174, 24552}, {7191, 49446}, {9369, 36846}, {10582, 17140}, {11320, 54329}, {11346, 16485}, {11348, 26006}, {12526, 17751}, {14206, 20928}, {14212, 20920}, {14213, 20927}, {14555, 50107}, {15492, 19723}, {16469, 17150}, {16475, 32928}, {16496, 32943}, {16672, 37869}, {16777, 19747}, {16814, 19732}, {17022, 31035}, {17064, 33115}, {17123, 49493}, {17146, 30350}, {17184, 17284}, {17233, 33066}, {17242, 17778}, {17264, 18134}, {17274, 33172}, {17277, 42029}, {17280, 27184}, {17282, 33146}, {17286, 32782}, {17296, 32859}, {17298, 17483}, {17316, 56024}, {17333, 37653}, {17352, 19796}, {17353, 19785}, {17354, 19786}, {17484, 32858}, {17495, 23511}, {17526, 34937}, {17594, 32931}, {17597, 28582}, {17598, 49517}, {17599, 49523}, {17720, 44416}, {17742, 22001}, {17753, 29988}, {18056, 52049}, {18193, 30957}, {18655, 20336}, {19582, 19861}, {19591, 52664}, {20064, 50000}, {20075, 53661}, {20095, 53660}, {20214, 21296}, {20588, 24026}, {20688, 23543}, {21282, 50865}, {24210, 33163}, {24400, 42719}, {24411, 53340}, {24558, 28661}, {24589, 51780}, {25006, 27549}, {25242, 25930}, {25496, 49456}, {25507, 51488}, {25527, 33151}, {26237, 52155}, {26243, 41423}, {26685, 26723}, {26792, 33077}, {27002, 30861}, {27003, 46938}, {27131, 30578}, {27523, 30059}, {27538, 32932}, {27792, 29712}, {28606, 41242}, {29616, 30625}, {29652, 49520}, {29674, 33099}, {29679, 33100}, {29687, 33098}, {29820, 49532}, {29821, 49445}, {29855, 33152}, {30566, 30827}, {30713, 46109}, {30852, 32851}, {31053, 32849}, {31224, 37758}, {31231, 51583}, {31266, 33116}, {32912, 39594}, {32941, 42054}, {32942, 49447}, {32945, 50126}, {33092, 33096}, {33095, 33165}, {33101, 33158}, {33134, 33166}, {33154, 33159}, {37553, 46897}, {37674, 49721}, {37679, 42051}, {37680, 50106}, {39585, 52387}, {41816, 48630}, {41883, 51367}, {48644, 50308}, {48843, 50066}

X(56082) = reflection of X(i) in X(j) for these {i,j}: {10327, 4082}, {614, 4011}
X(56082) = anticomplement of X(24177)
X(56082) = perspector of circumconic {{A, B, C, X(51566), X(53647)}}
X(56082) = X(i)-Dao conjugate of X(j) for these {i, j}: {24177, 24177}, {53417, 23537}
X(56082) = X(i)-Ceva conjugate of X(j) for these {i, j}: {40424, 8}
X(56082) = intersection, other than A, B, C, of these circumconics: {{A, B, C, X(253), X(2997)}}, {{A, B, C, X(1751), X(2184)}}, {{A, B, C, X(4052), X(42471)}}, {{A, B, C, X(6336), X(23681)}}, {{A, B, C, X(6557), X(36624)}}
X(56082) = barycentric product X(i)*X(j) for these (i, j): {100, 17894}, {312, 34048}, {5687, 75}, {16228, 4561}, {38389, 7035}, {48303, 668}
X(56082) = barycentric quotient X(i)/X(j) for these (i, j): {5687, 1}, {16228, 7649}, {17894, 693}, {34048, 57}, {38389, 244}, {48303, 513}
X(56082) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 321, 5271}, {63, 190, 25734}, {144, 34255, 4001}, {190, 312, 63}, {192, 27064, 5256}, {226, 2325, 17776}, {329, 346, 306}, {516, 4082, 10327}, {726, 4011, 614}, {894, 41839, 5287}, {2999, 55998, 17147}, {3219, 4671, 11679}, {3685, 32937, 3870}, {3729, 30568, 2}, {3923, 3971, 612}, {3944, 33164, 29857}, {3952, 32929, 200}, {4358, 32933, 57}, {4415, 17340, 32777}, {4552, 28997, 223}, {4659, 7308, 4359}, {4901, 9580, 5014}, {5423, 17784, 49991}, {11679, 25728, 3219}, {17336, 42034, 333}, {17351, 35652, 940}, {17495, 26688, 23511}, {18743, 32939, 3306}, {26685, 30699, 26723}, {27065, 28605, 4384}, {30578, 33168, 27131}, {32911, 42044, 3875}, {32915, 32938, 3751}, {32925, 32930, 1}, {32931, 32936, 17594}, {33151, 33157, 25527}

X(56083) = KP2(X(8)) OF X(7) AND X(65)

Barycentrics    (a-b-c)*(-4*b^2*c^2+a^3*(b+c)+a*(b-c)^2*(b+c)+2*a^2*(b^2+c^2)) : :

X(56083) lies on these lines: {7, 8051}, {8, 10978}, {37, 56079}, {69, 2899}, {75, 19582}, {210, 314}, {319, 36926}, {1264, 1837}, {3057, 3596}, {3161, 4687}, {3175, 39774}, {3663, 25079}, {3701, 17183}, {3718, 4009}, {3948, 43216}, {3985, 20258}, {4357, 30818}, {4358, 20245}, {4460, 8834}, {4640, 55094}, {4679, 30479}, {5044, 10447}, {10436, 30568}, {10446, 46937}, {17790, 21871}, {18135, 24471}, {24993, 25253}, {25585, 31995}, {49518, 56080}

X(56084) = KP2(X(8)) OF X(7) AND X(69)

Barycentrics    a^3-b^3+3*b^2*c+3*b*c^2-c^3+a^2*(b+c)-a*(b^2+4*b*c+c^2) : :

X(56084) lies on these lines: {2, 45}, {4, 1265}, {7, 8051}, {8, 3967}, {57, 1997}, {63, 28808}, {65, 2899}, {69, 189}, {75, 18228}, {92, 55112}, {144, 14829}, {196, 6335}, {226, 344}, {239, 42047}, {306, 36889}, {320, 20942}, {321, 14555}, {341, 962}, {345, 908}, {346, 4417}, {388, 19582}, {391, 55095}, {497, 17777}, {527, 30567}, {573, 29418}, {668, 44723}, {1155, 44446}, {1214, 28978}, {1266, 23511}, {1332, 34048}, {1376, 24280}, {1699, 3717}, {1764, 29497}, {1836, 4009}, {1992, 1999}, {2550, 20716}, {2886, 27549}, {2999, 50101}, {3008, 4052}, {3161, 5226}, {3210, 26791}, {3262, 20921}, {3305, 4054}, {3434, 3952}, {3436, 25253}, {3452, 3729}, {3474, 5205}, {3596, 9535}, {3618, 27064}, {3619, 27184}, {3685, 25568}, {3687, 31142}, {3699, 17784}, {3701, 11415}, {3772, 26685}, {3886, 21060}, {3912, 28609}, {3928, 4480}, {3936, 26783}, {3971, 26098}, {3974, 4388}, {3977, 30852}, {3994, 33088}, {4011, 21093}, {4126, 31140}, {4295, 46937}, {4308, 28661}, {4358, 5905}, {4383, 30699}, {4488, 5435}, {4554, 7056}, {4561, 32815}, {4645, 4903}, {4656, 17321}, {4671, 5739}, {4673, 5815}, {4737, 30305}, {4756, 11680}, {4767, 49719}, {4899, 24392}, {5014, 53661}, {5057, 10327}, {5219, 56078}, {5273, 17336}, {5423, 9812}, {5698, 7081}, {5712, 41839}, {5745, 25728}, {5748, 32851}, {7228, 37682}, {9776, 30829}, {10580, 49499}, {11185, 33948}, {11269, 32938}, {11679, 24705}, {13386, 13458}, {13387, 13425}, {14923, 42020}, {17012, 50071}, {17132, 45204}, {17257, 44417}, {17262, 37662}, {17279, 26132}, {17316, 35652}, {17317, 41825}, {17347, 37655}, {17350, 37642}, {17483, 46938}, {17605, 30741}, {17720, 26065}, {17740, 27131}, {17776, 30828}, {18045, 18135}, {18229, 50093}, {19789, 37680}, {19795, 28836}, {20928, 30807}, {21281, 28809}, {24199, 51780}, {24349, 26105}, {24695, 29649}, {25101, 25525}, {26830, 30905}, {27287, 28803}, {27339, 28748}, {28016, 34860}, {28194, 51284}, {28739, 28754}, {28967, 28993}, {28996, 37800}, {29848, 32930}, {30115, 48817}, {34400, 34401}, {39595, 50127}, {41883, 51390}

X(56084) = X(i)-Ceva conjugate of X(j) for these {i, j}: {34399, 8}, {34401, 69}, {34523, 2}
X(56084) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {18811, 21285}, {34523, 6327}, {55989, 8}
X(56084) = intersection, other than A, B, C, of circumconics {{A, B, C, X(88), X(189)}}, {{A, B, C, X(309), X(903)}}, {{A, B, C, X(4997), X(34404)}}
X(56084) = barycentric product X(i)*X(j) for these (i, j): {16231, 4561}, {20296, 6335}, {34040, 3596}
X(56084) = barycentric quotient X(i)/X(j) for these (i, j): {16231, 7649}, {20296, 905}, {34040, 56}, {38384, 3756}
X(56084) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 8055, 18743}, {226, 30568, 344}, {312, 329, 69}, {312, 33066, 34255}, {321, 14555, 42696}, {321, 31018, 14555}, {329, 34255, 33066}, {908, 56082, 345}, {3161, 5226, 33116}, {3967, 24703, 8}, {4011, 21093, 33144}, {4358, 5905, 18141}, {4488, 6557, 5435}, {4671, 26792, 5739}, {5423, 9812, 32850}, {5435, 6557, 37758}, {17776, 31053, 30828}, {17777, 32937, 497}, {30566, 32933, 2}

X(56085) = KP2(X(8)) OF X(7) AND X(85)

Barycentrics    b*c*(-a+b+c)*(5*a^2+(b-c)^2-2*a*(b+c)) : :

X(56085) lies on these lines: {7, 8051}, {9, 312}, {75, 3161}, {85, 344}, {142, 30829}, {144, 4358}, {190, 1445}, {322, 17264}, {341, 390}, {346, 30854}, {480, 3685}, {516, 46937}, {518, 19582}, {644, 3759}, {1265, 5809}, {1997, 8732}, {2550, 2899}, {3059, 27538}, {3174, 3699}, {3644, 25268}, {3701, 52653}, {3952, 30628}, {3975, 30693}, {4009, 14100}, {4473, 20171}, {4554, 23062}, {4673, 5686}, {4687, 16705}, {4737, 30331}, {5205, 11495}, {5572, 32937}, {5853, 44720}, {6172, 20942}, {6666, 19804}, {11025, 49499}, {17158, 22040}, {17234, 41857}, {17277, 32088}, {17776, 20921}, {20059, 46938}, {20173, 26685}, {20923, 51052}, {22016, 27484}, {25067, 25242}, {25918, 27291}, {27544, 34852}, {28739, 31627}, {28778, 31225}, {29641, 42356}, {30090, 56080}

X(56085) = X(i)-Dao conjugate of X(j) for these {i, j}: {4515, 210}
X(56085) = X(i)-Ceva conjugate of X(j) for these {i, j}: {18153, 17158}
X(56085) = intersection, other than A, B, C, of circumconics {{A, B, C, X(312), X(22040)}}, {{A, B, C, X(314), X(17158)}}, {{A, B, C, X(333), X(8051)}}, {{A, B, C, X(27475), X(30568)}}
X(56085) = barycentric product X(i)*X(j) for these (i, j): {312, 37681}, {17158, 8}, {18153, 9}, {22040, 333}, {23819, 3699}
X(56085) = barycentric quotient X(i)/X(j) for these (i, j): {17158, 7}, {18153, 85}, {22040, 226}, {23819, 3676}, {37681, 57}
X(56085) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {190, 20946, 39126}, {22040, 37681, 17158}

X(56086) = KP3(X(8)) OF X(2) AND X(8)

Barycentrics    (a-b-c)*(a+3*b+c)*(a+b+3*c) : :

X(56086) lies on these lines: {2, 2321}, {8, 4082}, {9, 30711}, {29, 4720}, {85, 321}, {92, 4671}, {144, 189}, {145, 1220}, {329, 10405}, {333, 346}, {345, 30608}, {391, 42030}, {1121, 5739}, {1311, 8694}, {3175, 5232}, {3452, 56075}, {3617, 3714}, {3621, 27064}, {3687, 6557}, {3704, 46933}, {3912, 56054}, {3974, 14942}, {4007, 18228}, {4072, 18229}, {4102, 14555}, {4461, 21454}, {4519, 5274}, {4606, 5372}, {4624, 52156}, {4869, 42029}, {4873, 5273}, {5333, 29624}, {5686, 6057}, {6542, 56044}, {7172, 52133}, {8025, 56019}, {14626, 17135}, {17229, 42047}, {17281, 37666}, {17294, 55948}, {20055, 54120}, {32849, 56062}, {33077, 46873}, {37642, 53664}, {37655, 50107}, {41825, 49765}

X(56086) = isotomic conjugate of X(21454)
X(56086) = trilinear pole of line {20317, 522}
X(56086) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 3361}, {31, 21454}, {56, 1449}, {109, 4790}, {222, 5338}, {269, 4258}, {391, 1106}, {461, 7099}, {604, 3616}, {608, 4652}, {692, 30723}, {1333, 3671}, {1397, 19804}, {1402, 42028}, {1407, 4512}, {1408, 5257}, {1409, 31903}, {1412, 37593}, {1414, 4832}, {1415, 4778}, {1417, 4700}, {4565, 4822}, {4637, 8653}, {4673, 52410}, {4827, 6614}, {5342, 52411}, {5586, 34819}, {7177, 44100}
X(56086) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 1449}, {2, 21454}, {9, 3361}, {11, 4790}, {37, 3671}, {1086, 30723}, {1146, 4778}, {2092, 4719}, {2968, 4765}, {3161, 3616}, {6552, 391}, {6600, 4258}, {6741, 4841}, {24771, 4512}, {40599, 37593}, {40605, 42028}, {40608, 4832}, {40624, 4801}, {40625, 48580}, {51402, 4773}, {52871, 4700}, {55064, 4822}
X(56086) = X(i)-Ceva conjugate of X(j) for these {i, j}: {40023, 5936}
X(56086) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {7050, 41915}
X(56086) = X(i)-cross conjugate of X(j) for these {i, j}: {4007, 8}, {4866, 5936}, {18228, 2}, {23880, 646}, {51785, 7}
X(56086) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(45100)}}, {{A, B, C, X(2), X(8)}}, {{A, B, C, X(4), X(18250)}}, {{A, B, C, X(9), X(1255)}}, {{A, B, C, X(21), X(27789)}}, {{A, B, C, X(57), X(4900)}}, {{A, B, C, X(75), X(32087)}}, {{A, B, C, X(81), X(3680)}}, {{A, B, C, X(88), X(31509)}}, {{A, B, C, X(144), X(329)}}, {{A, B, C, X(145), X(3687)}}, {{A, B, C, X(200), X(29616)}}, {{A, B, C, X(210), X(40779)}}, {{A, B, C, X(253), X(40422)}}, {{A, B, C, X(279), X(12575)}}, {{A, B, C, X(306), X(1265)}}, {{A, B, C, X(314), X(3875)}}, {{A, B, C, X(321), X(346)}}, {{A, B, C, X(345), X(4671)}}, {{A, B, C, X(391), X(4007)}}, {{A, B, C, X(522), X(17133)}}, {{A, B, C, X(593), X(3478)}}, {{A, B, C, X(1000), X(2051)}}, {{A, B, C, X(1029), X(30513)}}, {{A, B, C, X(1219), X(34258)}}, {{A, B, C, X(1320), X(2339)}}, {{A, B, C, X(1392), X(2185)}}, {{A, B, C, X(2996), X(39703)}}, {{A, B, C, X(3596), X(4967)}}, {{A, B, C, X(3617), X(11679)}}, {{A, B, C, X(3661), X(7172)}}, {{A, B, C, X(3701), X(6539)}}, {{A, B, C, X(3702), X(8025)}}, {{A, B, C, X(3706), X(16748)}}, {{A, B, C, X(3902), X(42026)}}, {{A, B, C, X(3946), X(6601)}}, {{A, B, C, X(4061), X(29624)}}, {{A, B, C, X(4402), X(39721)}}, {{A, B, C, X(4451), X(27494)}}, {{A, B, C, X(4673), X(18228)}}, {{A, B, C, X(4866), X(25430)}}, {{A, B, C, X(5744), X(46873)}}, {{A, B, C, X(6332), X(30679)}}, {{A, B, C, X(6553), X(42360)}}, {{A, B, C, X(7155), X(17319)}}, {{A, B, C, X(7317), X(45098)}}, {{A, B, C, X(7320), X(44733)}}, {{A, B, C, X(9965), X(31018)}}, {{A, B, C, X(13478), X(43734)}}, {{A, B, C, X(14554), X(44794)}}, {{A, B, C, X(17117), X(52652)}}, {{A, B, C, X(17396), X(43749)}}, {{A, B, C, X(20078), X(26792)}}, {{A, B, C, X(27797), X(30713)}}, {{A, B, C, X(28605), X(42032)}}, {{A, B, C, X(28795), X(33091)}}, {{A, B, C, X(28916), X(31091)}}, {{A, B, C, X(30479), X(30712)}}, {{A, B, C, X(30680), X(44189)}}, {{A, B, C, X(30710), X(43533)}}, {{A, B, C, X(43740), X(55027)}}
X(56086) = barycentric product X(i)*X(j) for these (i, j): {522, 53658}, {2334, 3596}, {3239, 4624}, {3700, 4633}, {3701, 56048}, {4086, 4614}, {4391, 4606}, {4866, 75}, {5936, 8}, {25430, 312}, {34820, 76}, {35519, 8694}, {40023, 9}, {47915, 646}
X(56086) = barycentric quotient X(i)/X(j) for these (i, j): {1, 3361}, {2, 21454}, {8, 3616}, {9, 1449}, {10, 3671}, {29, 31903}, {33, 5338}, {78, 4652}, {200, 4512}, {210, 37593}, {220, 4258}, {312, 19804}, {318, 5342}, {333, 42028}, {341, 4673}, {346, 391}, {514, 30723}, {522, 4778}, {650, 4790}, {960, 4719}, {1639, 4773}, {1698, 5586}, {2321, 5257}, {2325, 4700}, {2334, 56}, {3239, 4765}, {3694, 4047}, {3700, 4841}, {3709, 4832}, {3710, 4101}, {3712, 4831}, {3716, 4830}, {3717, 4684}, {3985, 4771}, {4009, 4706}, {4041, 4822}, {4082, 4061}, {4086, 4815}, {4130, 4827}, {4391, 4801}, {4397, 4811}, {4451, 4835}, {4522, 4818}, {4524, 8653}, {4560, 48580}, {4606, 651}, {4614, 1414}, {4624, 658}, {4627, 4565}, {4633, 4573}, {4720, 17553}, {4723, 4742}, {4765, 53586}, {4866, 1}, {5936, 7}, {6558, 30728}, {6735, 51423}, {7046, 461}, {7071, 44100}, {8694, 109}, {14626, 1458}, {25430, 57}, {27538, 4734}, {34074, 1415}, {34820, 6}, {40023, 85}, {47915, 3669}, {50333, 50357}, {53658, 664}, {56048, 1014}
X(56086) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4461, 34255, 21454}, {5936, 25430, 2}

X(56087) = KP3(X(8)) OF X(8) AND X(9)

Barycentrics    (a-b-c)*(2*b*c+a*(2*b+c))*(2*b*c+a*(b+2*c)) : :

X(56087) lies on the Feuerbach hyperbola and on these lines: {1, 3696}, {4, 29311}, {7, 7243}, {9, 3706}, {21, 3886}, {104, 6013}, {256, 4496}, {941, 5257}, {2298, 17156}, {2321, 40779}, {2335, 4847}, {2346, 5271}, {3296, 50625}, {3714, 4866}, {4007, 4876}, {4923, 21246}, {10435, 17617}, {10436, 56048}, {35628, 45032}

X(56087) = isogonal conjugate of X(16878)
X(56087) = trilinear pole of line {650, 48264}
X(56087) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 16878}, {56, 17018}, {65, 39673}, {109, 6005}, {604, 4687}, {664, 8655}, {1414, 50483}, {1415, 47666}
X(56087) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 17018}, {3, 16878}, {11, 6005}, {1146, 47666}, {3161, 4687}, {6741, 48407}, {39025, 8655}, {40602, 39673}, {40608, 50483}
X(56087) = X(i)-cross conjugate of X(j) for these {i, j}: {53526, 522}
X(56087) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(29), X(16458)}}, {{A, B, C, X(75), X(2321)}}, {{A, B, C, X(200), X(17135)}}, {{A, B, C, X(210), X(13476)}}, {{A, B, C, X(312), X(3706)}}, {{A, B, C, X(333), X(4042)}}, {{A, B, C, X(391), X(30712)}}, {{A, B, C, X(521), X(29311)}}, {{A, B, C, X(522), X(28581)}}, {{A, B, C, X(670), X(4069)}}, {{A, B, C, X(2215), X(40505)}}, {{A, B, C, X(3685), X(4007)}}, {{A, B, C, X(3687), X(17156)}}, {{A, B, C, X(3701), X(39708)}}, {{A, B, C, X(3714), X(4673)}}, {{A, B, C, X(4102), X(4361)}}, {{A, B, C, X(4451), X(49459)}}, {{A, B, C, X(4518), X(40328)}}, {{A, B, C, X(4847), X(5271)}}, {{A, B, C, X(10472), X(11679)}}, {{A, B, C, X(27958), X(49717)}}, {{A, B, C, X(28639), X(36800)}}, {{A, B, C, X(39959), X(40422)}}
X(56087) = barycentric product X(i)*X(j) for these (i, j): {333, 46772}, {4391, 6013}, {10013, 312}, {56051, 8}
X(56087) = barycentric quotient X(i)/X(j) for these (i, j): {6, 16878}, {8, 4687}, {9, 17018}, {284, 39673}, {522, 47666}, {650, 6005}, {3063, 8655}, {3700, 48407}, {3709, 50483}, {6013, 651}, {10013, 57}, {46772, 226}, {56051, 7}
X(56087) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10013, 46772, 56051}

X(56088) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(1) AND X(2)

Barycentrics    (a-b-c)*(3*a^2+b^2-4*b*c+3*c^2-2*a*(2*b+c))*(3*a^2+3*b^2-4*b*c+c^2-2*a*(b+2*c)) : :

X(56088) lies on these lines: {1, 56054}, {2, 3158}, {8, 4936}, {85, 145}, {92, 20015}, {200, 6557}, {312, 6555}, {519, 55948}, {1121, 31145}, {1280, 4373}, {3617, 32008}, {3621, 10025}, {3622, 32015}, {3935, 50442}, {12630, 40719}, {12632, 31359}, {12640, 46872}, {20052, 36605}, {36845, 42315}, {42309, 51351}, {46933, 56060}, {52156, 52164}

X(56088) = isogonal conjugate of X(42314)
X(56088) = isotomic conjugate of X(51351)
X(56088) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 42314}, {6, 51302}, {31, 51351}, {56, 3243}, {604, 29627}, {1106, 10005}
X(56088) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 3243}, {2, 51351}, {3, 42314}, {9, 51302}, {3161, 29627}, {6552, 10005}
X(56088) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(6605)}}, {{A, B, C, X(2), X(8)}}, {{A, B, C, X(7), X(8236)}}, {{A, B, C, X(9), X(30712)}}, {{A, B, C, X(78), X(20015)}}, {{A, B, C, X(81), X(7218)}}, {{A, B, C, X(144), X(10025)}}, {{A, B, C, X(145), X(200)}}, {{A, B, C, X(280), X(43745)}}, {{A, B, C, X(281), X(38200)}}, {{A, B, C, X(346), X(522)}}, {{A, B, C, X(390), X(3886)}}, {{A, B, C, X(461), X(17589)}}, {{A, B, C, X(903), X(50839)}}, {{A, B, C, X(996), X(46916)}}, {{A, B, C, X(1002), X(7220)}}, {{A, B, C, X(1043), X(6553)}}, {{A, B, C, X(1088), X(7319)}}, {{A, B, C, X(1219), X(15998)}}, {{A, B, C, X(2287), X(42470)}}, {{A, B, C, X(3254), X(36916)}}, {{A, B, C, X(3617), X(4847)}}, {{A, B, C, X(3870), X(20007)}}, {{A, B, C, X(4900), X(39959)}}, {{A, B, C, X(6556), X(6598)}}, {{A, B, C, X(6745), X(31145)}}, {{A, B, C, X(7320), X(21453)}}, {{A, B, C, X(19605), X(31509)}}, {{A, B, C, X(36910), X(51102)}}, {{A, B, C, X(37658), X(40779)}}, {{A, B, C, X(43672), X(43734)}}
X(56088) = barycentric product X(i)*X(j) for these (i, j): {341, 42315}, {42318, 8}
X(56088) = barycentric quotient X(i)/X(j) for these (i, j): {1, 51302}, {2, 51351}, {6, 42314}, {8, 29627}, {9, 3243}, {346, 10005}, {42315, 269}, {42318, 7}

X(56089) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(1) AND X(4)

Barycentrics    (a-b-c)*(a^3+(b-c)^2*(b+c)-a^2*(3*b+c)-a*(3*b^2-8*b*c+c^2))*(a^3+(b-c)^2*(b+c)-a^2*(b+3*c)-a*(b^2-8*b*c+3*c^2)) : :
X(56089) = -3*X[2]+2*X[15347]

X(56089) lies on the Feuerbach hyperbola and on these lines: {1, 6692}, {2, 15347}, {4, 3880}, {7, 13601}, {8, 17622}, {9, 45193}, {10, 56038}, {84, 519}, {104, 5854}, {145, 1476}, {355, 38307}, {497, 34918}, {517, 10309}, {518, 10307}, {521, 23836}, {758, 16005}, {952, 34256}, {1000, 17559}, {1156, 3621}, {1320, 7080}, {1389, 34619}, {1392, 27383}, {2136, 3476}, {2802, 12667}, {2804, 24128}, {3062, 5853}, {3189, 7284}, {3241, 56029}, {3296, 10107}, {3625, 55931}, {3632, 38271}, {3680, 6736}, {3885, 30513}, {3893, 6601}, {3913, 15179}, {4900, 21627}, {5176, 7319}, {5555, 12648}, {8058, 23838}, {10308, 44669}, {12625, 33576}, {14839, 55001}, {20050, 55921}, {24392, 31509}, {30201, 43728}

X(56089) = isogonal conjugate of X(41426)
X(56089) = anticomplement of X(15347)
X(56089) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 41426}, {56, 36846}, {109, 30198}, {269, 52804}, {604, 1997}, {1106, 42020}
X(56089) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 36846}, {3, 41426}, {11, 30198}, {3161, 1997}, {6552, 42020}, {6600, 52804}, {15347, 15347}
X(56089) = X(i)-cross conjugate of X(j) for these {i, j}: {3756, 522}, {34524, 2}
X(56089) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(2), X(6692)}}, {{A, B, C, X(6), X(3057)}}, {{A, B, C, X(29), X(17567)}}, {{A, B, C, X(55), X(13601)}}, {{A, B, C, X(68), X(34901)}}, {{A, B, C, X(69), X(32049)}}, {{A, B, C, X(145), X(346)}}, {{A, B, C, X(281), X(1222)}}, {{A, B, C, X(318), X(36596)}}, {{A, B, C, X(341), X(1120)}}, {{A, B, C, X(513), X(33963)}}, {{A, B, C, X(517), X(10310)}}, {{A, B, C, X(519), X(7080)}}, {{A, B, C, X(521), X(1265)}}, {{A, B, C, X(522), X(6553)}}, {{A, B, C, X(1413), X(17622)}}, {{A, B, C, X(2123), X(51565)}}, {{A, B, C, X(2804), X(5854)}}, {{A, B, C, X(3445), X(17648)}}, {{A, B, C, X(3452), X(44794)}}, {{A, B, C, X(3621), X(6745)}}, {{A, B, C, X(3632), X(27383)}}, {{A, B, C, X(5435), X(6557)}}, {{A, B, C, X(7046), X(14923)}}, {{A, B, C, X(9368), X(39969)}}, {{A, B, C, X(10107), X(42696)}}, {{A, B, C, X(11051), X(18236)}}, {{A, B, C, X(12667), X(15500)}}, {{A, B, C, X(15347), X(34524)}}, {{A, B, C, X(17519), X(17559)}}, {{A, B, C, X(30701), X(52517)}}
X(56089) = barycentric product X(i)*X(j) for these (i, j): {346, 52803}, {30236, 4391}
X(56089) = barycentric quotient X(i)/X(j) for these (i, j): {6, 41426}, {8, 1997}, {9, 36846}, {220, 52804}, {346, 42020}, {650, 30198}, {30236, 651}, {34524, 15347}, {52803, 279}

X(56090) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(1) AND X(7)

Barycentrics    (a-b-c)*(a^3+(b-c)^2*(b+c)-a^2*(5*b+c)-a*(5*b^2-14*b*c+c^2))*(a^3+(b-c)^2*(b+c)-a^2*(b+5*c)-a*(b^2-14*b*c+5*c^2)) : :

X(56090) lies on the Feuerbach hyperbola and on these lines: {4, 12541}, {7, 3880}, {84, 28234}, {104, 6244}, {145, 7091}, {517, 10307}, {519, 3062}, {1156, 5854}, {3296, 39779}, {3621, 33576}, {3680, 4345}, {3900, 23836}, {4866, 8275}, {4900, 5328}, {5853, 55922}, {7320, 10179}, {9785, 17648}, {11041, 15179}, {11525, 56038}, {21627, 31509}, {36922, 55931}

X(56090) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(81), X(18228)}}, {{A, B, C, X(145), X(1043)}}, {{A, B, C, X(312), X(44794)}}, {{A, B, C, X(341), X(6553)}}, {{A, B, C, X(346), X(1120)}}, {{A, B, C, X(514), X(6557)}}, {{A, B, C, X(517), X(6244)}}, {{A, B, C, X(959), X(3057)}}, {{A, B, C, X(1265), X(12541)}}, {{A, B, C, X(3241), X(36916)}}, {{A, B, C, X(3880), X(3900)}}, {{A, B, C, X(4873), X(16236)}}, {{A, B, C, X(5854), X(6366)}}, {{A, B, C, X(6556), X(34860)}}, {{A, B, C, X(8058), X(28234)}}, {{A, B, C, X(36588), X(36596)}}, {{A, B, C, X(39749), X(52517)}}, {{A, B, C, X(51567), X(56088)}}

X(56091) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(1) AND X(21)

Barycentrics    a*(a+b-4*c)*(a-b-c)*(a-4*b+c) : :
X(56091) = -4*X[3626]+3*X[5559]

X(56091) lies on the Feuerbach hyperbola and on these lines: {1, 3833}, {4, 3621}, {7, 10944}, {8, 11238}, {9, 3885}, {10, 13606}, {21, 3880}, {79, 519}, {80, 3625}, {100, 56036}, {104, 3579}, {145, 3296}, {496, 1000}, {515, 16005}, {517, 10308}, {523, 23836}, {941, 16672}, {1159, 5551}, {1320, 3893}, {1389, 3935}, {1392, 10912}, {1476, 32636}, {2298, 16666}, {2320, 3871}, {2802, 3065}, {3057, 32635}, {3255, 5853}, {3626, 5559}, {3632, 5560}, {3634, 13602}, {3680, 5330}, {3869, 36599}, {3877, 4866}, {4193, 56089}, {4816, 43731}, {5854, 11604}, {5919, 17546}, {7284, 14923}, {7320, 9780}, {7962, 31509}, {10266, 44669}, {10914, 15179}, {11278, 16615}, {12641, 21627}, {17648, 34894}, {23838, 35057}, {25722, 31507}, {37524, 54391}, {37567, 55921}, {38251, 49492}

X(56091) = reflection of X(i) in X(j) for these {i,j}: {20050, 39777}
X(56091) = X(i)-isoconjugate-of-X(j) for these {i, j}: {56, 3244}, {57, 16669}, {101, 30726}, {109, 28217}, {4935, 16945}
X(56091) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 3244}, {8, 4935}, {11, 28217}, {1015, 30726}, {5452, 16669}, {51577, 39781}
X(56091) = X(i)-Ceva conjugate of X(j) for these {i, j}: {39710, 39962}
X(56091) = X(i)-cross conjugate of X(j) for these {i, j}: {4959, 644}
X(56091) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(3), X(8148)}}, {{A, B, C, X(10), X(3918)}}, {{A, B, C, X(29), X(17531)}}, {{A, B, C, X(78), X(3621)}}, {{A, B, C, X(81), X(4102)}}, {{A, B, C, X(88), X(312)}}, {{A, B, C, X(105), X(11238)}}, {{A, B, C, X(145), X(4917)}}, {{A, B, C, X(200), X(20050)}}, {{A, B, C, X(333), X(40434)}}, {{A, B, C, X(517), X(3579)}}, {{A, B, C, X(519), X(4420)}}, {{A, B, C, X(521), X(5844)}}, {{A, B, C, X(523), X(3701)}}, {{A, B, C, X(596), X(52409)}}, {{A, B, C, X(958), X(16672)}}, {{A, B, C, X(960), X(3902)}}, {{A, B, C, X(1043), X(17160)}}, {{A, B, C, X(1126), X(41432)}}, {{A, B, C, X(1222), X(6740)}}, {{A, B, C, X(1255), X(42030)}}, {{A, B, C, X(1261), X(10944)}}, {{A, B, C, X(1807), X(37705)}}, {{A, B, C, X(1809), X(12645)}}, {{A, B, C, X(2349), X(40399)}}, {{A, B, C, X(3057), X(3702)}}, {{A, B, C, X(3617), X(3872)}}, {{A, B, C, X(3625), X(4511)}}, {{A, B, C, X(3626), X(4861)}}, {{A, B, C, X(3723), X(5302)}}, {{A, B, C, X(3871), X(4720)}}, {{A, B, C, X(3877), X(4673)}}, {{A, B, C, X(3893), X(4723)}}, {{A, B, C, X(4853), X(9780)}}, {{A, B, C, X(4915), X(5550)}}, {{A, B, C, X(5330), X(16948)}}, {{A, B, C, X(5697), X(37524)}}, {{A, B, C, X(5854), X(8674)}}, {{A, B, C, X(6553), X(51786)}}, {{A, B, C, X(6557), X(39963)}}, {{A, B, C, X(7131), X(36605)}}, {{A, B, C, X(8702), X(44669)}}, {{A, B, C, X(11107), X(15679)}}, {{A, B, C, X(11278), X(13624)}}, {{A, B, C, X(17124), X(52133)}}, {{A, B, C, X(29298), X(35104)}}
X(56091) = barycentric product X(i)*X(j) for these (i, j): {28218, 4391}, {39710, 9}, {39962, 8}
X(56091) = barycentric quotient X(i)/X(j) for these (i, j): {9, 3244}, {55, 16669}, {513, 30726}, {650, 28217}, {3161, 4935}, {4578, 30732}, {16814, 39777}, {16885, 39781}, {28218, 651}, {39710, 85}, {39962, 7}

X(56092) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(1) AND X(30)

Barycentrics    (a-b-c)*(b-c)*(2*a^3+a^2*(b+c)-(b-c)^2*(b+c)-2*a*(b^2+b*c+c^2)) : :

X(56092) lies on these lines: {8, 52355}, {30, 511}, {1320, 14224}, {1389, 43737}, {4105, 47887}, {4895, 21119}, {6742, 55017}, {7178, 48293}, {7629, 53527}, {8611, 14400}, {10015, 48303}, {11278, 42750}, {13254, 16156}, {13255, 16157}, {21120, 48307}, {21180, 39540}, {34958, 48292}, {43728, 56091}, {44811, 48391}, {48962, 48966}, {48994, 48998}

X(56092) = perspector of circumconic {{A, B, C, X(2), X(17781)}}
X(56092) = X(i)-isoconjugate-of-X(j) for these {i, j}: {56, 55185}, {109, 10308}
X(56092) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 55185}, {11, 10308}, {8818, 38340}, {41800, 4467}
X(56092) = X(i)-Ceva conjugate of X(j) for these {i, j}: {38340, 9}, {55186, 41800}
X(56092) = X(i)-complementary conjugate of X(j) for these {i, j}: {10308, 124}, {55185, 1329}
X(56092) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {10308, 33650}, {55185, 3436}
X(56092) = intersection, other than A, B, C, of circumconics {{A, B, C, X(8), X(30)}}, {{A, B, C, X(314), X(29301)}}, {{A, B, C, X(514), X(41800)}}, {{A, B, C, X(515), X(5559)}}, {{A, B, C, X(517), X(3579)}}, {{A, B, C, X(527), X(17781)}}, {{A, B, C, X(758), X(3680)}}, {{A, B, C, X(900), X(14224)}}, {{A, B, C, X(971), X(2346)}}, {{A, B, C, X(1320), X(2771)}}, {{A, B, C, X(1389), X(6001)}}, {{A, B, C, X(2800), X(13143)}}, {{A, B, C, X(4802), X(44426)}}, {{A, B, C, X(6601), X(17768)}}, {{A, B, C, X(9033), X(52355)}}, {{A, B, C, X(28217), X(43728)}}, {{A, B, C, X(44669), X(56089)}}
X(56092) = barycentric product X(i)*X(j) for these (i, j): {3579, 4391}, {17781, 522}, {41800, 8}, {55186, 9}
X(56092) = barycentric quotient X(i)/X(j) for these (i, j): {9, 55185}, {650, 10308}, {3579, 651}, {17781, 664}, {41800, 7}, {55186, 85}
X(56092) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {521, 8058, 2804}, {522, 3738, 28217}, {28217, 42337, 522}

X(56093) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(1) AND X(55)

Barycentrics    a*(a-b-c)*(a^2*b-2*b*c^2+a*(b^2-b*c-2*c^2))*(a^2*c-2*b^2*c+a*(-2*b^2-b*c+c^2)) : :

X(56093) lies on these lines: {1, 45787}, {8, 52196}, {42, 750}, {55, 35104}, {65, 7223}, {69, 13576}, {210, 4042}, {518, 1824}, {573, 29310}, {958, 1334}, {10371, 41506}, {10441, 40516}, {13478, 29311}

X(56093) = trilinear pole of line {3709, 17418}
X(56093) = X(i)-isoconjugate-of-X(j) for these {i, j}: {56, 49470}, {57, 37657}, {109, 48080}, {604, 30830}
X(56093) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 49470}, {11, 48080}, {3161, 30830}, {5452, 37657}
X(56093) = X(i)-Ceva conjugate of X(j) for these {i, j}: {55945, 39981}
X(56093) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(333)}}, {{A, B, C, X(6), X(314)}}, {{A, B, C, X(8), X(42)}}, {{A, B, C, X(9), X(969)}}, {{A, B, C, X(21), X(1889)}}, {{A, B, C, X(56), X(18021)}}, {{A, B, C, X(69), X(219)}}, {{A, B, C, X(78), X(17156)}}, {{A, B, C, X(171), X(37614)}}, {{A, B, C, X(200), X(49495)}}, {{A, B, C, X(261), X(10013)}}, {{A, B, C, X(291), X(312)}}, {{A, B, C, X(523), X(3596)}}, {{A, B, C, X(573), X(29311)}}, {{A, B, C, X(750), X(1320)}}, {{A, B, C, X(960), X(51223)}}, {{A, B, C, X(1037), X(2997)}}, {{A, B, C, X(1126), X(45032)}}, {{A, B, C, X(1222), X(1376)}}, {{A, B, C, X(2481), X(52013)}}, {{A, B, C, X(3868), X(10371)}}, {{A, B, C, X(3872), X(29828)}}, {{A, B, C, X(3880), X(14077)}}, {{A, B, C, X(3913), X(3996)}}, {{A, B, C, X(4492), X(11609)}}, {{A, B, C, X(4900), X(7220)}}, {{A, B, C, X(4997), X(52654)}}, {{A, B, C, X(6366), X(14839)}}, {{A, B, C, X(7155), X(52030)}}, {{A, B, C, X(10441), X(16678)}}, {{A, B, C, X(13476), X(30479)}}, {{A, B, C, X(20029), X(43740)}}, {{A, B, C, X(30571), X(30608)}}, {{A, B, C, X(31509), X(36630)}}, {{A, B, C, X(37581), X(41600)}}
X(56093) = barycentric product X(i)*X(j) for these (i, j): {39981, 8}, {40030, 55}, {55945, 9}
X(56093) = barycentric quotient X(i)/X(j) for these (i, j): {8, 30830}, {9, 49470}, {55, 37657}, {650, 48080}, {39981, 7}, {40030, 6063}, {55945, 85}

X(56094) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(1) AND X(75)

Barycentrics    (2*a+2*b-c)*(-a+b+c)^2*(2*a-b+2*c) : :

X(56094) lies on these lines: {8, 2320}, {75, 519}, {89, 1219}, {145, 30588}, {190, 36922}, {312, 52409}, {318, 4673}, {341, 6737}, {515, 17347}, {952, 30273}, {1222, 2163}, {2364, 4007}, {2370, 4588}, {3996, 51565}, {4451, 44669}, {4597, 18025}, {6556, 20007}, {17740, 31145}, {20014, 30589}

X(56094) = trilinear pole of line {3239, 14427}
X(56094) = X(i)-isoconjugate-of-X(j) for these {i, j}: {45, 1407}, {56, 2099}, {57, 1405}, {269, 2177}, {604, 5219}, {934, 4775}, {1042, 4653}, {1106, 3679}, {1398, 3940}, {1415, 43052}, {1417, 36920}, {1427, 4273}, {1461, 4893}, {3711, 7023}, {4671, 52410}, {4814, 6614}, {4833, 53321}, {4873, 7366}, {4957, 23979}
X(56094) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 2099}, {1146, 43052}, {2968, 4777}, {3161, 5219}, {5452, 1405}, {6552, 3679}, {6600, 2177}, {14714, 4775}, {24771, 45}, {35508, 4893}, {52871, 36920}, {55068, 4833}
X(56094) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1098)}}, {{A, B, C, X(8), X(75)}}, {{A, B, C, X(9), X(50116)}}, {{A, B, C, X(21), X(3897)}}, {{A, B, C, X(29), X(6910)}}, {{A, B, C, X(80), X(37740)}}, {{A, B, C, X(145), X(20007)}}, {{A, B, C, X(200), X(519)}}, {{A, B, C, X(220), X(49490)}}, {{A, B, C, X(312), X(1016)}}, {{A, B, C, X(332), X(1265)}}, {{A, B, C, X(1000), X(1065)}}, {{A, B, C, X(1088), X(3427)}}, {{A, B, C, X(1120), X(6601)}}, {{A, B, C, X(1220), X(30478)}}, {{A, B, C, X(1320), X(2287)}}, {{A, B, C, X(2320), X(39704)}}, {{A, B, C, X(2328), X(41434)}}, {{A, B, C, X(3057), X(37603)}}, {{A, B, C, X(3239), X(49780)}}, {{A, B, C, X(3632), X(6736)}}, {{A, B, C, X(3680), X(3879)}}, {{A, B, C, X(3907), X(44669)}}, {{A, B, C, X(4183), X(48816)}}, {{A, B, C, X(4397), X(50751)}}, {{A, B, C, X(4515), X(4709)}}, {{A, B, C, X(4853), X(6743)}}, {{A, B, C, X(6598), X(34860)}}, {{A, B, C, X(7073), X(48825)}}, {{A, B, C, X(7110), X(10570)}}, {{A, B, C, X(11604), X(39707)}}, {{A, B, C, X(17947), X(27475)}}, {{A, B, C, X(20569), X(30608)}}, {{A, B, C, X(28071), X(49720)}}, {{A, B, C, X(39702), X(43740)}}, {{A, B, C, X(42064), X(50301)}}, {{A, B, C, X(43731), X(44040)}}, {{A, B, C, X(51567), X(56088)}}
X(56094) = barycentric product X(i)*X(j) for these (i, j): {200, 20569}, {341, 89}, {346, 39704}, {1043, 30588}, {2320, 312}, {2364, 3596}, {3239, 4597}, {4397, 4604}, {4588, 52622}, {24026, 5385}, {30608, 8}, {35519, 5549}, {52620, 6558}, {55246, 7258}
X(56094) = barycentric quotient X(i)/X(j) for these (i, j): {8, 5219}, {9, 2099}, {55, 1405}, {89, 269}, {200, 45}, {220, 2177}, {341, 4671}, {346, 3679}, {522, 43052}, {657, 4775}, {728, 3711}, {1021, 4833}, {1043, 5235}, {2163, 1407}, {2287, 4653}, {2320, 57}, {2325, 36920}, {2328, 4273}, {2364, 56}, {3239, 4777}, {3686, 4870}, {3692, 3940}, {3707, 39782}, {3900, 4893}, {4130, 4814}, {4148, 4800}, {4163, 4944}, {4171, 4770}, {4397, 4791}, {4529, 4774}, {4578, 4752}, {4588, 1461}, {4597, 658}, {4604, 934}, {5385, 7045}, {5423, 4873}, {5549, 109}, {6558, 4767}, {7253, 47683}, {7258, 55245}, {20569, 1088}, {24026, 4957}, {28607, 1106}, {28658, 1042}, {28808, 36595}, {30588, 3668}, {30608, 7}, {32851, 36589}, {39704, 279}, {53114, 1427}, {55246, 7216}, {55979, 7053}

X(56095) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(1) AND X(79)

Barycentrics    (a-b-c)*(a^3+(b-c)^2*(b+c)-a^2*(4*b+c)-a*(4*b^2-11*b*c+c^2))*(a^3+(b-c)^2*(b+c)-a^2*(b+4*c)-a*(b^2-11*b*c+4*c^2)) : :

X(56095) lies on the Feuerbach hyperbola and on these lines: {79, 3880}, {84, 5844}, {517, 16005}, {519, 10308}, {1329, 4900}, {3065, 5854}, {3244, 15179}, {3633, 7284}, {3740, 5559}, {7091, 37738}, {11373, 56038}, {23836, 35057}, {23838, 56092}

X(56095) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(596), X(36596)}}, {{A, B, C, X(3880), X(35057)}}, {{A, B, C, X(5844), X(8058)}}

X(56096) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(1) AND X(84)

Barycentrics    a*(a-b-c)*(a^4-6*a^3*c+(b-c)^2*(b^2-4*b*c-5*c^2)-2*a^2*(b^2-5*b*c-2*c^2)+2*a*c*(5*b^2-12*b*c+3*c^2))*(a^4-6*a^3*b-(b-c)^2*(5*b^2+4*b*c-c^2)+2*a^2*(2*b^2+5*b*c-c^2)+2*a*b*(3*b^2-12*b*c+5*c^2)) : :

X(56096) lies on the Feuerbach hyperbola and on these lines: {1, 15347}, {84, 3880}, {104, 12629}, {519, 10309}, {1320, 2057}, {2802, 34256}, {5853, 10307}, {5854, 46435}, {7320, 24982}, {8058, 23836}, {16005, 44669}, {23340, 38308}, {23838, 30201}

X(56096) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(519), X(2057)}}, {{A, B, C, X(3737), X(39123)}}, {{A, B, C, X(3880), X(8058)}}, {{A, B, C, X(4853), X(24982)}}, {{A, B, C, X(6735), X(12629)}}, {{A, B, C, X(15347), X(36846)}}, {{A, B, C, X(21164), X(23340)}}

X(56097) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(1) AND X(104)

Barycentrics    a*(a-b-c)*(a^4-5*a^3*c+(b-c)^2*(b^2-3*b*c-4*c^2)+a^2*(-2*b^2+7*b*c+3*c^2)+a*c*(7*b^2-16*b*c+5*c^2))*(a^4-5*a^3*b+a^2*(3*b^2+7*b*c-2*c^2)-(b-c)^2*(4*b^2+3*b*c-c^2)+a*b*(5*b^2-16*b*c+7*c^2)) : :

X(56097) lies on the Feuerbach hyperbola and on these lines: {4, 5854}, {11, 56089}, {84, 2802}, {100, 15347}, {104, 3880}, {517, 34256}, {519, 46435}, {528, 10307}, {952, 10309}, {1000, 3816}, {2804, 23836}, {9951, 33576}, {12758, 38271}, {18254, 55931}, {30201, 46041}

X(56097) = reflection of X(i) in X(j) for these {i,j}: {100, 15347}, {56089, 11}
X(56097) = trilinear pole of line {650, 34524}
X(56097) = X(i)-Dao conjugate of X(j) for these {i, j}: {1145, 18802}
X(56097) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(517), X(13528)}}, {{A, B, C, X(521), X(1811)}}, {{A, B, C, X(952), X(30201)}}, {{A, B, C, X(2316), X(38452)}}, {{A, B, C, X(2802), X(8058)}}, {{A, B, C, X(2804), X(3880)}}
X(56097) = barycentric product X(i)*X(j) for these (i, j): {4391, 53897}
X(56097) = barycentric quotient X(i)/X(j) for these (i, j): {53897, 651}

X(56098) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(8) AND X(2)

Barycentrics    a*(a-b-c)*(a^3-b^3+b^2*c-b*c^2+c^3-a^2*(b+c)+a*(b^2-2*b*c-c^2))*(a^3+b^3-b^2*c+b*c^2-c^3-a^2*(b+c)+a*(-b^2-2*b*c+c^2)) : :

X(56098) lies on these lines: {1, 348}, {2, 33}, {3, 7131}, {21, 2332}, {55, 63}, {64, 10884}, {75, 4319}, {78, 220}, {103, 6183}, {200, 345}, {243, 55963}, {990, 40719}, {997, 4845}, {1005, 36100}, {1253, 4712}, {1791, 3601}, {1812, 2328}, {2192, 41081}, {2339, 13615}, {2342, 36819}, {2808, 18446}, {3744, 7050}, {3749, 51476}, {3811, 10482}, {3872, 42064}, {3935, 30680}, {3957, 30679}, {4189, 55986}, {4326, 7218}, {4327, 21453}, {4666, 7073}, {5307, 10431}, {6513, 7072}, {7007, 41514}, {7411, 10319}, {8299, 52001}, {10393, 34259}, {13436, 30400}, {13453, 30401}, {20111, 34772}, {21258, 54392}, {24218, 24283}, {36721, 37697}, {39959, 54440}, {52351, 52371}

X(56098) = isogonal conjugate of X(2263)
X(56098) = trilinear pole of line {657, 521}
X(56098) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 2263}, {6, 948}, {7, 37580}, {56, 2550}, {57, 40131}, {109, 47123}, {269, 28043}, {607, 23603}, {934, 6182}, {1400, 16054}
X(56098) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 2550}, {3, 2263}, {9, 948}, {11, 47123}, {5452, 40131}, {6600, 28043}, {14714, 6182}, {40582, 16054}
X(56098) = X(i)-cross conjugate of X(j) for these {i, j}: {949, 39273}
X(56098) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(33)}}, {{A, B, C, X(2), X(21)}}, {{A, B, C, X(3), X(1040)}}, {{A, B, C, X(7), X(2287)}}, {{A, B, C, X(8), X(1280)}}, {{A, B, C, X(9), X(75)}}, {{A, B, C, X(20), X(10884)}}, {{A, B, C, X(29), X(20835)}}, {{A, B, C, X(34), X(8852)}}, {{A, B, C, X(77), X(3100)}}, {{A, B, C, X(84), X(1088)}}, {{A, B, C, X(86), X(282)}}, {{A, B, C, X(90), X(43672)}}, {{A, B, C, X(243), X(2734)}}, {{A, B, C, X(268), X(326)}}, {{A, B, C, X(271), X(52365)}}, {{A, B, C, X(284), X(36740)}}, {{A, B, C, X(294), X(1002)}}, {{A, B, C, X(341), X(7160)}}, {{A, B, C, X(346), X(2346)}}, {{A, B, C, X(596), X(3811)}}, {{A, B, C, X(650), X(39954)}}, {{A, B, C, X(893), X(9398)}}, {{A, B, C, X(949), X(3423)}}, {{A, B, C, X(969), X(1172)}}, {{A, B, C, X(990), X(991)}}, {{A, B, C, X(997), X(6745)}}, {{A, B, C, X(1010), X(13615)}}, {{A, B, C, X(1253), X(1458)}}, {{A, B, C, X(1320), X(56088)}}, {{A, B, C, X(1390), X(40779)}}, {{A, B, C, X(1697), X(3744)}}, {{A, B, C, X(1807), X(9817)}}, {{A, B, C, X(2293), X(4327)}}, {{A, B, C, X(2389), X(29066)}}, {{A, B, C, X(2646), X(17594)}}, {{A, B, C, X(2862), X(52133)}}, {{A, B, C, X(3057), X(3749)}}, {{A, B, C, X(3576), X(9371)}}, {{A, B, C, X(3601), X(3666)}}, {{A, B, C, X(3786), X(51837)}}, {{A, B, C, X(3872), X(3935)}}, {{A, B, C, X(3900), X(28849)}}, {{A, B, C, X(4183), X(36706)}}, {{A, B, C, X(4297), X(12520)}}, {{A, B, C, X(4321), X(4326)}}, {{A, B, C, X(4420), X(4666)}}, {{A, B, C, X(4640), X(19605)}}, {{A, B, C, X(4689), X(13384)}}, {{A, B, C, X(4866), X(41711)}}, {{A, B, C, X(5307), X(10393)}}, {{A, B, C, X(7162), X(44040)}}, {{A, B, C, X(8021), X(13727)}}, {{A, B, C, X(16054), X(23151)}}, {{A, B, C, X(17512), X(33305)}}, {{A, B, C, X(25723), X(36627)}}, {{A, B, C, X(31359), X(44692)}}, {{A, B, C, X(34525), X(51565)}}, {{A, B, C, X(34894), X(36916)}}, {{A, B, C, X(34919), X(52663)}}, {{A, B, C, X(36796), X(42310)}}
X(56098) = barycentric product X(i)*X(j) for these (i, j): {75, 949}, {312, 3423}, {3239, 6183}, {39273, 8}, {45974, 52652}
X(56098) = barycentric quotient X(i)/X(j) for these (i, j): {1, 948}, {6, 2263}, {9, 2550}, {21, 16054}, {41, 37580}, {55, 40131}, {77, 23603}, {220, 28043}, {650, 47123}, {657, 6182}, {949, 1}, {3423, 57}, {6183, 658}, {39273, 7}, {45974, 7146}

X(56099) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(8) AND X(3)

Barycentrics    (a-b-c)*(a^6-a^5*c+2*a^3*c^2*(-b+c)+a*(b-c)^3*c*(b+c)-a^4*(2*b^2-2*b*c+c^2)+(-(b^2*c)+c^3)^2+a^2*(b^4-2*b^3*c+4*b^2*c^2-2*b*c^3-c^4))*(a^6-a^5*b+2*a^3*b^2*(b-c)-a*b*(b-c)^3*(b+c)-a^4*(b^2-2*b*c+2*c^2)+(b^3-b*c^2)^2+a^2*(-b^4-2*b^3*c+4*b^2*c^2-2*b*c^3+c^4)) : :

X(56099) lies on these lines: {3, 318}, {8, 255}, {75, 1804}, {341, 1259}, {346, 2289}, {2193, 2322}, {11109, 36055}, {37094, 40445}, {37727, 51565}, {45392, 52409}

X(56099) = trilinear pole of line {3239, 36054}
X(56099) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2734)}}, {{A, B, C, X(3), X(21)}}, {{A, B, C, X(8), X(75)}}, {{A, B, C, X(271), X(10538)}}, {{A, B, C, X(333), X(7361)}}, {{A, B, C, X(2320), X(41904)}}, {{A, B, C, X(10623), X(43743)}}, {{A, B, C, X(26703), X(52133)}}

X(56100) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(8) AND X(4)

Barycentrics    a*(a-b-c)*(a^4-2*a^3*b+2*a^2*(b-c)*c-(b-c)^3*(b+c)+2*a*b*(b^2-b*c+c^2))*(a^4-2*a^2*b*(b-c)-2*a^3*c+(b-c)^3*(b+c)+2*a*c*(b^2-b*c+c^2)) : :

X(56100) lies on the Feuerbach hyperbola and on these lines: {4, 4511}, {7, 44179}, {78, 80}, {104, 3869}, {200, 43731}, {404, 17097}, {1000, 4861}, {1389, 14923}, {1858, 55961}, {3485, 5555}, {3486, 30513}, {3872, 5559}, {4420, 43734}, {5553, 21740}, {6261, 12119}, {6597, 15829}, {10309, 11415}, {12514, 15446}, {30144, 39599}

X(56100) = X(i)-isoconjugate-of-X(j) for these {i, j}: {34, 37700}, {56, 10573}
X(56100) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 10573}, {11517, 37700}
X(56100) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(78), X(4511)}}, {{A, B, C, X(312), X(2167)}}, {{A, B, C, X(921), X(14987)}}, {{A, B, C, X(1043), X(44179)}}, {{A, B, C, X(1318), X(41505)}}, {{A, B, C, X(1385), X(37533)}}, {{A, B, C, X(1807), X(39167)}}, {{A, B, C, X(3872), X(4861)}}, {{A, B, C, X(6261), X(15500)}}, {{A, B, C, X(6557), X(36100)}}, {{A, B, C, X(6857), X(17519)}}, {{A, B, C, X(24467), X(51379)}}, {{A, B, C, X(37531), X(37611)}}, {{A, B, C, X(40436), X(51565)}}
X(56100) = barycentric quotient X(i)/X(j) for these (i, j): {9, 10573}, {219, 37700}

X(56101) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(8) AND X(7)

Barycentrics    a*(a-b-c)*(a^4-2*a^3*b+2*a^2*(b-c)*c-(b-c)^3*(b+c)+2*a*b*(b^2+c^2))*(a^4-2*a^2*b*(b-c)-2*a^3*c+(b-c)^3*(b+c)+2*a*c*(b^2+c^2)) : :

X(56101) lies on the Feuerbach hyperbola and on these lines: {1, 1259}, {4, 78}, {7, 326}, {9, 51379}, {20, 10309}, {63, 104}, {80, 200}, {84, 5693}, {90, 5692}, {224, 5553}, {294, 34526}, {377, 5555}, {1000, 3872}, {1012, 41389}, {1043, 1896}, {1156, 41228}, {1172, 2327}, {1260, 37533}, {1476, 3868}, {2057, 5587}, {2298, 3553}, {2997, 20895}, {3062, 5538}, {3577, 37569}, {4420, 7319}, {4853, 5559}, {4861, 7320}, {4867, 7284}, {4882, 43731}, {5251, 7162}, {5438, 5665}, {5727, 34918}, {6061, 52380}, {6065, 52377}, {6264, 36922}, {6326, 46435}, {6332, 43728}, {6598, 9581}, {7675, 34919}, {8809, 15394}, {10305, 10884}, {11520, 15179}, {15446, 31424}, {15909, 43166}, {20588, 51506}

X(56101) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 54366}, {34, 18446}, {56, 18391}, {57, 8557}, {278, 19350}, {608, 6350}, {4017, 54442}
X(56101) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 18391}, {9, 54366}, {1145, 1512}, {5452, 8557}, {11517, 18446}, {34961, 54442}
X(56101) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(3), X(37531)}}, {{A, B, C, X(29), X(37248)}}, {{A, B, C, X(63), X(312)}}, {{A, B, C, X(78), X(326)}}, {{A, B, C, X(165), X(5538)}}, {{A, B, C, X(200), X(2750)}}, {{A, B, C, X(268), X(1807)}}, {{A, B, C, X(271), X(1793)}}, {{A, B, C, X(280), X(1257)}}, {{A, B, C, X(282), X(6740)}}, {{A, B, C, X(517), X(37611)}}, {{A, B, C, X(518), X(34526)}}, {{A, B, C, X(759), X(39943)}}, {{A, B, C, X(960), X(3553)}}, {{A, B, C, X(998), X(2316)}}, {{A, B, C, X(1036), X(2259)}}, {{A, B, C, X(1295), X(51497)}}, {{A, B, C, X(3306), X(30608)}}, {{A, B, C, X(3423), X(3478)}}, {{A, B, C, X(3576), X(37569)}}, {{A, B, C, X(3868), X(20895)}}, {{A, B, C, X(4853), X(4861)}}, {{A, B, C, X(4867), X(4873)}}, {{A, B, C, X(7020), X(40431)}}, {{A, B, C, X(7218), X(41432)}}, {{A, B, C, X(14942), X(34525)}}, {{A, B, C, X(17515), X(37358)}}, {{A, B, C, X(18443), X(37533)}}, {{A, B, C, X(30806), X(41228)}}, {{A, B, C, X(36626), X(44692)}}, {{A, B, C, X(40399), X(41514)}}, {{A, B, C, X(51567), X(56098)}}
X(56101) = barycentric product X(i)*X(j) for these (i, j): {55963, 78}
X(56101) = barycentric quotient X(i)/X(j) for these (i, j): {1, 54366}, {9, 18391}, {55, 8557}, {78, 6350}, {212, 19350}, {219, 18446}, {5546, 54442}, {55963, 273}

X(56102) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(8) AND X(33)

Barycentrics    (a-b-c)*(a^2+b^2-2*a*c-2*b*c-c^2)*(a^2-2*a*b-b^2-2*b*c+c^2) : :

X(56102) lies on these lines: {1, 6392}, {2, 968}, {85, 350}, {92, 4207}, {145, 54120}, {189, 10453}, {333, 497}, {346, 4518}, {390, 52133}, {1220, 54291}, {1311, 28847}, {2994, 17135}, {3974, 4102}, {4514, 42030}, {20012, 34527}, {27518, 46880}, {30943, 34234}

X(56102) = trilinear pole of line {4148, 522}
X(56102) = X(i)-isoconjugate-of-X(j) for these {i, j}: {56, 3751}, {109, 50336}, {604, 17316}, {1106, 27549}, {1397, 30758}, {1408, 4078}, {1409, 14013}, {1415, 28846}
X(56102) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 3751}, {11, 50336}, {1146, 28846}, {3161, 17316}, {6552, 27549}, {6741, 48047}
X(56102) = X(i)-Ceva conjugate of X(j) for these {i, j}: {40028, 39721}
X(56102) = X(i)-cross conjugate of X(j) for these {i, j}: {3886, 8}
X(56102) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(17594)}}, {{A, B, C, X(2), X(8)}}, {{A, B, C, X(4), X(24210)}}, {{A, B, C, X(7), X(4451)}}, {{A, B, C, X(9), X(30571)}}, {{A, B, C, X(21), X(33)}}, {{A, B, C, X(42), X(1036)}}, {{A, B, C, X(60), X(39961)}}, {{A, B, C, X(105), X(1096)}}, {{A, B, C, X(225), X(497)}}, {{A, B, C, X(280), X(32932)}}, {{A, B, C, X(281), X(314)}}, {{A, B, C, X(291), X(3680)}}, {{A, B, C, X(310), X(318)}}, {{A, B, C, X(341), X(6384)}}, {{A, B, C, X(346), X(350)}}, {{A, B, C, X(390), X(3790)}}, {{A, B, C, X(522), X(28580)}}, {{A, B, C, X(1002), X(1320)}}, {{A, B, C, X(1043), X(18156)}}, {{A, B, C, X(1219), X(7033)}}, {{A, B, C, X(1738), X(3596)}}, {{A, B, C, X(1929), X(36623)}}, {{A, B, C, X(2321), X(30479)}}, {{A, B, C, X(3254), X(50080)}}, {{A, B, C, X(3424), X(7261)}}, {{A, B, C, X(3702), X(3974)}}, {{A, B, C, X(3886), X(27549)}}, {{A, B, C, X(4391), X(40030)}}, {{A, B, C, X(4651), X(10527)}}, {{A, B, C, X(4720), X(32631)}}, {{A, B, C, X(4876), X(7220)}}, {{A, B, C, X(4900), X(52654)}}, {{A, B, C, X(5552), X(17135)}}, {{A, B, C, X(6598), X(17064)}}, {{A, B, C, X(7018), X(43533)}}, {{A, B, C, X(7080), X(10453)}}, {{A, B, C, X(10449), X(27517)}}, {{A, B, C, X(11604), X(33134)}}, {{A, B, C, X(17751), X(27518)}}, {{A, B, C, X(20007), X(29839)}}, {{A, B, C, X(32929), X(36626)}}, {{A, B, C, X(33131), X(43741)}}, {{A, B, C, X(36798), X(36916)}}, {{A, B, C, X(36910), X(50126)}}, {{A, B, C, X(39967), X(53089)}}
X(56102) = barycentric product X(i)*X(j) for these (i, j): {312, 39954}, {28847, 35519}, {39721, 8}, {40028, 9}
X(56102) = barycentric quotient X(i)/X(j) for these (i, j): {8, 17316}, {9, 3751}, {29, 14013}, {312, 30758}, {346, 27549}, {522, 28846}, {650, 50336}, {2321, 4078}, {3700, 48047}, {28847, 109}, {39721, 7}, {39954, 57}, {40028, 85}

X(56103) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(8) AND X(74)

Barycentrics    (a-b-c)*(a^6-a^4*(2*b^2+c^2)+(-(b^2*c)+c^3)^2+a^2*(b^4+2*b^2*c^2-c^4))*(a^6-a^4*(b^2+2*c^2)+(b^3-b*c^2)^2+a^2*(-b^4+2*b^2*c^2+c^4)) : :

X(56103) lies on these lines: {10, 1331}, {100, 1300}, {281, 5546}, {1441, 6516}, {1793, 52356}, {2321, 4587}, {3701, 4571}, {5504, 38955}, {6757, 25440}, {14624, 14910}, {18878, 35141}

X(56103) = trilinear pole of line {219, 3700}
X(56103) = X(i)-isoconjugate-of-X(j) for these {i, j}: {34, 13754}, {56, 1725}, {57, 3003}, {77, 44084}, {278, 2315}, {403, 603}, {604, 3580}, {1400, 18609}, {1414, 21731}, {4017, 15329}, {14264, 51654}, {51651, 52451}
X(56103) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 1725}, {3161, 3580}, {5452, 3003}, {6739, 113}, {6741, 55121}, {7952, 403}, {11517, 13754}, {34961, 15329}, {40582, 18609}, {40608, 21731}
X(56103) = intersection, other than A, B, C, of circumconics {{A, B, C, X(8), X(10)}}, {{A, B, C, X(21), X(74)}}, {{A, B, C, X(69), X(36626)}}, {{A, B, C, X(98), X(52380)}}, {{A, B, C, X(100), X(1331)}}, {{A, B, C, X(312), X(52412)}}, {{A, B, C, X(1265), X(5552)}}, {{A, B, C, X(1300), X(36053)}}, {{A, B, C, X(1320), X(43655)}}, {{A, B, C, X(2341), X(2372)}}, {{A, B, C, X(8759), X(32706)}}, {{A, B, C, X(15742), X(52409)}}, {{A, B, C, X(56099), X(56100)}}
X(56103) = barycentric product X(i)*X(j) for these (i, j): {312, 36053}, {1300, 345}, {2986, 8}, {5504, 7017}, {14910, 3596}, {15328, 645}, {15421, 36797}, {15627, 52552}, {18878, 3700}, {40423, 7359}, {40832, 55}, {52355, 687}
X(56103) = barycentric quotient X(i)/X(j) for these (i, j): {8, 3580}, {9, 1725}, {21, 18609}, {55, 3003}, {212, 2315}, {219, 13754}, {281, 403}, {607, 44084}, {1300, 278}, {2986, 7}, {3700, 55121}, {3709, 21731}, {5504, 222}, {5546, 15329}, {7017, 44138}, {7359, 113}, {10420, 4565}, {14910, 56}, {15328, 7178}, {15421, 17094}, {15454, 6357}, {15627, 14264}, {15628, 52451}, {18878, 4573}, {36053, 57}, {36797, 16237}, {40832, 6063}, {52355, 6334}

X(56104) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(8) AND X(75)

Barycentrics    a*(a-b-c)*(a^4-a^3*b-b^4+b^3*c-b*c^3+c^4-a^2*c*(b+2*c)+a*(b^3-b*c^2))*(a^4+b^4-a^3*c-b^3*c+b*c^3-c^4-a^2*b*(2*b+c)+a*(-(b^2*c)+c^3)) : :

X(56104) lies on these lines: {1, 5125}, {2, 1807}, {3, 3218}, {77, 17078}, {78, 32851}, {219, 4511}, {284, 17515}, {296, 12739}, {945, 21740}, {1036, 45230}, {1794, 22836}, {2167, 37525}, {3152, 7100}, {37591, 40442}

X(56104) = trilinear pole of line {652, 3738}
X(56104) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 37695}, {56, 3419}, {57, 54324}, {65, 36011}
X(56104) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 3419}, {9, 37695}, {5452, 54324}, {40602, 36011}
X(56104) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3)}}, {{A, B, C, X(2), X(2167)}}, {{A, B, C, X(4), X(44687)}}, {{A, B, C, X(7), X(18444)}}, {{A, B, C, X(8), X(5174)}}, {{A, B, C, X(21), X(75)}}, {{A, B, C, X(60), X(977)}}, {{A, B, C, X(104), X(273)}}, {{A, B, C, X(270), X(51223)}}, {{A, B, C, X(281), X(44693)}}, {{A, B, C, X(318), X(943)}}, {{A, B, C, X(388), X(45230)}}, {{A, B, C, X(522), X(15175)}}, {{A, B, C, X(596), X(6734)}}, {{A, B, C, X(765), X(30513)}}, {{A, B, C, X(944), X(21740)}}, {{A, B, C, X(1034), X(7320)}}, {{A, B, C, X(1098), X(43740)}}, {{A, B, C, X(1320), X(2287)}}, {{A, B, C, X(1870), X(3431)}}, {{A, B, C, X(2218), X(7105)}}, {{A, B, C, X(2646), X(37591)}}, {{A, B, C, X(5882), X(40257)}}, {{A, B, C, X(15446), X(24475)}}, {{A, B, C, X(26877), X(40836)}}, {{A, B, C, X(27385), X(30144)}}, {{A, B, C, X(51567), X(56098)}}
X(56104) = barycentric product X(i)*X(j) for these (i, j): {312, 3418}
X(56104) = barycentric quotient X(i)/X(j) for these (i, j): {1, 37695}, {9, 3419}, {55, 54324}, {284, 36011}, {3418, 57}

X(56105) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(8) AND X(80)

Barycentrics    a*(a-b-c)*(a^4-2*a^3*b+2*a^2*(b-c)*c-(b-c)^3*(b+c)+a*b*(2*b^2-3*b*c+2*c^2))*(a^4-2*a^2*b*(b-c)-2*a^3*c+(b-c)^3*(b+c)+a*c*(2*b^2-3*b*c+2*c^2)) : :

X(56105) lies on the Feuerbach hyperbola and on these lines: {1, 4996}, {4, 6224}, {21, 30538}, {78, 43731}, {79, 39778}, {80, 3814}, {84, 9964}, {100, 1389}, {104, 14988}, {943, 51683}, {2802, 21398}, {3218, 56036}, {3255, 30284}, {3878, 15446}, {4861, 5559}, {5553, 5731}, {5560, 45764}, {11604, 12740}

X(56105) = X(i)-isoconjugate-of-X(j) for these {i, j}: {56, 41684}
X(56105) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 41684}
X(56105) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(3), X(46920)}}, {{A, B, C, X(1411), X(18771)}}, {{A, B, C, X(1807), X(6265)}}, {{A, B, C, X(1809), X(6224)}}, {{A, B, C, X(2804), X(14988)}}, {{A, B, C, X(3218), X(4997)}}, {{A, B, C, X(4511), X(4996)}}, {{A, B, C, X(6065), X(42064)}}, {{A, B, C, X(12611), X(51379)}}
X(56105) = barycentric product X(i)*X(j) for these (i, j): {43355, 4391}
X(56105) = barycentric quotient X(i)/X(j) for these (i, j): {9, 41684}, {43355, 651}

X(56106) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(8) AND X(84)

Barycentrics    a*(a-b-c)*(2*a^4-3*a^3*c+(b-c)^2*(2*b^2+b*c-c^2)-a^2*(4*b^2-3*b*c+c^2)+a*c*(3*b^2-2*b*c+3*c^2))*(2*a^4-3*a^3*b-(b-c)^2*(b^2-b*c-2*c^2)+a*b*(3*b^2-2*b*c+3*c^2)-a^2*(b^2-3*b*c+4*c^2)) : :

X(56106) lies on the Feuerbach hyperbola and on these lines: {4, 5440}, {20, 46435}, {78, 38271}, {80, 7080}, {84, 4511}, {104, 5730}, {1259, 1320}, {4313, 30513}, {4420, 55931}, {4861, 56038}, {5560, 6745}, {6736, 43731}, {10309, 50371}

X(56106) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(63), X(5748)}}, {{A, B, C, X(78), X(27383)}}, {{A, B, C, X(280), X(40436)}}, {{A, B, C, X(1259), X(5440)}}, {{A, B, C, X(1319), X(33963)}}, {{A, B, C, X(4511), X(7080)}}, {{A, B, C, X(10310), X(50371)}}

X(56107) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(8) AND X(86)

Barycentrics    (a+b)*(a-b-c)*(a+c)*(a^2-4*a*b+b^2-c^2)*(a^2-b^2-4*a*c+c^2) : :

X(56107) lies on these lines: {21, 145}, {29, 936}, {86, 7190}, {333, 36596}, {376, 3426}, {452, 14556}, {1010, 3615}, {1043, 44720}, {1098, 30606}, {2287, 3161}, {4234, 6580}, {6740, 51564}, {28193, 51705}

X(56107) = trilinear pole of line {1021, 4521}
X(56107) = X(i)-isoconjugate-of-X(j) for these {i, j}: {56, 3753}, {65, 999}, {213, 17079}, {604, 4054}, {1042, 3872}, {1400, 3306}, {1402, 42697}, {1425, 17519}, {1880, 22129}, {3668, 52428}, {4017, 35281}
X(56107) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 3753}, {3161, 4054}, {6626, 17079}, {34961, 35281}, {40582, 3306}, {40602, 999}, {40605, 42697}, {40625, 21183}
X(56107) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3295)}}, {{A, B, C, X(8), X(145)}}, {{A, B, C, X(9), X(956)}}, {{A, B, C, X(21), X(29)}}, {{A, B, C, X(78), X(268)}}, {{A, B, C, X(79), X(15174)}}, {{A, B, C, X(80), X(37728)}}, {{A, B, C, X(90), X(40446)}}, {{A, B, C, X(280), X(5936)}}, {{A, B, C, X(332), X(1793)}}, {{A, B, C, X(333), X(4560)}}, {{A, B, C, X(1000), X(36596)}}, {{A, B, C, X(1010), X(11107)}}, {{A, B, C, X(1065), X(15175)}}, {{A, B, C, X(1067), X(15446)}}, {{A, B, C, X(1222), X(32635)}}, {{A, B, C, X(2320), X(14942)}}, {{A, B, C, X(2370), X(40417)}}, {{A, B, C, X(3478), X(7220)}}, {{A, B, C, X(4102), X(39700)}}, {{A, B, C, X(7361), X(40435)}}, {{A, B, C, X(28194), X(51705)}}, {{A, B, C, X(31359), X(36626)}}, {{A, B, C, X(32013), X(36796)}}, {{A, B, C, X(34446), X(52429)}}, {{A, B, C, X(36910), X(42285)}}, {{A, B, C, X(39702), X(43745)}}, {{A, B, C, X(39707), X(43740)}}, {{A, B, C, X(51567), X(56098)}}
X(56107) = barycentric product X(i)*X(j) for these (i, j): {29, 30680}, {274, 52429}, {1000, 333}, {4560, 51564}, {16704, 36596}, {28660, 34446}, {36916, 86}
X(56107) = barycentric quotient X(i)/X(j) for these (i, j): {8, 4054}, {9, 3753}, {21, 3306}, {86, 17079}, {283, 22129}, {284, 999}, {314, 20925}, {333, 42697}, {1000, 226}, {1043, 28808}, {2287, 3872}, {2326, 17519}, {4560, 21183}, {5235, 36595}, {5546, 35281}, {30680, 307}, {34446, 1400}, {36596, 4080}, {36916, 10}, {51564, 4552}, {52429, 37}

X(56108) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(8) AND X(90)

Barycentrics    a*(a-b-c)*(2*a^4-3*a^3*c+(b-c)^2*(2*b^2+b*c-c^2)-a^2*(4*b^2-3*b*c+c^2)+a*c*(3*b^2-4*b*c+3*c^2))*(2*a^4-3*a^3*b-(b-c)^2*(b^2-b*c-2*c^2)+a*b*(3*b^2-4*b*c+3*c^2)-a^2*(b^2-3*b*c+4*c^2)) : :

X(56108) lies on the Feuerbach hyperbola and on these lines: {80, 5552}, {90, 4511}, {1320, 10965}, {1389, 10679}, {4188, 17098}, {5553, 11415}, {5560, 27385}, {6735, 43731}, {11509, 17097}, {45230, 55961}

X(56108) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(280), X(4511)}}, {{A, B, C, X(1319), X(10965)}}, {{A, B, C, X(1385), X(10679)}}, {{A, B, C, X(2646), X(11509)}}, {{A, B, C, X(2745), X(11248)}}, {{A, B, C, X(8686), X(41505)}}, {{A, B, C, X(10269), X(33596)}}, {{A, B, C, X(24927), X(37622)}}, {{A, B, C, X(36100), X(38255)}}

X(56109) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(8) AND X(98)

Barycentrics    a^2*(a-b-c)*(a^4+b^4-b^2*c^2+2*c^4-a^2*(2*b^2+c^2))*(a^4+2*b^4-b^2*c^2+c^4-a^2*(b^2+2*c^2)) : :

X(56109) lies on these lines: {42, 1331}, {65, 6516}, {100, 1824}, {210, 4571}, {607, 5546}, {1334, 4587}, {1857, 36797}, {8781, 13576}, {10425, 28471}, {35142, 54952}

X(56109) = trilinear pole of line {219, 3709}
X(56109) = X(i)-isoconjugate-of-X(j) for these {i, j}: {7, 8772}, {34, 3564}, {56, 1733}, {57, 230}, {77, 460}, {85, 1692}, {273, 52144}, {603, 44145}, {604, 51481}, {1414, 55122}, {4017, 4226}, {4625, 42663}, {7182, 44099}, {14265, 51651}, {36875, 51654}, {51653, 52450}
X(56109) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 1733}, {3161, 51481}, {5452, 230}, {7952, 44145}, {11517, 3564}, {34961, 4226}, {40608, 55122}, {50440, 114}
X(56109) = X(i)-Ceva conjugate of X(j) for these {i, j}: {8773, 2987}
X(56109) = intersection, other than A, B, C, of circumconics {{A, B, C, X(8), X(42)}}, {{A, B, C, X(9), X(7095)}}, {{A, B, C, X(21), X(98)}}, {{A, B, C, X(60), X(893)}}, {{A, B, C, X(100), X(1331)}}, {{A, B, C, X(345), X(42700)}}, {{A, B, C, X(1252), X(4518)}}, {{A, B, C, X(1320), X(53873)}}, {{A, B, C, X(2311), X(28482)}}, {{A, B, C, X(2337), X(30479)}}, {{A, B, C, X(2339), X(24624)}}, {{A, B, C, X(3563), X(36051)}}, {{A, B, C, X(4451), X(7054)}}, {{A, B, C, X(56098), X(56100)}}
X(56109) = barycentric product X(i)*X(j) for these (i, j): {55, 8781}, {219, 35142}, {281, 43705}, {312, 36051}, {345, 3563}, {2987, 8}, {8773, 9}, {10425, 3700}, {15627, 36891}, {15628, 52091}, {32654, 3596}, {32697, 52355}, {35364, 645}, {36105, 8611}, {42065, 7017}
X(56109) = barycentric quotient X(i)/X(j) for these (i, j): {8, 51481}, {9, 1733}, {41, 8772}, {55, 230}, {219, 3564}, {281, 44145}, {607, 460}, {2175, 1692}, {2987, 7}, {3563, 278}, {3709, 55122}, {5546, 4226}, {5547, 52450}, {8773, 85}, {8781, 6063}, {10425, 4573}, {15627, 36875}, {15628, 14265}, {32654, 56}, {34157, 43034}, {35142, 331}, {35364, 7178}, {36051, 57}, {42065, 222}, {43705, 348}, {52425, 52144}

X(56110) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(8) AND X(103)

Barycentrics    (a-b-c)*(a^5-a^4*b+(b-c)^2*c^2*(b+c)-a^3*(b^2+c^2)+a^2*(b^3+2*b*c^2-c^3))*(a^5-a^4*c+b^2*(b-c)^2*(b+c)-a^3*(b^2+c^2)+a^2*(-b^3+2*b^2*c+c^3)) : :

X(56110) lies on these lines: {2, 1331}, {8, 4587}, {29, 5546}, {55, 55019}, {85, 404}, {92, 100}, {312, 4571}, {1259, 34387}, {1311, 35182}, {1952, 4511}, {7360, 18359}, {10405, 54233}, {27506, 41791}

X(56110) = trilinear pole of line {219, 522}
X(56110) = X(i)-isoconjugate-of-X(j) for these {i, j}: {34, 916}, {56, 1736}, {57, 8608}, {278, 2253}, {604, 48381}, {1415, 55125}, {1456, 54232}, {4017, 4243}
X(56110) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 1736}, {1146, 55125}, {3161, 48381}, {5452, 8608}, {11517, 916}, {34961, 4243}, {50441, 118}
X(56110) = X(i)-cross conjugate of X(j) for these {i, j}: {31897, 318}
X(56110) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(8)}}, {{A, B, C, X(21), X(103)}}, {{A, B, C, X(95), X(2287)}}, {{A, B, C, X(98), X(294)}}, {{A, B, C, X(100), X(1331)}}, {{A, B, C, X(272), X(39943)}}, {{A, B, C, X(404), X(1261)}}, {{A, B, C, X(1320), X(36122)}}, {{A, B, C, X(2322), X(40424)}}, {{A, B, C, X(3615), X(32021)}}, {{A, B, C, X(4511), X(7360)}}, {{A, B, C, X(7045), X(41905)}}, {{A, B, C, X(36796), X(37202)}}, {{A, B, C, X(56099), X(56106)}}
X(56110) = barycentric product X(i)*X(j) for these (i, j): {345, 917}, {2989, 8}, {35182, 35519}, {35518, 36107}
X(56110) = barycentric quotient X(i)/X(j) for these (i, j): {8, 48381}, {9, 1736}, {55, 8608}, {212, 2253}, {219, 916}, {522, 55125}, {917, 278}, {2338, 54232}, {2989, 7}, {5546, 4243}, {32699, 32674}, {35182, 109}, {36107, 108}, {40869, 118}, {54233, 43035}

X(56111) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(8) AND X(105)

Barycentrics    a*(a-b-c)*(a^3-a^2*c+a*(b^2-2*b*c-c^2)+c*(b^2+c^2))*(a^3-a^2*b+b*(b^2+c^2)+a*(-b^2-2*b*c+c^2)) : :

X(56111) lies on these lines: {25, 100}, {31, 1331}, {41, 4587}, {55, 4126}, {56, 6337}, {105, 3263}, {884, 50333}, {2204, 5546}, {4518, 28071}, {6187, 49991}

X(56111) = trilinear pole of line {219, 3063}
X(56111) = X(i)-isoconjugate-of-X(j) for these {i, j}: {34, 34381}, {56, 1738}, {57, 3290}, {109, 23770}, {120, 1416}, {1400, 16752}, {1412, 21956}, {1457, 51832}, {1458, 14267}, {1462, 17464}, {4017, 4236}, {20504, 32735}, {43924, 53358}
X(56111) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 1738}, {11, 23770}, {4904, 55137}, {5452, 3290}, {11517, 34381}, {34961, 4236}, {40582, 16752}, {40599, 21956}, {40609, 120}
X(56111) = X(i)-cross conjugate of X(j) for these {i, j}: {926, 644}
X(56111) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3749)}}, {{A, B, C, X(8), X(1280)}}, {{A, B, C, X(9), X(291)}}, {{A, B, C, X(21), X(25)}}, {{A, B, C, X(88), X(2339)}}, {{A, B, C, X(100), X(1331)}}, {{A, B, C, X(200), X(56102)}}, {{A, B, C, X(285), X(38251)}}, {{A, B, C, X(345), X(17776)}}, {{A, B, C, X(753), X(33635)}}, {{A, B, C, X(943), X(15323)}}, {{A, B, C, X(985), X(36630)}}, {{A, B, C, X(1252), X(26703)}}, {{A, B, C, X(1320), X(1862)}}, {{A, B, C, X(1792), X(6337)}}, {{A, B, C, X(1821), X(36799)}}, {{A, B, C, X(2287), X(7155)}}, {{A, B, C, X(3263), X(3693)}}, {{A, B, C, X(3685), X(8299)}}, {{A, B, C, X(4076), X(34894)}}, {{A, B, C, X(4126), X(32635)}}, {{A, B, C, X(4511), X(49991)}}, {{A, B, C, X(4723), X(14191)}}, {{A, B, C, X(4876), X(7281)}}, {{A, B, C, X(14947), X(36122)}}, {{A, B, C, X(36798), X(52663)}}
X(56111) = barycentric product X(i)*X(j) for these (i, j): {2991, 8}, {15344, 345}, {34159, 36796}, {35574, 650}
X(56111) = barycentric quotient X(i)/X(j) for these (i, j): {9, 1738}, {21, 16752}, {55, 3290}, {210, 21956}, {219, 34381}, {294, 14267}, {644, 53358}, {650, 23770}, {2340, 17464}, {2991, 7}, {3693, 120}, {3717, 20431}, {5546, 4236}, {15344, 278}, {15382, 1462}, {34159, 241}, {35574, 4554}, {52663, 51832}

X(56112) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(8) AND X(109)

Barycentrics    (a-b)*(a-c)*(a-b-c)*(a^3+b^3+a*(b-c)*c-b*c^2)*(a^3-b^2*c+c^3+a*b*(-b+c)) : :

X(56112) lies on these lines: {100, 7461}, {1331, 3952}, {1793, 52409}, {1808, 4518}, {1810, 13478}, {1811, 2217}, {1897, 36108}, {3239, 32739}, {4391, 53279}, {4587, 30730}, {5552, 10570}, {53658, 54951}

X(56112) = trilinear pole of line {219, 2321}
X(56112) = X(i)-isoconjugate-of-X(j) for these {i, j}: {56, 21189}, {57, 6589}, {513, 10571}, {573, 3669}, {649, 17080}, {1019, 40590}, {1396, 52310}, {1400, 16754}, {1461, 38345}, {3185, 3676}, {3869, 43924}, {4017, 4225}, {7203, 22276}, {32714, 47411}, {34242, 53314}
X(56112) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 21189}, {2968, 124}, {5375, 17080}, {5452, 6589}, {7358, 34588}, {34961, 4225}, {35508, 38345}, {39026, 10571}, {40582, 16754}
X(56112) = X(i)-cross conjugate of X(j) for these {i, j}: {4557, 644}
X(56112) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(32704)}}, {{A, B, C, X(8), X(1897)}}, {{A, B, C, X(21), X(109)}}, {{A, B, C, X(55), X(32739)}}, {{A, B, C, X(100), X(1331)}}, {{A, B, C, X(162), X(9056)}}, {{A, B, C, X(333), X(43190)}}, {{A, B, C, X(643), X(835)}}, {{A, B, C, X(644), X(7256)}}, {{A, B, C, X(931), X(5549)}}, {{A, B, C, X(1309), X(13138)}}, {{A, B, C, X(3161), X(43290)}}, {{A, B, C, X(3699), X(3952)}}, {{A, B, C, X(4076), X(46649)}}, {{A, B, C, X(5552), X(17780)}}, {{A, B, C, X(8706), X(31343)}}, {{A, B, C, X(9057), X(52133)}}, {{A, B, C, X(26704), X(36050)}}, {{A, B, C, X(27506), X(46541)}}, {{A, B, C, X(36037), X(41906)}}
X(56112) = barycentric product X(i)*X(j) for these (i, j): {312, 36050}, {2217, 646}, {2321, 54951}, {2995, 644}, {10570, 190}, {13478, 3699}, {15232, 645}, {15386, 52622}, {19607, 3952}, {19608, 8707}, {26704, 345}, {32653, 3596}, {40160, 7256}, {44765, 8}
X(56112) = barycentric quotient X(i)/X(j) for these (i, j): {9, 21189}, {21, 16754}, {55, 6589}, {100, 17080}, {101, 10571}, {644, 3869}, {2217, 3669}, {2318, 52310}, {2995, 24002}, {3239, 124}, {3699, 4417}, {3900, 38345}, {3939, 573}, {4069, 21078}, {4557, 40590}, {5546, 4225}, {10570, 514}, {13478, 3676}, {15232, 7178}, {15386, 1461}, {19607, 7192}, {19608, 3004}, {26704, 278}, {32653, 56}, {36050, 57}, {44765, 7}, {54951, 1434}

X(56113) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(8) AND X(145)

Barycentrics    a*(a^3+b^3-3*b^2*c-3*b*c^2+c^3-a^2*(3*b+c)-a*(3*b^2-10*b*c+c^2))*(a^3+b^3-3*b^2*c-3*b*c^2+c^3-a^2*(b+3*c)-a*(b^2-10*b*c+3*c^2)) : :

X(56113) lies on these lines: {1, 42020}, {6, 38496}, {34, 38460}, {56, 3880}, {106, 11512}, {269, 1266}, {341, 1120}, {522, 37627}, {2191, 4861}, {3445, 3872}, {19860, 41436}

X(56113) = X(i)-cross conjugate of X(j) for these {i, j}: {17648, 8}
X(56113) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(6)}}, {{A, B, C, X(8), X(36846)}}, {{A, B, C, X(21), X(145)}}, {{A, B, C, X(78), X(38460)}}, {{A, B, C, X(90), X(519)}}, {{A, B, C, X(280), X(1320)}}, {{A, B, C, X(341), X(522)}}, {{A, B, C, X(1280), X(1392)}}, {{A, B, C, X(2339), X(42360)}}, {{A, B, C, X(3241), X(19860)}}, {{A, B, C, X(3577), X(39702)}}, {{A, B, C, X(3811), X(22837)}}, {{A, B, C, X(3870), X(4861)}}, {{A, B, C, X(4666), X(20057)}}, {{A, B, C, X(7131), X(39456)}}, {{A, B, C, X(8056), X(38496)}}, {{A, B, C, X(21398), X(24858)}}, {{A, B, C, X(36795), X(39694)}}

X(56114) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(9) AND X(7)

Barycentrics    a*(a-b-c)*(2*a^3-(b-2*c)*(b-c)^2-a^2*(5*b+2*c)+a*(4*b^2+6*b*c-2*c^2))*(2*a^3+(b-c)^2*(2*b-c)-a^2*(2*b+5*c)+a*(-2*b^2+6*b*c+4*c^2)) : :

X(56114) lies on the Feuerbach hyperbola and on these lines: {1, 25076}, {7, 3689}, {480, 1320}, {518, 55921}, {1000, 18230}, {3306, 10390}, {3935, 55922}, {4105, 23838}, {5328, 6601}, {7091, 30318}

X(56114) = X(i)-isoconjugate-of-X(j) for these {i, j}: {56, 31146}
X(56114) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 31146}
X(56114) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(480), X(3689)}}, {{A, B, C, X(765), X(56088)}}, {{A, B, C, X(1445), X(5328)}}, {{A, B, C, X(3306), X(18230)}}
X(56114) = barycentric quotient X(i)/X(j) for these (i, j): {9, 31146}

X(56115) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(9) AND X(21)

Barycentrics    a*(a-b-c)*(a+4*b+c)*(a+b+4*c) : :

X(56115) lies on the Feuerbach hyperbola and on these lines: {1, 4015}, {2, 18490}, {4, 4678}, {7, 11237}, {10, 5557}, {21, 3689}, {79, 4691}, {80, 4669}, {100, 51570}, {104, 17502}, {210, 1320}, {256, 49984}, {314, 4723}, {495, 3296}, {517, 14496}, {519, 13602}, {941, 16675}, {960, 56091}, {1000, 15170}, {1156, 15481}, {1392, 5289}, {2298, 16669}, {2320, 3711}, {2478, 15998}, {2551, 43745}, {3036, 11604}, {3254, 24393}, {3255, 6735}, {3617, 43733}, {3626, 17501}, {3679, 5561}, {3680, 3876}, {3877, 4900}, {3885, 31509}, {3895, 4866}, {4041, 23838}, {4701, 5559}, {5551, 50237}, {5558, 19877}, {5686, 34919}, {7320, 20053}, {10266, 21677}, {10308, 16139}, {15180, 54391}, {17547, 42819}, {30329, 45834}

X(56115) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 4031}, {7, 21747}, {56, 551}, {57, 16666}, {101, 30722}, {109, 28209}, {278, 22357}, {604, 24589}, {1014, 21806}, {1106, 3902}, {1400, 26860}, {1404, 42026}, {1407, 3707}, {1408, 4714}, {2163, 39782}, {4781, 43924}
X(56115) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 551}, {9, 4031}, {11, 28209}, {1015, 30722}, {3161, 24589}, {5452, 16666}, {6552, 3902}, {24771, 3707}, {40582, 26860}, {40587, 39782}
X(56115) = X(i)-Ceva conjugate of X(j) for these {i, j}: {55955, 40434}
X(56115) = X(i)-cross conjugate of X(j) for these {i, j}: {4711, 8}, {4814, 644}
X(56115) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(10), X(4015)}}, {{A, B, C, X(29), X(17536)}}, {{A, B, C, X(78), X(4678)}}, {{A, B, C, X(210), X(1261)}}, {{A, B, C, X(333), X(37222)}}, {{A, B, C, X(391), X(3895)}}, {{A, B, C, X(517), X(17502)}}, {{A, B, C, X(521), X(28212)}}, {{A, B, C, X(958), X(16675)}}, {{A, B, C, X(960), X(16669)}}, {{A, B, C, X(1807), X(38138)}}, {{A, B, C, X(2160), X(46187)}}, {{A, B, C, X(2287), X(17271)}}, {{A, B, C, X(2316), X(41432)}}, {{A, B, C, X(3701), X(4662)}}, {{A, B, C, X(3872), X(31145)}}, {{A, B, C, X(3876), X(44720)}}, {{A, B, C, X(3902), X(4711)}}, {{A, B, C, X(4511), X(4669)}}, {{A, B, C, X(4701), X(4861)}}, {{A, B, C, X(4853), X(20053)}}, {{A, B, C, X(4882), X(19877)}}, {{A, B, C, X(5289), X(16885)}}, {{A, B, C, X(6603), X(15481)}}, {{A, B, C, X(6605), X(36590)}}, {{A, B, C, X(7081), X(49984)}}, {{A, B, C, X(8686), X(9353)}}, {{A, B, C, X(17125), X(52133)}}, {{A, B, C, X(52409), X(55076)}}
X(56115) = barycentric product X(i)*X(j) for these (i, j): {21, 27797}, {312, 41434}, {28210, 4391}, {40434, 8}, {55955, 9}
X(56115) = barycentric quotient X(i)/X(j) for these (i, j): {1, 4031}, {8, 24589}, {9, 551}, {21, 26860}, {41, 21747}, {45, 39782}, {55, 16666}, {200, 3707}, {212, 22357}, {346, 3902}, {513, 30722}, {644, 4781}, {650, 28209}, {1320, 42026}, {1334, 21806}, {2321, 4714}, {3711, 16590}, {4578, 30727}, {4873, 4793}, {4895, 14435}, {27797, 1441}, {28210, 651}, {40434, 7}, {41434, 57}, {55955, 85}

X(56116) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(9) AND X(55)

Barycentrics    a*(a-b-c)*(a*(b-2*c)-2*b*c)*(2*a*b-a*c+2*b*c) : :

X(56116) lies on these lines: {6, 750}, {9, 4009}, {55, 4390}, {57, 7223}, {649, 17119}, {673, 1150}, {893, 17599}, {909, 45145}, {956, 2291}, {2161, 5282}, {2258, 3745}, {2316, 37658}, {2319, 4042}, {2364, 3684}, {3711, 7077}, {4003, 16975}, {9319, 16506}, {16704, 42302}, {21061, 41441}

X(56116) = trilinear pole of line {663, 4526}
X(56116) = X(i)-isoconjugate-of-X(j) for these {i, j}: {7, 54981}, {56, 4664}, {57, 3240}, {109, 4776}, {651, 29350}
X(56116) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 4664}, {11, 4776}, {5452, 3240}, {38991, 29350}
X(56116) = X(i)-Ceva conjugate of X(j) for these {i, j}: {36871, 55919}
X(56116) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(9)}}, {{A, B, C, X(8), X(650)}}, {{A, B, C, X(171), X(17599)}}, {{A, B, C, X(200), X(16833)}}, {{A, B, C, X(210), X(30711)}}, {{A, B, C, X(220), X(1021)}}, {{A, B, C, X(750), X(1320)}}, {{A, B, C, X(940), X(3745)}}, {{A, B, C, X(956), X(6603)}}, {{A, B, C, X(996), X(4413)}}, {{A, B, C, X(2053), X(7252)}}, {{A, B, C, X(3218), X(5282)}}, {{A, B, C, X(3684), X(3711)}}, {{A, B, C, X(3689), X(16704)}}, {{A, B, C, X(4003), X(37540)}}, {{A, B, C, X(4876), X(30608)}}, {{A, B, C, X(5289), X(5291)}}, {{A, B, C, X(7050), X(13478)}}, {{A, B, C, X(8611), X(52388)}}, {{A, B, C, X(16788), X(34522)}}
X(56116) = barycentric product X(i)*X(j) for these (i, j): {1, 56077}, {29351, 522}, {36871, 9}, {37209, 650}, {55919, 8}
X(56116) = barycentric quotient X(i)/X(j) for these (i, j): {9, 4664}, {41, 54981}, {55, 3240}, {650, 4776}, {663, 29350}, {29351, 664}, {36871, 85}, {37209, 4554}, {55919, 7}, {56077, 75}

X(56117) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(9) AND X(80)

Barycentrics    a*(a-b-c)*(2*a^4-3*a^3*c+(b-c)^2*(2*b^2+b*c-c^2)-a^2*(4*b^2-2*b*c+c^2)+a*c*(2*b^2-b*c+3*c^2))*(2*a^4-3*a^3*b-(b-c)^2*(b^2-b*c-2*c^2)+a*b*(3*b^2-b*c+2*c^2)-a^2*(b^2-2*b*c+4*c^2)) : :

X(56117) lies on the Feuerbach hyperbola and on these lines: {4, 5660}, {7, 214}, {80, 3689}, {100, 55924}, {104, 4867}, {1000, 26726}, {2346, 51506}, {3062, 6326}, {3577, 5541}, {5561, 9945}, {5692, 55918}, {14217, 15909}, {23838, 53285}

X(56117) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(214), X(3689)}}, {{A, B, C, X(1807), X(5660)}}, {{A, B, C, X(4511), X(36910)}}, {{A, B, C, X(4867), X(51362)}}, {{A, B, C, X(5537), X(50371)}}

X(56118) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(9) AND X(86)

Barycentrics    (a-b-c)*(a^2+b*(b-c)-a*(2*b+c))*(a^2+c*(-b+c)-a*(b+2*c)) : :

X(56118) lies on these lines: {8, 344}, {69, 10509}, {75, 200}, {86, 2340}, {190, 3059}, {319, 6606}, {341, 3886}, {346, 3996}, {1043, 3717}, {1170, 1219}, {1222, 6737}, {1229, 3699}, {2321, 6559}, {2370, 53243}, {3935, 25001}, {4360, 28043}, {4687, 42310}, {4847, 17263}, {7172, 16992}, {16284, 42311}, {17295, 30620}, {20070, 22334}, {28057, 42696}, {28133, 32089}, {47487, 51565}

X(56118) = isotomic conjugate of X(10481)
X(56118) = trilinear pole of line {3239, 28058}
X(56118) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 1418}, {31, 10481}, {34, 22053}, {56, 354}, {57, 1475}, {77, 40983}, {109, 48151}, {142, 604}, {184, 53237}, {269, 2293}, {279, 20229}, {667, 35312}, {738, 8012}, {934, 2488}, {1014, 52020}, {1042, 17194}, {1106, 4847}, {1119, 22079}, {1212, 1407}, {1229, 52410}, {1333, 52023}, {1397, 20880}, {1400, 18164}, {1402, 17169}, {1408, 3925}, {1409, 53238}, {1412, 21808}, {1415, 21104}, {1417, 51463}, {1461, 21127}, {1827, 7053}, {1855, 7099}, {2175, 53242}, {2199, 13156}, {3059, 7023}, {3669, 35326}, {4617, 10581}, {6608, 6614}, {7366, 51972}, {23599, 32739}, {35338, 43924}, {52635, 53241}
X(56118) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 354}, {2, 10481}, {9, 1418}, {11, 48151}, {37, 52023}, {1146, 21104}, {2968, 6362}, {3161, 142}, {5452, 1475}, {6552, 4847}, {6600, 2293}, {6631, 35312}, {6741, 55282}, {11517, 22053}, {14714, 2488}, {23050, 1827}, {24771, 1212}, {35508, 21127}, {40582, 18164}, {40593, 53242}, {40599, 21808}, {40605, 17169}, {40619, 23599}, {52871, 51463}
X(56118) = X(i)-cross conjugate of X(j) for these {i, j}: {4130, 190}, {4391, 3699}, {6605, 32008}
X(56118) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3303)}}, {{A, B, C, X(2), X(18230)}}, {{A, B, C, X(6), X(7220)}}, {{A, B, C, X(7), X(8236)}}, {{A, B, C, X(8), X(75)}}, {{A, B, C, X(9), X(86)}}, {{A, B, C, X(10), X(6743)}}, {{A, B, C, X(29), X(5047)}}, {{A, B, C, X(55), X(40433)}}, {{A, B, C, X(69), X(30681)}}, {{A, B, C, X(82), X(294)}}, {{A, B, C, X(200), X(480)}}, {{A, B, C, X(210), X(18082)}}, {{A, B, C, X(281), X(1268)}}, {{A, B, C, X(312), X(344)}}, {{A, B, C, X(313), X(2321)}}, {{A, B, C, X(314), X(4076)}}, {{A, B, C, X(333), X(3996)}}, {{A, B, C, X(522), X(39710)}}, {{A, B, C, X(765), X(2287)}}, {{A, B, C, X(903), X(6601)}}, {{A, B, C, X(1120), X(4900)}}, {{A, B, C, X(1220), X(4866)}}, {{A, B, C, X(1229), X(4391)}}, {{A, B, C, X(1320), X(56107)}}, {{A, B, C, X(2346), X(6605)}}, {{A, B, C, X(3059), X(4130)}}, {{A, B, C, X(3522), X(20070)}}, {{A, B, C, X(4102), X(7017)}}, {{A, B, C, X(4373), X(12630)}}, {{A, B, C, X(5493), X(12512)}}, {{A, B, C, X(5559), X(45081)}}, {{A, B, C, X(6736), X(6737)}}, {{A, B, C, X(7218), X(51341)}}, {{A, B, C, X(9365), X(40505)}}, {{A, B, C, X(15742), X(40417)}}, {{A, B, C, X(15998), X(34860)}}, {{A, B, C, X(20895), X(49698)}}, {{A, B, C, X(31618), X(32008)}}, {{A, B, C, X(36910), X(55076)}}, {{A, B, C, X(39737), X(40779)}}, {{A, B, C, X(42470), X(56098)}}
X(56118) = barycentric product X(i)*X(j) for these (i, j): {200, 31618}, {1170, 341}, {1174, 3596}, {2346, 312}, {3239, 6606}, {3700, 55281}, {3886, 42310}, {6605, 75}, {10482, 76}, {10509, 5423}, {21453, 346}, {32008, 8}, {40443, 7101}, {42311, 728}, {47487, 7017}, {52622, 53243}
X(56118) = barycentric quotient X(i)/X(j) for these (i, j): {1, 1418}, {2, 10481}, {8, 142}, {9, 354}, {10, 52023}, {21, 18164}, {29, 53238}, {55, 1475}, {85, 53242}, {92, 53237}, {190, 35312}, {200, 1212}, {210, 21808}, {219, 22053}, {220, 2293}, {280, 13156}, {312, 20880}, {314, 16708}, {333, 17169}, {341, 1229}, {346, 4847}, {480, 8012}, {522, 21104}, {607, 40983}, {644, 35338}, {650, 48151}, {657, 2488}, {693, 23599}, {728, 3059}, {1043, 16713}, {1170, 269}, {1174, 56}, {1253, 20229}, {1334, 52020}, {1802, 22079}, {1803, 7053}, {2287, 17194}, {2321, 3925}, {2325, 51463}, {2346, 57}, {3239, 6362}, {3294, 43915}, {3596, 1233}, {3700, 55282}, {3717, 51384}, {3900, 21127}, {3939, 35326}, {4069, 35310}, {4105, 10581}, {4130, 6608}, {4515, 21039}, {4518, 53239}, {4578, 35341}, {4997, 53240}, {5423, 51972}, {6605, 1}, {6606, 658}, {7046, 1855}, {7079, 1827}, {10482, 6}, {10509, 479}, {14942, 53241}, {21453, 279}, {28660, 53236}, {31618, 1088}, {32008, 7}, {40443, 7177}, {42311, 23062}, {47487, 222}, {51972, 6067}, {53243, 1461}, {55281, 4573}
X(56118) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 480, 17277}

X(56119) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(9) AND X(104)

Barycentrics    a*(a-b-c)*(a^4+3*a^3*b+a*b*(-3*b^2+16*b*c-5*c^2)+(b-c)^2*(4*b^2+5*b*c+c^2)-a^2*(5*b^2+5*b*c+2*c^2))*(a^4+3*a^3*c+a*c*(-5*b^2+16*b*c-3*c^2)+(b-c)^2*(b^2+5*b*c+4*c^2)-a^2*(2*b^2+5*b*c+5*c^2)) : :

X(56119) lies on the Feuerbach hyperbola and on these lines: {4, 13996}, {7, 1145}, {84, 38665}, {100, 55921}, {104, 3689}, {1320, 51380}, {3036, 6601}, {3062, 5541}, {4528, 43728}, {4900, 15558}, {53055, 56114}

X(56119) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(1145), X(3689)}}, {{A, B, C, X(1811), X(13996)}}, {{A, B, C, X(36596), X(52663)}}

X(56120) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(21) AND X(4)

Barycentrics    a*(a-b-c)*(a^4-a^3*c+b*(b-c)^2*(b+c)-a^2*(2*b^2+b*c+c^2)+a*c*(-b^2+6*b*c+c^2))*(a^4-a^3*b+(b-c)^2*c*(b+c)+a*b*(b^2+6*b*c-c^2)-a^2*(b^2+b*c+2*c^2)) : :

X(56120) lies on the Feuerbach hyperbola and on these lines: {4, 44455}, {7, 11501}, {79, 48696}, {90, 3681}, {404, 3296}, {1000, 5047}, {3065, 46685}, {3811, 7284}, {3935, 10308}, {4193, 6601}, {5555, 26482}, {7411, 10305}, {14923, 17098}, {15179, 34772}, {20078, 35448}

X(56120) = X(i)-isoconjugate-of-X(j) for these {i, j}: {56, 49627}
X(56120) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 49627}
X(56120) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(3), X(44455)}}, {{A, B, C, X(1261), X(11501)}}, {{A, B, C, X(4193), X(4233)}}, {{A, B, C, X(5047), X(17519)}}
X(56120) = barycentric quotient X(i)/X(j) for these (i, j): {9, 49627}

X(56121) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(21) AND X(80)

Barycentrics    a*(a-b-c)*(a^4-a^3*c+b*(b-c)^2*(b+c)+a*c^2*(2*b+c)-a^2*(2*b^2+c^2))*(a^4-a^3*b+(b-c)^2*c*(b+c)+a*b^2*(b+2*c)-a^2*(b^2+2*c^2)) : :

X(56121) lies on the Feuerbach hyperbola and on these lines: {4, 11698}, {11, 43741}, {79, 100}, {1476, 12739}, {2975, 11279}, {3065, 47320}, {3467, 3678}, {5260, 5559}, {5424, 51506}, {10308, 12738}, {10385, 30513}, {13278, 34918}, {13606, 26726}, {17484, 35000}, {43728, 53342}, {54391, 56036}

X(56121) = reflection of X(i) in X(j) for these {i,j}: {43741, 11}
X(56121) = trilinear pole of line {650, 52405}
X(56121) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(765), X(6740)}}, {{A, B, C, X(1807), X(11698)}}, {{A, B, C, X(1809), X(12331)}}, {{A, B, C, X(2752), X(4518)}}, {{A, B, C, X(11107), X(35982)}}
X(56121) = barycentric quotient X(i)/X(j) for these (i, j): {17796, 33667}

X(56122) = KIMBERLING-PAVLOV X(10)-CONJUGATE OF X(2) AND X(75)

Barycentrics    (b+c)*(a^2*c+b^2*c+a*(b+c)^2)*(a^2*b+b*c^2+a*(b+c)^2) : :

X(56122) lies on these lines: {37, 239}, {75, 40085}, {242, 1824}, {274, 335}, {321, 1921}, {514, 27495}, {594, 3948}, {740, 756}, {984, 31036}, {2171, 16609}, {3294, 4366}, {3807, 27483}, {6652, 18098}, {18082, 40607}, {22035, 27478}

X(56122) = trilinear pole of line {4010, 4129}
X(56122) = X(i)-isoconjugate-of-X(j) for these {i, j}: {28, 22099}, {58, 24512}, {81, 20985}, {163, 21146}, {1333, 24325}, {2206, 20913}, {17031, 18268}
X(56122) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 24512}, {37, 24325}, {115, 21146}, {35068, 17031}, {40586, 20985}, {40591, 22099}, {40603, 20913}
X(56122) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4043)}}, {{A, B, C, X(10), X(239)}}, {{A, B, C, X(37), X(321)}}, {{A, B, C, X(75), X(3995)}}, {{A, B, C, X(81), X(40504)}}, {{A, B, C, X(226), X(17260)}}, {{A, B, C, X(762), X(3954)}}, {{A, B, C, X(3696), X(4026)}}, {{A, B, C, X(3807), X(27495)}}, {{A, B, C, X(4080), X(27475)}}, {{A, B, C, X(4451), X(30713)}}, {{A, B, C, X(4852), X(46772)}}, {{A, B, C, X(6385), X(30582)}}, {{A, B, C, X(13576), X(14621)}}, {{A, B, C, X(17319), X(42027)}}, {{A, B, C, X(22016), X(31993)}}, {{A, B, C, X(25322), X(39957)}}, {{A, B, C, X(26580), X(37787)}}, {{A, B, C, X(27494), X(27797)}}, {{A, B, C, X(31323), X(43534)}}, {{A, B, C, X(32009), X(40515)}}, {{A, B, C, X(32018), X(42471)}}, {{A, B, C, X(39700), X(39737)}}, {{A, B, C, X(39971), X(40024)}}
X(56122) = barycentric product X(i)*X(j) for these (i, j): {10, 39717}, {37, 40024}, {321, 39971}
X(56122) = barycentric quotient X(i)/X(j) for these (i, j): {10, 24325}, {37, 24512}, {42, 20985}, {71, 22099}, {321, 20913}, {523, 21146}, {740, 17031}, {39717, 86}, {39971, 81}, {40024, 274}

X(56123) = KIMBERLING-PAVLOV X(10)-CONJUGATE OF X(7) AND X(7)

Barycentrics    (b+c)*(a*(b-2*c)+b*(b+c))*(a*(-2*b+c)+c*(b+c)) : :

X(56123) lies on these lines: {7, 3175}, {9, 32923}, {37, 2275}, {321, 3662}, {335, 22016}, {594, 3721}, {756, 3778}, {894, 1255}, {1824, 15733}, {2161, 5279}, {2171, 3671}, {8690, 53686}, {21078, 22035}, {22036, 42712}

X(56123) = trilinear pole of line {2512, 4705}
X(56123) = X(i)-isoconjugate-of-X(j) for these {i, j}: {58, 4383}, {60, 28387}, {81, 3915}, {86, 16946}, {110, 4498}, {163, 4106}, {249, 21963}, {593, 3214}, {849, 3175}, {1014, 3217}, {1252, 17214}, {1333, 3875}, {1408, 30568}, {1412, 3913}, {1790, 4186}, {2206, 18135}, {4139, 4556}, {4565, 42312}, {4567, 17477}
X(56123) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 4383}, {37, 3875}, {115, 4106}, {244, 4498}, {661, 17214}, {4075, 3175}, {6741, 20317}, {40586, 3915}, {40599, 3913}, {40600, 16946}, {40603, 18135}, {40627, 17477}, {55064, 42312}
X(56123) = X(i)-Ceva conjugate of X(j) for these {i, j}: {42304, 10}
X(56123) = X(i)-cross conjugate of X(j) for these {i, j}: {6057, 10}, {22036, 321}
X(56123) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(17526)}}, {{A, B, C, X(6), X(5069)}}, {{A, B, C, X(7), X(10)}}, {{A, B, C, X(9), X(3970)}}, {{A, B, C, X(19), X(39700)}}, {{A, B, C, X(37), X(321)}}, {{A, B, C, X(76), X(941)}}, {{A, B, C, X(226), X(5749)}}, {{A, B, C, X(313), X(41683)}}, {{A, B, C, X(523), X(28582)}}, {{A, B, C, X(525), X(3694)}}, {{A, B, C, X(608), X(33146)}}, {{A, B, C, X(894), X(21021)}}, {{A, B, C, X(1213), X(42025)}}, {{A, B, C, X(1400), X(2275)}}, {{A, B, C, X(1441), X(21101)}}, {{A, B, C, X(1826), X(4080)}}, {{A, B, C, X(2285), X(26580)}}, {{A, B, C, X(2321), X(3161)}}, {{A, B, C, X(2994), X(5839)}}, {{A, B, C, X(3175), X(6057)}}, {{A, B, C, X(3701), X(7155)}}, {{A, B, C, X(3930), X(40704)}}, {{A, B, C, X(4013), X(41013)}}, {{A, B, C, X(4037), X(22016)}}, {{A, B, C, X(21061), X(22021)}}, {{A, B, C, X(22174), X(27447)}}, {{A, B, C, X(34895), X(43749)}}, {{A, B, C, X(39798), X(39994)}}, {{A, B, C, X(39956), X(40012)}}, {{A, B, C, X(39975), X(40021)}}
X(56123) = barycentric product X(i)*X(j) for these (i, j): {10, 34860}, {37, 40012}, {321, 39956}, {2321, 42304}, {4036, 8690}
X(56123) = barycentric quotient X(i)/X(j) for these (i, j): {10, 3875}, {37, 4383}, {42, 3915}, {210, 3913}, {213, 16946}, {244, 17214}, {321, 18135}, {523, 4106}, {594, 3175}, {661, 4498}, {756, 3214}, {1334, 3217}, {1824, 4186}, {2171, 28387}, {2321, 30568}, {2643, 21963}, {3122, 17477}, {3700, 20317}, {4041, 42312}, {4052, 27813}, {4705, 4139}, {8690, 52935}, {34860, 86}, {39956, 81}, {40012, 274}, {42304, 1434}

X(56124) = KIMBERLING-PAVLOV X(10)-CONJUGATE OF X(7) AND X(37)

Barycentrics    (a^2*(b-c)+a*(b^2-b*c-c^2)+b*(2*b^2+b*c+c^2))*(a^2*(b-c)+a*(b^2+b*c-c^2)-c*(b^2+b*c+2*c^2)) : :

X(56124) lies on these lines: {2, 21101}, {7, 726}, {75, 3844}, {86, 24349}, {192, 14621}, {335, 17232}, {673, 4361}, {1278, 6650}, {1440, 41352}, {3662, 27494}, {5749, 27481}, {6384, 33931}, {20947, 40027}, {32087, 39721}, {39716, 49528}, {51837, 53677}

X(56124) = trilinear pole of line {21261, 514}
X(56124) = X(i)-cross conjugate of X(j) for these {i, j}: {29674, 2}
X(56124) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(7)}}, {{A, B, C, X(76), X(39714)}}, {{A, B, C, X(192), X(33931)}}, {{A, B, C, X(313), X(27809)}}, {{A, B, C, X(330), X(334)}}, {{A, B, C, X(347), X(41352)}}, {{A, B, C, X(518), X(50995)}}, {{A, B, C, X(522), X(726)}}, {{A, B, C, X(536), X(28898)}}, {{A, B, C, X(561), X(39694)}}, {{A, B, C, X(918), X(6664)}}, {{A, B, C, X(941), X(984)}}, {{A, B, C, X(985), X(39742)}}, {{A, B, C, X(1278), X(20947)}}, {{A, B, C, X(1441), X(21101)}}, {{A, B, C, X(2298), X(17038)}}, {{A, B, C, X(3844), X(13476)}}, {{A, B, C, X(4361), X(4408)}}, {{A, B, C, X(6383), X(24002)}}, {{A, B, C, X(7018), X(39703)}}, {{A, B, C, X(7192), X(40021)}}, {{A, B, C, X(7233), X(34860)}}, {{A, B, C, X(7241), X(52030)}}, {{A, B, C, X(7261), X(30701)}}, {{A, B, C, X(17232), X(33295)}}, {{A, B, C, X(30635), X(39698)}}, {{A, B, C, X(30636), X(35058)}}, {{A, B, C, X(30663), X(39956)}}, {{A, B, C, X(40013), X(54128)}}, {{A, B, C, X(40030), X(54456)}}

X(56125) = KIMBERLING-PAVLOV X(10)-CONJUGATE OF X(10) AND X(37)

Barycentrics    (b+c)*(a*(b-2*c)-2*b*c)*(2*a*b-a*c+2*b*c) : :

X(56125) lies on these lines: {1, 536}, {10, 714}, {19, 56116}, {37, 2229}, {65, 44671}, {75, 4392}, {192, 39737}, {321, 41683}, {518, 994}, {726, 42285}, {740, 53114}, {759, 29351}, {876, 4777}, {897, 37209}, {1266, 39712}, {1278, 39739}, {2363, 19848}, {3670, 39708}, {3696, 4674}, {3728, 46772}, {3739, 17038}, {3962, 34434}, {3967, 52875}, {4003, 4688}, {4686, 13476}, {4726, 39742}, {4804, 55244}, {4968, 31359}, {21342, 31136}, {39697, 50117}

X(56125) = trilinear pole of line {661, 14431}
X(56125) = X(i)-isoconjugate-of-X(j) for these {i, j}: {58, 3240}, {81, 54981}, {110, 29350}, {163, 4776}, {1333, 4664}
X(56125) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 3240}, {37, 4664}, {115, 4776}, {244, 29350}, {40586, 54981}
X(56125) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}}, {{A, B, C, X(4), X(16394)}}, {{A, B, C, X(42), X(4492)}}, {{A, B, C, X(210), X(522)}}, {{A, B, C, X(256), X(28625)}}, {{A, B, C, X(291), X(28658)}}, {{A, B, C, X(310), X(513)}}, {{A, B, C, X(313), X(49493)}}, {{A, B, C, X(321), X(523)}}, {{A, B, C, X(335), X(4670)}}, {{A, B, C, X(594), X(49462)}}, {{A, B, C, X(740), X(4693)}}, {{A, B, C, X(903), X(40718)}}, {{A, B, C, X(1219), X(15232)}}, {{A, B, C, X(1400), X(7241)}}, {{A, B, C, X(1441), X(40085)}}, {{A, B, C, X(2321), X(49468)}}, {{A, B, C, X(3696), X(3943)}}, {{A, B, C, X(3842), X(52706)}}, {{A, B, C, X(3962), X(52357)}}, {{A, B, C, X(4043), X(4686)}}, {{A, B, C, X(4080), X(4363)}}, {{A, B, C, X(4373), X(14624)}}, {{A, B, C, X(4392), X(4735)}}, {{A, B, C, X(4651), X(50001)}}, {{A, B, C, X(4726), X(22016)}}, {{A, B, C, X(13576), X(36588)}}, {{A, B, C, X(17318), X(27797)}}, {{A, B, C, X(18082), X(39710)}}, {{A, B, C, X(19998), X(31136)}}, {{A, B, C, X(24696), X(54980)}}, {{A, B, C, X(27483), X(53034)}}, {{A, B, C, X(29822), X(30970)}}, {{A, B, C, X(31178), X(43534)}}, {{A, B, C, X(39747), X(43927)}}
X(56125) = barycentric product X(i)*X(j) for these (i, j): {10, 36871}, {226, 56077}, {321, 55919}, {1441, 56116}, {1577, 29351}, {37209, 523}
X(56125) = barycentric quotient X(i)/X(j) for these (i, j): {10, 4664}, {37, 3240}, {42, 54981}, {523, 4776}, {661, 29350}, {29351, 662}, {36871, 86}, {37209, 99}, {55919, 81}, {56077, 333}, {56116, 21}
X(56125) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {36871, 56077, 55919}

X(56126) = KIMBERLING-PAVLOV X(10)-CONJUGATE OF X(10) AND X(75)

Barycentrics    (b+c)*(b*c+a*(4*b+c))*(b*c+a*(b+4*c)) : :

X(56126) lies on these lines: {1, 4753}, {2, 52875}, {37, 19998}, {75, 3994}, {596, 49447}, {756, 41683}, {876, 28209}, {984, 39697}, {3842, 4674}, {4043, 46772}, {4687, 13476}, {4824, 55244}, {17250, 39712}, {39708, 46937}

X(56126) = X(i)-isoconjugate-of-X(j) for these {i, j}: {58, 30950}, {81, 16971}, {1333, 4688}, {1408, 4519}
X(56126) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 30950}, {37, 4688}, {40586, 16971}
X(56126) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}}, {{A, B, C, X(2), X(19998)}}, {{A, B, C, X(4), X(51595)}}, {{A, B, C, X(321), X(51488)}}, {{A, B, C, X(335), X(27797)}}, {{A, B, C, X(740), X(27922)}}, {{A, B, C, X(749), X(52555)}}, {{A, B, C, X(756), X(3994)}}, {{A, B, C, X(3842), X(3943)}}, {{A, B, C, X(3986), X(49468)}}, {{A, B, C, X(3993), X(52706)}}, {{A, B, C, X(4043), X(4687)}}, {{A, B, C, X(4080), X(27475)}}, {{A, B, C, X(4389), X(7677)}}, {{A, B, C, X(5257), X(49462)}}, {{A, B, C, X(13576), X(39704)}}, {{A, B, C, X(14624), X(28650)}}, {{A, B, C, X(17335), X(30588)}}, {{A, B, C, X(18082), X(30598)}}, {{A, B, C, X(27809), X(39706)}}, {{A, B, C, X(43534), X(50094)}}
X(56126) = barycentric product X(i)*X(j) for these (i, j): {321, 55932}
X(56126) = barycentric quotient X(i)/X(j) for these (i, j): {10, 4688}, {37, 30950}, {42, 16971}, {2321, 4519}, {55932, 81}

X(56127) = KIMBERLING-PAVLOV X(10)-CONJUGATE OF X(10) AND X(85)

Barycentrics    b*c*(b+c)*(a^2+b*(b-c)-a*(2*b+c))*(a^2+c*(-b+c)-a*(b+2*c)) : :

X(56127) lies on these lines: {75, 28742}, {85, 3930}, {312, 728}, {318, 56118}, {321, 4515}, {349, 2321}, {2346, 46738}, {3696, 3701}, {4044, 30713}, {17762, 48280}, {21615, 28659}, {24044, 52623}, {31618, 40023}, {42310, 56051}

X(56127) = isotomic conjugate of X(18164)
X(56127) = trilinear pole of line {4086, 4804}
X(56127) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 18164}, {32, 17169}, {58, 1475}, {142, 2206}, {163, 48151}, {184, 53238}, {354, 1333}, {560, 16708}, {593, 52020}, {604, 17194}, {849, 21808}, {1014, 20229}, {1212, 1408}, {1396, 22079}, {1397, 16713}, {1412, 2293}, {1418, 2194}, {1474, 22053}, {1501, 53236}, {1576, 21104}, {1790, 40983}, {2488, 4565}, {3733, 35326}, {4847, 16947}, {7341, 21795}
X(56127) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 18164}, {10, 1475}, {37, 354}, {115, 48151}, {1214, 1418}, {3161, 17194}, {4075, 21808}, {4858, 21104}, {6374, 16708}, {6376, 17169}, {6741, 21127}, {40599, 2293}, {40603, 142}, {51574, 22053}, {55064, 2488}
X(56127) = X(i)-cross conjugate of X(j) for these {i, j}: {850, 4033}, {17163, 75}
X(56127) = intersection, other than A, B, C, of circumconics {{A, B, C, X(10), X(85)}}, {{A, B, C, X(75), X(4043)}}, {{A, B, C, X(92), X(6539)}}, {{A, B, C, X(226), X(3983)}}, {{A, B, C, X(312), X(318)}}, {{A, B, C, X(728), X(2321)}}, {{A, B, C, X(874), X(17762)}}, {{A, B, C, X(1089), X(52623)}}, {{A, B, C, X(3995), X(39700)}}, {{A, B, C, X(4103), X(24044)}}, {{A, B, C, X(4651), X(28742)}}, {{A, B, C, X(4674), X(9311)}}, {{A, B, C, X(13576), X(18097)}}, {{A, B, C, X(16708), X(17163)}}, {{A, B, C, X(18359), X(27797)}}, {{A, B, C, X(27475), X(40515)}}, {{A, B, C, X(27809), X(34860)}}, {{A, B, C, X(40011), X(43533)}}, {{A, B, C, X(42714), X(46738)}}
X(56127) = barycentric product X(i)*X(j) for these (i, j): {349, 6605}, {1170, 30713}, {1174, 27801}, {1441, 56118}, {2321, 31618}, {2346, 313}, {4036, 55281}, {4044, 42310}, {4082, 42311}, {4086, 6606}, {21453, 3701}, {32008, 321}
X(56127) = barycentric quotient X(i)/X(j) for these (i, j): {2, 18164}, {8, 17194}, {10, 354}, {37, 1475}, {72, 22053}, {75, 17169}, {76, 16708}, {92, 53238}, {210, 2293}, {226, 1418}, {312, 16713}, {313, 20880}, {321, 142}, {523, 48151}, {561, 53236}, {594, 21808}, {756, 52020}, {1018, 35326}, {1089, 3925}, {1170, 1412}, {1174, 1333}, {1334, 20229}, {1441, 10481}, {1577, 21104}, {1824, 40983}, {2318, 22079}, {2321, 1212}, {2346, 58}, {3700, 21127}, {3701, 4847}, {3952, 35338}, {3992, 51463}, {4006, 40606}, {4036, 55282}, {4041, 2488}, {4082, 3059}, {4086, 6362}, {4103, 35310}, {4171, 10581}, {4515, 8012}, {6057, 21039}, {6358, 52023}, {6605, 284}, {6606, 1414}, {10482, 2194}, {21453, 1014}, {27801, 1233}, {30713, 1229}, {30730, 35341}, {31618, 1434}, {32008, 81}, {42310, 42302}, {47487, 1437}, {53008, 1827}, {55281, 52935}, {56118, 21}

X(56128) = KIMBERLING-PAVLOV X(10)-CONJUGATE OF X(37) AND X(1)

Barycentrics    (a*b^3+b^2*c*(b+c)+a^2*(b^2-c^2))*(-(a*c^3)-b*c^2*(b+c)+a^2*(b^2-c^2)) : :

X(56128) lies on these lines: {1, 714}, {10, 4443}, {37, 4009}, {65, 536}, {75, 35532}, {312, 41683}, {726, 53114}, {740, 994}, {2363, 19840}, {4674, 49474}, {13476, 17157}, {30942, 56125}, {34434, 44671}, {48090, 55244}

X(56128) = trilinear pole of line {661, 14430}
X(56128) = X(i)-isoconjugate-of-X(j) for these {i, j}: {32, 30964}, {27773, 34073}
X(56128) = X(i)-Dao conjugate of X(j) for these {i, j}: {6376, 30964}
X(56128) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}}, {{A, B, C, X(87), X(40010)}}, {{A, B, C, X(291), X(46018)}}, {{A, B, C, X(310), X(4492)}}, {{A, B, C, X(312), X(522)}}, {{A, B, C, X(335), X(32931)}}, {{A, B, C, X(513), X(3223)}}, {{A, B, C, X(523), X(561)}}, {{A, B, C, X(726), X(4777)}}, {{A, B, C, X(871), X(4443)}}, {{A, B, C, X(2998), X(6385)}}, {{A, B, C, X(3240), X(30942)}}, {{A, B, C, X(4581), X(35058)}}, {{A, B, C, X(5312), X(50605)}}, {{A, B, C, X(6383), X(42328)}}, {{A, B, C, X(6664), X(20567)}}, {{A, B, C, X(9348), X(32010)}}, {{A, B, C, X(9462), X(18031)}}, {{A, B, C, X(9516), X(37208)}}, {{A, B, C, X(14973), X(44671)}}, {{A, B, C, X(17157), X(40088)}}, {{A, B, C, X(17763), X(33077)}}, {{A, B, C, X(26227), X(29643)}}, {{A, B, C, X(27494), X(39698)}}, {{A, B, C, X(30939), X(48090)}}, {{A, B, C, X(31137), X(49988)}}, {{A, B, C, X(40039), X(52654)}}, {{A, B, C, X(45988), X(52150)}}
X(56128) = barycentric product X(i)*X(j) for these (i, j): {36873, 76}
X(56128) = barycentric quotient X(i)/X(j) for these (i, j): {75, 30964}, {4777, 27773}, {36873, 6}

X(56129) = KIMBERLING-PAVLOV X(10)-CONJUGATE OF X(37) AND X(76)

Barycentrics    b*c*(a*b*(b-c)+b^2*c+a^2*(b+c))*(b*c^2+a*c*(-b+c)+a^2*(b+c)) : :

X(56129) lies on these lines: {37, 6383}, {75, 899}, {76, 536}, {85, 52896}, {192, 6385}, {274, 2176}, {286, 52890}, {334, 4389}, {668, 4492}, {2481, 52902}, {4664, 30964}, {20568, 52900}, {20569, 52901}, {23493, 53679}

X(56129) = isotomic conjugate of X(16975)
X(56129) = trilinear pole of line {693, 50491}
X(56129) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 16975}, {32, 30942}
X(56129) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 16975}, {6376, 30942}
X(56129) = X(i)-cross conjugate of X(j) for these {i, j}: {4776, 668}
X(56129) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(43095)}}, {{A, B, C, X(2), X(513)}}, {{A, B, C, X(6), X(39745)}}, {{A, B, C, X(7), X(308)}}, {{A, B, C, X(37), X(192)}}, {{A, B, C, X(75), X(76)}}, {{A, B, C, X(335), X(32931)}}, {{A, B, C, X(693), X(40826)}}, {{A, B, C, X(714), X(1215)}}, {{A, B, C, X(1002), X(3228)}}, {{A, B, C, X(1239), X(39723)}}, {{A, B, C, X(1278), X(3739)}}, {{A, B, C, X(1502), X(54121)}}, {{A, B, C, X(1921), X(4389)}}, {{A, B, C, X(2998), X(13476)}}, {{A, B, C, X(3644), X(4687)}}, {{A, B, C, X(3797), X(24357)}}, {{A, B, C, X(3963), X(8818)}}, {{A, B, C, X(4080), X(4363)}}, {{A, B, C, X(4601), X(7033)}}, {{A, B, C, X(4681), X(4704)}}, {{A, B, C, X(4686), X(4699)}}, {{A, B, C, X(4688), X(4740)}}, {{A, B, C, X(4698), X(4788)}}, {{A, B, C, X(4718), X(27268)}}, {{A, B, C, X(4726), X(4772)}}, {{A, B, C, X(4739), X(4821)}}, {{A, B, C, X(4751), X(4764)}}, {{A, B, C, X(7241), X(54117)}}, {{A, B, C, X(9309), X(39968)}}, {{A, B, C, X(9462), X(39925)}}, {{A, B, C, X(10009), X(39995)}}, {{A, B, C, X(16705), X(18135)}}, {{A, B, C, X(17139), X(44144)}}, {{A, B, C, X(27475), X(36805)}}, {{A, B, C, X(32020), X(39704)}}, {{A, B, C, X(34816), X(39746)}}, {{A, B, C, X(39742), X(42328)}}, {{A, B, C, X(40031), X(40039)}}, {{A, B, C, X(40515), X(42027)}}
X(56129) = barycentric quotient X(i)/X(j) for these (i, j): {2, 16975}, {75, 30942}

X(56130) = KIMBERLING-PAVLOV X(10)-CONJUGATE OF X(37) AND X(86)

Barycentrics    (a^2*(b-c)+a*(2*b^2-c^2)+b*(2*b^2+2*b*c+c^2))*(a^2*(b-c)+a*(b^2-2*c^2)-c*(b^2+2*b*c+2*c^2)) : :

X(56130) lies on these lines: {86, 726}, {141, 27494}, {310, 35538}, {335, 17231}, {1268, 49521}, {1278, 39720}, {4360, 14621}, {6650, 9055}, {24325, 30598}, {27483, 28633}, {28554, 39704}, {32922, 55970}

X(56130) = trilinear pole of line {21053, 514}
X(56130) = isotomic conjugate of X(49477)
X(56130) = X(i)-cross conjugate of X(j) for these {i, j}: {29078, 190}
X(56130) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(7)}}, {{A, B, C, X(76), X(3226)}}, {{A, B, C, X(313), X(523)}}, {{A, B, C, X(334), X(596)}}, {{A, B, C, X(984), X(40433)}}, {{A, B, C, X(1222), X(35162)}}, {{A, B, C, X(1269), X(49521)}}, {{A, B, C, X(2786), X(9055)}}, {{A, B, C, X(4777), X(28554)}}, {{A, B, C, X(32018), X(39717)}}, {{A, B, C, X(35150), X(40417)}}
X(56130) = barycentric quotient X(i)/X(j) for these (i, j): {2, 49477}

X(56131) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(1) AND X(2)

Barycentrics    a*(b+c)*(a^2*c+b^2*c+a*(b+c)^2)*(a^2*b+b*c^2+a*(b+c)^2) : :

X(56131) lies on these lines: {10, 350}, {42, 238}, {86, 291}, {181, 1284}, {513, 40774}, {740, 756}, {1500, 2238}, {2201, 2333}, {3799, 30571}, {4368, 18082}, {7148, 26115}, {9505, 40796}, {22279, 34585}, {22323, 28600}

X(56131) = trilinear pole of line {4079, 21832}
X(56131) = X(i)-isoconjugate-of-X(j) for these {i, j}: {27, 22099}, {58, 24325}, {81, 24512}, {86, 20985}, {110, 21146}, {741, 17031}, {1333, 20913}
X(56131) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 24325}, {37, 20913}, {244, 21146}, {8299, 17031}, {40586, 24512}, {40600, 20985}
X(56131) = X(i)-Ceva conjugate of X(j) for these {i, j}: {39717, 56122}
X(56131) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1621)}}, {{A, B, C, X(2), X(3293)}}, {{A, B, C, X(10), X(42)}}, {{A, B, C, X(37), X(86)}}, {{A, B, C, X(43), X(26115)}}, {{A, B, C, X(58), X(40147)}}, {{A, B, C, X(65), X(3750)}}, {{A, B, C, X(75), X(52555)}}, {{A, B, C, X(310), X(42471)}}, {{A, B, C, X(985), X(18785)}}, {{A, B, C, X(1002), X(4674)}}, {{A, B, C, X(2078), X(4424)}}, {{A, B, C, X(3214), X(43223)}}, {{A, B, C, X(3720), X(43972)}}, {{A, B, C, X(3799), X(40774)}}, {{A, B, C, X(4492), X(41683)}}, {{A, B, C, X(14624), X(17038)}}, {{A, B, C, X(27033), X(31008)}}, {{A, B, C, X(29822), X(31855)}}, {{A, B, C, X(38277), X(52654)}}, {{A, B, C, X(39971), X(40024)}}, {{A, B, C, X(40433), X(40504)}}, {{A, B, C, X(40786), X(40794)}}, {{A, B, C, X(43534), X(52651)}}
X(56131) = barycentric product X(i)*X(j) for these (i, j): {1, 56122}, {10, 39971}, {37, 39717}, {40024, 42}
X(56131) = barycentric quotient X(i)/X(j) for these (i, j): {10, 20913}, {37, 24325}, {42, 24512}, {213, 20985}, {228, 22099}, {661, 21146}, {2238, 17031}, {39717, 274}, {39971, 86}, {40024, 310}, {56122, 75}

X(56132) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(1) AND X(4)

Barycentrics    (b+c)*(a^3+b^3-b*c^2-a*c*(2*b+c))*(a^3-b^2*c+c^3-a*b*(b+2*c)) : :

X(56132) lies on these lines: {10, 1621}, {12, 3293}, {313, 5564}, {334, 33297}, {594, 3294}, {1089, 4015}, {1220, 47033}, {1268, 33954}, {1734, 29070}, {1826, 5526}, {3214, 45095}, {31855, 51870}

X(56132) = X(i)-isoconjugate-of-X(j) for these {i, j}: {58, 3874}, {81, 583}, {1333, 18139}
X(56132) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 3874}, {37, 18139}, {40586, 583}
X(56132) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1621)}}, {{A, B, C, X(4), X(5047)}}, {{A, B, C, X(8), X(3293)}}, {{A, B, C, X(10), X(12)}}, {{A, B, C, X(37), X(79)}}, {{A, B, C, X(65), X(3746)}}, {{A, B, C, X(72), X(5526)}}, {{A, B, C, X(210), X(10482)}}, {{A, B, C, X(321), X(33157)}}, {{A, B, C, X(740), X(29070)}}, {{A, B, C, X(1126), X(40504)}}, {{A, B, C, X(1734), X(4006)}}, {{A, B, C, X(2321), X(23604)}}, {{A, B, C, X(3679), X(26115)}}, {{A, B, C, X(3696), X(7247)}}, {{A, B, C, X(3701), X(6598)}}, {{A, B, C, X(4024), X(7206)}}, {{A, B, C, X(4080), X(32019)}}, {{A, B, C, X(4647), X(33954)}}, {{A, B, C, X(5178), X(41013)}}, {{A, B, C, X(5557), X(15320)}}, {{A, B, C, X(13602), X(31503)}}, {{A, B, C, X(13606), X(53114)}}, {{A, B, C, X(14624), X(39708)}}, {{A, B, C, X(15065), X(41501)}}, {{A, B, C, X(17751), X(31855)}}, {{A, B, C, X(27797), X(39729)}}, {{A, B, C, X(32008), X(40515)}}, {{A, B, C, X(37702), X(52383)}}, {{A, B, C, X(38955), X(43731)}}
X(56132) = barycentric quotient X(i)/X(j) for these (i, j): {10, 18139}, {37, 3874}, {42, 583}, {18082, 29568}

X(56133) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(1) AND X(8)

Barycentrics    (b+c)*(a^3+b^3+a*(2*b-c)*c-b*c^2)*(a^3-a*b*(b-2*c)-b^2*c+c^3) : :

X(56133) lies on these lines: {1, 51870}, {10, 36}, {12, 1464}, {58, 80}, {313, 320}, {513, 3585}, {594, 2245}, {758, 1089}, {952, 3293}, {1826, 52413}, {3072, 41506}, {5053, 21011}, {18395, 54300}, {26115, 51111}, {37701, 45095}

X(56133) = trilinear pole of line {4024, 21828}
X(56133) = X(i)-isoconjugate-of-X(j) for these {i, j}: {58, 3878}, {81, 4271}, {283, 1866}, {1333, 5741}, {1437, 11105}
X(56133) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 3878}, {37, 5741}, {40586, 4271}
X(56133) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2975)}}, {{A, B, C, X(4), X(404)}}, {{A, B, C, X(10), X(12)}}, {{A, B, C, X(36), X(58)}}, {{A, B, C, X(37), X(5258)}}, {{A, B, C, X(83), X(24614)}}, {{A, B, C, X(225), X(45287)}}, {{A, B, C, X(226), X(34234)}}, {{A, B, C, X(252), X(5397)}}, {{A, B, C, X(267), X(40453)}}, {{A, B, C, X(514), X(18097)}}, {{A, B, C, X(1222), X(42471)}}, {{A, B, C, X(3668), X(4311)}}, {{A, B, C, X(3679), X(19874)}}, {{A, B, C, X(3701), X(34918)}}, {{A, B, C, X(5176), X(41013)}}, {{A, B, C, X(5445), X(8818)}}, {{A, B, C, X(5557), X(53114)}}, {{A, B, C, X(5560), X(13576)}}, {{A, B, C, X(5561), X(36604)}}, {{A, B, C, X(6757), X(37710)}}, {{A, B, C, X(14452), X(40663)}}, {{A, B, C, X(15320), X(37129)}}, {{A, B, C, X(32918), X(40718)}}, {{A, B, C, X(33119), X(43534)}}
X(56133) = barycentric quotient X(i)/X(j) for these (i, j): {10, 5741}, {37, 3878}, {42, 4271}, {1826, 11105}, {1880, 1866}, {18082, 29534}

X(56134) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(1) AND X(37)

Barycentrics    a*(b+c)*(a+4*b+c)*(a+b+4*c) : :

X(56134) lies on these lines: {1, 4015}, {2, 39697}, {10, 27797}, {37, 3921}, {75, 3992}, {596, 1698}, {740, 56126}, {756, 3968}, {759, 28210}, {897, 51294}, {1018, 21822}, {1743, 2214}, {1757, 55925}, {3679, 31035}, {3842, 41683}, {3956, 21806}, {4134, 53114}, {4533, 31503}, {4705, 55244}, {9330, 17461}, {13476, 49448}, {34595, 39702}, {36478, 39714}

X(56134) = trilinear pole of line {661, 4145}
X(56134) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 26860}, {27, 22357}, {58, 551}, {81, 16666}, {86, 21747}, {110, 28209}, {284, 4031}, {757, 21806}, {849, 4714}, {1333, 24589}, {1408, 3902}, {1412, 3707}, {3285, 42026}, {3733, 4781}, {4591, 14435}, {5546, 30722}
X(56134) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 26860}, {10, 551}, {37, 24589}, {244, 28209}, {4075, 4714}, {40586, 16666}, {40590, 4031}, {40599, 3707}, {40600, 21747}, {40607, 21806}
X(56134) = X(i)-Ceva conjugate of X(j) for these {i, j}: {55955, 27797}
X(56134) = X(i)-cross conjugate of X(j) for these {i, j}: {4770, 1018}
X(56134) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}}, {{A, B, C, X(2), X(18145)}}, {{A, B, C, X(4), X(17536)}}, {{A, B, C, X(12), X(4015)}}, {{A, B, C, X(42), X(19875)}}, {{A, B, C, X(226), X(3921)}}, {{A, B, C, X(512), X(28554)}}, {{A, B, C, X(756), X(3992)}}, {{A, B, C, X(979), X(1698)}}, {{A, B, C, X(1126), X(32089)}}, {{A, B, C, X(1213), X(4868)}}, {{A, B, C, X(1743), X(52353)}}, {{A, B, C, X(3294), X(49448)}}, {{A, B, C, X(3696), X(52708)}}, {{A, B, C, X(3701), X(4866)}}, {{A, B, C, X(3842), X(52959)}}, {{A, B, C, X(3968), X(40663)}}, {{A, B, C, X(4026), X(16611)}}, {{A, B, C, X(4424), X(13462)}}, {{A, B, C, X(4732), X(16589)}}, {{A, B, C, X(4770), X(21822)}}, {{A, B, C, X(5561), X(13576)}}, {{A, B, C, X(6539), X(25430)}}, {{A, B, C, X(17125), X(40718)}}, {{A, B, C, X(20121), X(42289)}}, {{A, B, C, X(21839), X(51294)}}, {{A, B, C, X(27797), X(40434)}}, {{A, B, C, X(27809), X(36871)}}, {{A, B, C, X(31025), X(31035)}}, {{A, B, C, X(38277), X(52654)}}, {{A, B, C, X(43972), X(55093)}}
X(56134) = barycentric product X(i)*X(j) for these (i, j): {1, 27797}, {10, 40434}, {37, 55955}, {226, 56115}, {321, 41434}, {1577, 28210}
X(56134) = barycentric quotient X(i)/X(j) for these (i, j): {1, 26860}, {10, 24589}, {37, 551}, {42, 16666}, {65, 4031}, {210, 3707}, {213, 21747}, {228, 22357}, {594, 4714}, {661, 28209}, {1018, 4781}, {1500, 21806}, {2321, 3902}, {4017, 30722}, {4069, 30727}, {4674, 42026}, {4730, 14435}, {27797, 75}, {28210, 662}, {40434, 86}, {41434, 81}, {55955, 274}, {56115, 333}
X(56134) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {40434, 56115, 41434}

X(56135) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(1) AND X(65)

Barycentrics    a*(a+b-4*c)*(a-4*b+c)*(b+c) : :

X(56135) lies on these lines: {1, 3833}, {8, 39697}, {10, 48642}, {19, 3973}, {37, 3987}, {65, 31855}, {75, 32101}, {596, 3679}, {759, 28218}, {994, 6048}, {1698, 42285}, {2166, 51975}, {2214, 16667}, {2292, 56134}, {3293, 53114}, {3678, 4674}, {3753, 31503}, {4668, 34860}, {4677, 39702}, {11010, 53391}, {13476, 49498}, {19875, 31359}, {39708, 51066}, {40663, 52382}

X(56135) = X(i)-isoconjugate-of-X(j) for these {i, j}: {58, 3244}, {81, 16669}, {110, 28217}, {5546, 30726}
X(56135) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 3244}, {244, 28217}, {40586, 16669}
X(56135) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}}, {{A, B, C, X(4), X(17531)}}, {{A, B, C, X(8), X(31855)}}, {{A, B, C, X(12), X(3918)}}, {{A, B, C, X(57), X(6539)}}, {{A, B, C, X(72), X(3973)}}, {{A, B, C, X(88), X(27797)}}, {{A, B, C, X(226), X(4002)}}, {{A, B, C, X(321), X(3987)}}, {{A, B, C, X(758), X(28221)}}, {{A, B, C, X(1089), X(4695)}}, {{A, B, C, X(1126), X(32101)}}, {{A, B, C, X(2292), X(4714)}}, {{A, B, C, X(3214), X(4668)}}, {{A, B, C, X(3293), X(3679)}}, {{A, B, C, X(3294), X(49498)}}, {{A, B, C, X(3361), X(4424)}}, {{A, B, C, X(3678), X(40663)}}, {{A, B, C, X(3697), X(4848)}}, {{A, B, C, X(3698), X(3947)}}, {{A, B, C, X(3701), X(4900)}}, {{A, B, C, X(3753), X(10563)}}, {{A, B, C, X(4080), X(39963)}}, {{A, B, C, X(4642), X(4647)}}, {{A, B, C, X(5560), X(13576)}}, {{A, B, C, X(17124), X(40718)}}, {{A, B, C, X(25417), X(30582)}}, {{A, B, C, X(38955), X(43731)}}, {{A, B, C, X(39748), X(39960)}}, {{A, B, C, X(39975), X(43533)}}, {{A, B, C, X(43534), X(48642)}}
X(56135) = barycentric product X(i)*X(j) for these (i, j): {10, 39962}, {37, 39710}, {226, 56091}, {1577, 28218}
X(56135) = barycentric quotient X(i)/X(j) for these (i, j): {37, 3244}, {42, 16669}, {661, 28217}, {3950, 4935}, {4017, 30726}, {4069, 30732}, {28218, 662}, {39710, 274}, {39962, 86}, {56091, 333}

X(56136) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(10) AND X(19)

Barycentrics    a*(a^3+3*b^3+b^2*c-b*c^2+c^3-a^2*(b+c)+a*(b^2-c^2))*(a^3+b^3-b^2*c+b*c^2+3*c^3-a^2*(b+c)+a*(-b^2+c^2)) : :

X(56136) lies on these lines: {1, 55939}, {8, 23604}, {19, 758}, {37, 9620}, {63, 759}, {65, 3689}, {200, 4674}, {225, 49168}, {267, 3901}, {519, 3668}, {2218, 12514}, {3771, 34895}, {3900, 55244}, {5711, 31503}, {18785, 54330}, {26942, 52383}, {54336, 54421}

X(56136) = isogonal conjugate of X(37817)
X(56136) = trilinear pole of line {661, 14427}
X(56136) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 37817}, {6, 24597}
X(56136) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 37817}, {9, 24597}
X(56136) = X(i)-cross conjugate of X(j) for these {i, j}: {49454, 1}
X(56136) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}}, {{A, B, C, X(4), X(1257)}}, {{A, B, C, X(8), X(3811)}}, {{A, B, C, X(9), X(56104)}}, {{A, B, C, X(21), X(12559)}}, {{A, B, C, X(63), X(525)}}, {{A, B, C, X(66), X(80)}}, {{A, B, C, X(76), X(44178)}}, {{A, B, C, X(78), X(6598)}}, {{A, B, C, X(90), X(40436)}}, {{A, B, C, X(104), X(4373)}}, {{A, B, C, X(106), X(608)}}, {{A, B, C, X(191), X(3901)}}, {{A, B, C, X(200), X(519)}}, {{A, B, C, X(281), X(1320)}}, {{A, B, C, X(291), X(998)}}, {{A, B, C, X(459), X(40399)}}, {{A, B, C, X(517), X(8270)}}, {{A, B, C, X(522), X(56101)}}, {{A, B, C, X(726), X(1938)}}, {{A, B, C, X(903), X(7284)}}, {{A, B, C, X(936), X(6738)}}, {{A, B, C, X(943), X(43533)}}, {{A, B, C, X(996), X(1065)}}, {{A, B, C, X(997), X(18391)}}, {{A, B, C, X(1000), X(1280)}}, {{A, B, C, X(1170), X(18840)}}, {{A, B, C, X(1219), X(1389)}}, {{A, B, C, X(1220), X(17098)}}, {{A, B, C, X(1222), X(11501)}}, {{A, B, C, X(1224), X(15173)}}, {{A, B, C, X(1411), X(7241)}}, {{A, B, C, X(1698), X(30143)}}, {{A, B, C, X(2184), X(4052)}}, {{A, B, C, X(2320), X(36588)}}, {{A, B, C, X(2995), X(39768)}}, {{A, B, C, X(2996), X(40403)}}, {{A, B, C, X(2997), X(38955)}}, {{A, B, C, X(3340), X(5711)}}, {{A, B, C, X(3426), X(7123)}}, {{A, B, C, X(3427), X(42361)}}, {{A, B, C, X(3680), X(5687)}}, {{A, B, C, X(3745), X(18421)}}, {{A, B, C, X(3868), X(12514)}}, {{A, B, C, X(3872), X(45701)}}, {{A, B, C, X(3874), X(5250)}}, {{A, B, C, X(5248), X(11520)}}, {{A, B, C, X(5485), X(36101)}}, {{A, B, C, X(5665), X(40446)}}, {{A, B, C, X(6743), X(6765)}}, {{A, B, C, X(8056), X(40509)}}, {{A, B, C, X(8666), X(11682)}}, {{A, B, C, X(9623), X(13405)}}, {{A, B, C, X(10198), X(19860)}}, {{A, B, C, X(11529), X(37543)}}, {{A, B, C, X(15910), X(22836)}}, {{A, B, C, X(19611), X(28786)}}, {{A, B, C, X(36121), X(51497)}}, {{A, B, C, X(36123), X(40424)}}, {{A, B, C, X(36125), X(39956)}}, {{A, B, C, X(37131), X(40029)}}, {{A, B, C, X(37817), X(49454)}}, {{A, B, C, X(39700), X(40149)}}, {{A, B, C, X(43708), X(52387)}}
X(56136) = barycentric product X(i)*X(j) for these (i, j): {10, 55939}
X(56136) = barycentric quotient X(i)/X(j) for these (i, j): {1, 24597}, {6, 37817}, {55939, 86}

X(56137) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(10) AND X(28)

Barycentrics    a*(a^3+2*b^3-a^2*c+b^2*c+c^3+a*(b^2-2*b*c-c^2))*(a^3-a^2*b+b^3+b*c^2+2*c^3+a*(-b^2-2*b*c+c^2)) : :

X(56137) lies on these lines: {1, 4284}, {8, 15474}, {28, 518}, {57, 3811}, {72, 105}, {81, 5266}, {88, 4420}, {141, 277}, {145, 56050}, {279, 53997}, {519, 52374}, {957, 12635}, {961, 3555}, {1002, 1009}, {1022, 35057}, {1231, 34018}, {2006, 10916}, {14839, 16100}, {35637, 53083}, {41610, 52376}

X(56137) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 26723}
X(56137) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 26723}
X(56137) = X(i)-cross conjugate of X(j) for these {i, j}: {50350, 100}
X(56137) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(8), X(3811)}}, {{A, B, C, X(9), X(41863)}}, {{A, B, C, X(10), X(2346)}}, {{A, B, C, X(21), X(596)}}, {{A, B, C, X(58), X(4284)}}, {{A, B, C, X(65), X(5266)}}, {{A, B, C, X(72), X(518)}}, {{A, B, C, X(75), X(943)}}, {{A, B, C, X(76), X(2991)}}, {{A, B, C, X(78), X(6601)}}, {{A, B, C, X(79), X(23617)}}, {{A, B, C, X(90), X(4373)}}, {{A, B, C, X(104), X(34860)}}, {{A, B, C, X(141), X(41610)}}, {{A, B, C, X(285), X(3254)}}, {{A, B, C, X(318), X(34894)}}, {{A, B, C, X(335), X(40403)}}, {{A, B, C, X(392), X(34791)}}, {{A, B, C, X(447), X(3651)}}, {{A, B, C, X(519), X(4420)}}, {{A, B, C, X(749), X(977)}}, {{A, B, C, X(903), X(10308)}}, {{A, B, C, X(956), X(12635)}}, {{A, B, C, X(960), X(3555)}}, {{A, B, C, X(979), X(36125)}}, {{A, B, C, X(987), X(39742)}}, {{A, B, C, X(996), X(17097)}}, {{A, B, C, X(1009), X(31926)}}, {{A, B, C, X(1065), X(1222)}}, {{A, B, C, X(1067), X(40424)}}, {{A, B, C, X(1126), X(38813)}}, {{A, B, C, X(1320), X(10570)}}, {{A, B, C, X(1476), X(39697)}}, {{A, B, C, X(1814), X(14376)}}, {{A, B, C, X(2218), X(7241)}}, {{A, B, C, X(2334), X(34250)}}, {{A, B, C, X(2775), X(9041)}}, {{A, B, C, X(2975), X(35637)}}, {{A, B, C, X(3242), X(16466)}}, {{A, B, C, X(3243), X(31435)}}, {{A, B, C, X(4511), X(10916)}}, {{A, B, C, X(4867), X(5288)}}, {{A, B, C, X(5258), X(41696)}}, {{A, B, C, X(5730), X(12513)}}, {{A, B, C, X(6051), X(49478)}}, {{A, B, C, X(7162), X(43533)}}, {{A, B, C, X(15175), X(39711)}}, {{A, B, C, X(15179), X(39702)}}, {{A, B, C, X(16496), X(54386)}}, {{A, B, C, X(18840), X(39273)}}, {{A, B, C, X(36121), X(42019)}}, {{A, B, C, X(39700), X(40406)}}, {{A, B, C, X(39749), X(44178)}}, {{A, B, C, X(39982), X(52372)}}, {{A, B, C, X(42470), X(44692)}}, {{A, B, C, X(43740), X(52663)}}
X(56137) = barycentric quotient X(i)/X(j) for these (i, j): {1, 26723}

X(56138) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(10) AND X(31)

Barycentrics    (a^3*b+b*c^2*(b+c)+a^2*(b^2-c^2))*(a^3*c+b^2*c*(b+c)+a^2*(-b^2+c^2)) : :

X(56138) lies on these lines: {1, 35544}, {31, 740}, {42, 50281}, {75, 741}, {213, 2901}, {523, 875}, {964, 23493}, {1402, 4362}, {29016, 49127}, {40148, 50302}

X(56138) = trilinear pole of line {798, 6133}
X(56138) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 24598}
X(56138) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 24598}
X(56138) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(31)}}, {{A, B, C, X(2), X(17982)}}, {{A, B, C, X(4), X(34527)}}, {{A, B, C, X(8), X(4362)}}, {{A, B, C, X(10), X(2901)}}, {{A, B, C, X(75), X(523)}}, {{A, B, C, X(86), X(9348)}}, {{A, B, C, X(92), X(43534)}}, {{A, B, C, X(98), X(2985)}}, {{A, B, C, X(145), X(29670)}}, {{A, B, C, X(291), X(7033)}}, {{A, B, C, X(430), X(11104)}}, {{A, B, C, X(519), X(26227)}}, {{A, B, C, X(596), X(32929)}}, {{A, B, C, X(870), X(30571)}}, {{A, B, C, X(985), X(3226)}}, {{A, B, C, X(996), X(1390)}}, {{A, B, C, X(1255), X(43531)}}, {{A, B, C, X(1280), X(1389)}}, {{A, B, C, X(2214), X(18082)}}, {{A, B, C, X(2997), X(42027)}}, {{A, B, C, X(2998), X(38810)}}, {{A, B, C, X(3679), X(50756)}}, {{A, B, C, X(3791), X(31359)}}, {{A, B, C, X(3875), X(50314)}}, {{A, B, C, X(4360), X(50302)}}, {{A, B, C, X(5263), X(32921)}}, {{A, B, C, X(7035), X(52654)}}, {{A, B, C, X(9462), X(37130)}}, {{A, B, C, X(11113), X(15150)}}, {{A, B, C, X(11599), X(39700)}}, {{A, B, C, X(13576), X(35058)}}, {{A, B, C, X(13588), X(56137)}}, {{A, B, C, X(17393), X(50293)}}, {{A, B, C, X(24325), X(49470)}}, {{A, B, C, X(32922), X(32941)}}
X(56138) = barycentric quotient X(i)/X(j) for these (i, j): {1, 24598}

X(56139) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(10) AND X(33)

Barycentrics    a*(a^5+b^5-b^4*c+2*a^3*(b-c)*c-b*c^4+c^5+a^4*(-b+c)-2*a^2*c^2*(b+c)-a*(b-c)*(b+c)^3)*(a^5+b^5+a^4*(b-c)-2*a^3*b*(b-c)-b^4*c-b*c^4+c^5-2*a^2*b^2*(b+c)+a*(b-c)*(b+c)^3) : :

X(56139) lies on these lines: {33, 516}, {40, 2332}, {55, 45126}, {77, 103}, {118, 46344}, {200, 5739}, {220, 12514}, {991, 56098}, {1214, 2192}, {1742, 7281}, {1801, 2328}, {5089, 54370}, {9746, 47800}

X(56139) = isogonal conjugate of X(990)
X(56139) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 42467}
X(56139) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(33)}}, {{A, B, C, X(2), X(972)}}, {{A, B, C, X(3), X(1801)}}, {{A, B, C, X(4), X(81)}}, {{A, B, C, X(9), X(77)}}, {{A, B, C, X(10), X(40)}}, {{A, B, C, X(34), X(9315)}}, {{A, B, C, X(57), X(43672)}}, {{A, B, C, X(84), X(39958)}}, {{A, B, C, X(88), X(45097)}}, {{A, B, C, X(90), X(2190)}}, {{A, B, C, X(104), X(3424)}}, {{A, B, C, X(284), X(1041)}}, {{A, B, C, X(573), X(50314)}}, {{A, B, C, X(928), X(28850)}}, {{A, B, C, X(941), X(14493)}}, {{A, B, C, X(969), X(15909)}}, {{A, B, C, X(985), X(9442)}}, {{A, B, C, X(991), X(2263)}}, {{A, B, C, X(997), X(2745)}}, {{A, B, C, X(998), X(1945)}}, {{A, B, C, X(1390), X(15731)}}, {{A, B, C, X(1706), X(43174)}}, {{A, B, C, X(1742), X(5018)}}, {{A, B, C, X(1766), X(50295)}}, {{A, B, C, X(2191), X(39964)}}, {{A, B, C, X(2717), X(5089)}}, {{A, B, C, X(2723), X(52133)}}, {{A, B, C, X(3345), X(43531)}}, {{A, B, C, X(3923), X(6210)}}, {{A, B, C, X(4296), X(12520)}}, {{A, B, C, X(4347), X(10884)}}, {{A, B, C, X(4660), X(6211)}}, {{A, B, C, X(5119), X(8758)}}, {{A, B, C, X(9357), X(52654)}}, {{A, B, C, X(10623), X(29290)}}, {{A, B, C, X(11372), X(51090)}}, {{A, B, C, X(12572), X(12705)}}, {{A, B, C, X(29056), X(40718)}}
X(56139) = barycentric quotient X(i)/X(j) for these (i, j): {6, 990}

X(56140) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(10) AND X(34)

Barycentrics    a*(a^3+b^3+a^2*(b-c)+b^2*c+b*c^2+c^3+a*(b^2-4*b*c-c^2))*(a^3+b^3+b^2*c+b*c^2+c^3+a^2*(-b+c)+a*(-b^2-4*b*c+c^2)) : :

X(56140) lies on these lines: {6, 3991}, {10, 2191}, {34, 519}, {56, 3555}, {58, 3870}, {78, 106}, {145, 998}, {269, 6765}, {521, 23345}, {997, 3445}, {1062, 9041}, {1438, 17742}, {1474, 7719}, {7194, 50581}, {8747, 15954}

X(56140) = trilinear pole of line {649, 14418}
X(56140) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(6)}}, {{A, B, C, X(4), X(1280)}}, {{A, B, C, X(8), X(3811)}}, {{A, B, C, X(9), X(596)}}, {{A, B, C, X(10), X(3870)}}, {{A, B, C, X(75), X(7162)}}, {{A, B, C, X(78), X(519)}}, {{A, B, C, X(81), X(18841)}}, {{A, B, C, X(84), X(39697)}}, {{A, B, C, X(90), X(765)}}, {{A, B, C, X(104), X(6553)}}, {{A, B, C, X(145), X(997)}}, {{A, B, C, X(200), X(6765)}}, {{A, B, C, X(280), X(34894)}}, {{A, B, C, X(518), X(17742)}}, {{A, B, C, X(595), X(9315)}}, {{A, B, C, X(903), X(36599)}}, {{A, B, C, X(943), X(1219)}}, {{A, B, C, X(947), X(56139)}}, {{A, B, C, X(1000), X(1257)}}, {{A, B, C, X(1059), X(7123)}}, {{A, B, C, X(1252), X(10623)}}, {{A, B, C, X(2287), X(15998)}}, {{A, B, C, X(2991), X(30701)}}, {{A, B, C, X(3244), X(19861)}}, {{A, B, C, X(3296), X(23617)}}, {{A, B, C, X(3340), X(37589)}}, {{A, B, C, X(3682), X(15954)}}, {{A, B, C, X(3872), X(22836)}}, {{A, B, C, X(3961), X(50581)}}, {{A, B, C, X(4866), X(41711)}}, {{A, B, C, X(5256), X(30145)}}, {{A, B, C, X(7131), X(34892)}}, {{A, B, C, X(7161), X(39711)}}, {{A, B, C, X(7284), X(39702)}}, {{A, B, C, X(10390), X(43972)}}, {{A, B, C, X(30144), X(36846)}}, {{A, B, C, X(39696), X(42467)}}, {{A, B, C, X(39979), X(40188)}}, {{A, B, C, X(40403), X(54123)}}

X(56141) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(10) AND X(35)

Barycentrics    (a^5-a^4*c-a^2*b*c^2-a^3*b*(2*b+c)+c*(b^2-c^2)^2+a*(b^4+b^3*c-b*c^3-c^4))*(a^5-a^4*b-a^2*b^2*c-a^3*c*(b+2*c)+b*(b^2-c^2)^2+a*(-b^4-b^3*c+b*c^3+c^4)) : :

X(56141) lies on these lines: {10, 13746}, {12, 30}, {74, 79}, {502, 10572}, {594, 7359}, {1089, 4420}, {1442, 7278}, {1784, 6198}, {1826, 41502}, {2166, 38336}, {10483, 37741}

X(56141) = trilinear pole of line {4024, 9404}
X(56141) = X(i)-cross conjugate of X(j) for these {i, j}: {48903, 1}
X(56141) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(35)}}, {{A, B, C, X(4), X(2166)}}, {{A, B, C, X(7), X(4324)}}, {{A, B, C, X(8), X(3584)}}, {{A, B, C, X(10), X(12)}}, {{A, B, C, X(29), X(30)}}, {{A, B, C, X(171), X(5697)}}, {{A, B, C, X(447), X(27555)}}, {{A, B, C, X(1043), X(5424)}}, {{A, B, C, X(1065), X(5559)}}, {{A, B, C, X(1836), X(10483)}}, {{A, B, C, X(3064), X(47160)}}, {{A, B, C, X(3065), X(3615)}}, {{A, B, C, X(3467), X(5397)}}, {{A, B, C, X(3649), X(5441)}}, {{A, B, C, X(4995), X(7278)}}, {{A, B, C, X(5119), X(37559)}}, {{A, B, C, X(5557), X(15338)}}, {{A, B, C, X(7095), X(39959)}}, {{A, B, C, X(10570), X(44693)}}, {{A, B, C, X(15175), X(54972)}}, {{A, B, C, X(15446), X(40430)}}, {{A, B, C, X(17098), X(44692)}}, {{A, B, C, X(35056), X(36129)}}, {{A, B, C, X(37525), X(37573)}}, {{A, B, C, X(43682), X(52412)}}

X(56142) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(10) AND X(43)

Barycentrics    a*(-(a*b*(b-2*c)*c^2)-b^2*c^2*(b+c)+a^3*(b^2-c^2)+a^2*(b^3-b^2*c-b*c^2-c^3))*(a*b^2*c*(-2*b+c)+b^2*c^2*(b+c)+a^3*(b^2-c^2)+a^2*(b^3+b^2*c+b*c^2-c^3)) : :

X(56142) lies on these lines: {43, 726}, {87, 727}, {893, 16557}, {978, 1575}, {979, 3500}, {1403, 1463}, {1742, 8927}, {3550, 13588}, {3551, 18793}, {17459, 39967}, {24524, 33296}, {51973, 52656}

X(56142) = trilinear pole of line {20979, 21348}
X(56142) = X(i)-cross conjugate of X(j) for these {i, j}: {24349, 1}
X(56142) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(43)}}, {{A, B, C, X(2), X(978)}}, {{A, B, C, X(4), X(291)}}, {{A, B, C, X(42), X(50581)}}, {{A, B, C, X(56), X(32011)}}, {{A, B, C, X(65), X(3550)}}, {{A, B, C, X(75), X(87)}}, {{A, B, C, X(1246), X(39742)}}, {{A, B, C, X(1929), X(24260)}}, {{A, B, C, X(3216), X(26102)}}, {{A, B, C, X(3293), X(42042)}}, {{A, B, C, X(7153), X(32020)}}, {{A, B, C, X(9361), X(39954)}}, {{A, B, C, X(16569), X(21214)}}, {{A, B, C, X(20615), X(40027)}}, {{A, B, C, X(36602), X(39966)}}

X(56143) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(10) AND X(54)

Barycentrics    (a-b-c)*(a^3+b^3+a*(2*b-c)*c-b*c^2)*(a^3-a*b*(b-2*c)-b^2*c+c^3) : :

X(56143) lies on these lines: {1, 15065}, {5, 953}, {10, 36}, {54, 952}, {59, 10944}, {60, 6740}, {355, 3417}, {519, 51803}, {529, 12946}, {1441, 1443}, {1870, 11109}, {2321, 2323}, {3701, 4511}, {3737, 13746}, {5587, 44759}

X(56143) = trilinear pole of line {654, 3700}
X(56143) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 1866}, {56, 3878}, {57, 4271}, {603, 11105}, {604, 5741}
X(56143) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 3878}, {3161, 5741}, {5452, 4271}, {7952, 11105}, {36103, 1866}
X(56143) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(36)}}, {{A, B, C, X(4), X(45287)}}, {{A, B, C, X(5), X(952)}}, {{A, B, C, X(7), X(4311)}}, {{A, B, C, X(8), X(10)}}, {{A, B, C, X(9), X(5258)}}, {{A, B, C, X(11), X(10944)}}, {{A, B, C, X(12), X(10950)}}, {{A, B, C, X(21), X(1220)}}, {{A, B, C, X(29), X(404)}}, {{A, B, C, X(80), X(2962)}}, {{A, B, C, X(83), X(4560)}}, {{A, B, C, X(145), X(27385)}}, {{A, B, C, X(280), X(30513)}}, {{A, B, C, X(318), X(5176)}}, {{A, B, C, X(495), X(37730)}}, {{A, B, C, X(519), X(27529)}}, {{A, B, C, X(596), X(11604)}}, {{A, B, C, X(958), X(49492)}}, {{A, B, C, X(1043), X(32635)}}, {{A, B, C, X(1065), X(17097)}}, {{A, B, C, X(1219), X(43740)}}, {{A, B, C, X(1411), X(8615)}}, {{A, B, C, X(1476), X(36123)}}, {{A, B, C, X(1483), X(5901)}}, {{A, B, C, X(1837), X(5252)}}, {{A, B, C, X(2320), X(43531)}}, {{A, B, C, X(2985), X(46880)}}, {{A, B, C, X(4242), X(6742)}}, {{A, B, C, X(4391), X(54120)}}, {{A, B, C, X(4518), X(33119)}}, {{A, B, C, X(5442), X(13606)}}, {{A, B, C, X(5445), X(5559)}}, {{A, B, C, X(5587), X(5881)}}, {{A, B, C, X(5727), X(9578)}}, {{A, B, C, X(5886), X(37727)}}, {{A, B, C, X(7412), X(11103)}}, {{A, B, C, X(7741), X(37707)}}, {{A, B, C, X(7951), X(37706)}}, {{A, B, C, X(7972), X(37735)}}, {{A, B, C, X(9581), X(37709)}}, {{A, B, C, X(10826), X(37708)}}, {{A, B, C, X(10827), X(37711)}}, {{A, B, C, X(11374), X(37739)}}, {{A, B, C, X(11375), X(37740)}}, {{A, B, C, X(11376), X(37738)}}, {{A, B, C, X(15950), X(37734)}}, {{A, B, C, X(17718), X(37724)}}, {{A, B, C, X(17947), X(39722)}}, {{A, B, C, X(18357), X(37705)}}, {{A, B, C, X(19607), X(30710)}}, {{A, B, C, X(31623), X(40394)}}, {{A, B, C, X(32918), X(52133)}}, {{A, B, C, X(34918), X(52409)}}, {{A, B, C, X(35058), X(46103)}}, {{A, B, C, X(37712), X(37714)}}, {{A, B, C, X(37728), X(37737)}}
X(56143) = barycentric product X(i)*X(j) for these (i, j): {333, 56133}
X(56143) = barycentric quotient X(i)/X(j) for these (i, j): {8, 5741}, {9, 3878}, {19, 1866}, {55, 4271}, {281, 11105}, {56133, 226}

X(56144) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(10) AND X(55)

Barycentrics    (a^4-a^3*(b+c)+b*(b-c)^2*(b+c)-a^2*c*(b+c)-a*(b-c)*(b+c)^2)*(a^4-a^3*(b+c)-a^2*b*(b+c)+(b-c)^2*c*(b+c)+a*(b-c)*(b+c)^2) : :

X(56144) lies on the Kiepert hyperbola and on these lines: {1, 1446}, {2, 1754}, {3, 17758}, {4, 2332}, {6, 43672}, {7, 103}, {10, 220}, {33, 40149}, {55, 226}, {64, 3671}, {76, 1043}, {83, 36652}, {118, 13576}, {200, 321}, {376, 54831}, {459, 461}, {740, 43683}, {946, 36907}, {963, 4298}, {990, 40719}, {991, 14828}, {1503, 5138}, {1541, 54668}, {1751, 8226}, {2051, 19541}, {2052, 14004}, {2192, 8808}, {2263, 56139}, {2784, 11608}, {3085, 10482}, {3839, 54622}, {3870, 29016}, {4049, 28292}, {4052, 28580}, {4262, 36028}, {4301, 53089}, {4307, 51476}, {4336, 24014}, {4349, 7050}, {4355, 44760}, {4444, 6003}, {4845, 18391}, {5542, 52013}, {5721, 54516}, {5733, 14548}, {5757, 33536}, {7073, 43682}, {7218, 43166}, {7281, 17861}, {8580, 27413}, {9746, 40131}, {10197, 28854}, {10883, 24624}, {11028, 30329}, {11500, 40515}, {15951, 21620}, {18841, 36682}, {28850, 42064}, {32022, 36660}, {36737, 37833}, {36738, 37830}, {37658, 48888}

X(56144) = polar conjugate of X(37448)
X(56144) = trilinear pole of line {657, 523}
X(56144) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 991}, {6, 24635}, {48, 37448}, {56, 41228}
X(56144) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 13478}
X(56144) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 41228}, {3, 991}, {9, 24635}, {1249, 37448}
X(56144) = X(i)-cross conjugate of X(j) for these {i, j}: {1536, 43672}, {42289, 1}
X(56144) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(33)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(4251)}}, {{A, B, C, X(6), X(13329)}}, {{A, B, C, X(7), X(281)}}, {{A, B, C, X(8), X(13405)}}, {{A, B, C, X(9), X(954)}}, {{A, B, C, X(12), X(17703)}}, {{A, B, C, X(20), X(461)}}, {{A, B, C, X(25), X(13727)}}, {{A, B, C, X(29), X(5665)}}, {{A, B, C, X(31), X(29015)}}, {{A, B, C, X(40), X(37543)}}, {{A, B, C, X(57), X(36124)}}, {{A, B, C, X(65), X(1754)}}, {{A, B, C, X(66), X(1826)}}, {{A, B, C, X(75), X(15909)}}, {{A, B, C, X(79), X(158)}}, {{A, B, C, X(80), X(17718)}}, {{A, B, C, X(81), X(972)}}, {{A, B, C, X(84), X(29310)}}, {{A, B, C, X(86), X(3062)}}, {{A, B, C, X(118), X(50441)}}, {{A, B, C, X(269), X(14553)}}, {{A, B, C, X(273), X(7110)}}, {{A, B, C, X(280), X(51512)}}, {{A, B, C, X(390), X(5542)}}, {{A, B, C, X(393), X(3332)}}, {{A, B, C, X(406), X(10431)}}, {{A, B, C, X(427), X(36652)}}, {{A, B, C, X(514), X(28849)}}, {{A, B, C, X(517), X(29066)}}, {{A, B, C, X(519), X(28292)}}, {{A, B, C, X(572), X(37502)}}, {{A, B, C, X(573), X(5138)}}, {{A, B, C, X(596), X(42361)}}, {{A, B, C, X(740), X(6003)}}, {{A, B, C, X(860), X(10883)}}, {{A, B, C, X(943), X(6605)}}, {{A, B, C, X(962), X(4298)}}, {{A, B, C, X(985), X(2717)}}, {{A, B, C, X(990), X(2263)}}, {{A, B, C, X(991), X(42289)}}, {{A, B, C, X(996), X(1065)}}, {{A, B, C, X(1000), X(56088)}}, {{A, B, C, X(1002), X(39421)}}, {{A, B, C, X(1013), X(36027)}}, {{A, B, C, X(1093), X(6757)}}, {{A, B, C, X(1246), X(32085)}}, {{A, B, C, X(1280), X(1389)}}, {{A, B, C, X(1323), X(53014)}}, {{A, B, C, X(1536), X(37448)}}, {{A, B, C, X(2297), X(40424)}}, {{A, B, C, X(2298), X(14493)}}, {{A, B, C, X(2364), X(23707)}}, {{A, B, C, X(2481), X(52133)}}, {{A, B, C, X(2736), X(51560)}}, {{A, B, C, X(2784), X(2785)}}, {{A, B, C, X(2980), X(15320)}}, {{A, B, C, X(3085), X(4847)}}, {{A, B, C, X(3427), X(42285)}}, {{A, B, C, X(3600), X(4301)}}, {{A, B, C, X(3615), X(5556)}}, {{A, B, C, X(3663), X(4307)}}, {{A, B, C, X(3667), X(28580)}}, {{A, B, C, X(3672), X(4349)}}, {{A, B, C, X(3811), X(3870)}}, {{A, B, C, X(3887), X(28850)}}, {{A, B, C, X(3945), X(4356)}}, {{A, B, C, X(4196), X(36660)}}, {{A, B, C, X(4207), X(36706)}}, {{A, B, C, X(4292), X(4295)}}, {{A, B, C, X(4302), X(11551)}}, {{A, B, C, X(4313), X(12563)}}, {{A, B, C, X(4314), X(11036)}}, {{A, B, C, X(4321), X(43166)}}, {{A, B, C, X(4344), X(4353)}}, {{A, B, C, X(4355), X(9589)}}, {{A, B, C, X(5125), X(8226)}}, {{A, B, C, X(5136), X(36002)}}, {{A, B, C, X(5231), X(31434)}}, {{A, B, C, X(5706), X(41342)}}, {{A, B, C, X(5732), X(12560)}}, {{A, B, C, X(6743), X(10578)}}, {{A, B, C, X(6745), X(18391)}}, {{A, B, C, X(7080), X(11019)}}, {{A, B, C, X(7378), X(36682)}}, {{A, B, C, X(7498), X(50696)}}, {{A, B, C, X(7513), X(13615)}}, {{A, B, C, X(7952), X(40960)}}, {{A, B, C, X(8727), X(17555)}}, {{A, B, C, X(8814), X(52223)}}, {{A, B, C, X(8818), X(24006)}}, {{A, B, C, X(9442), X(30571)}}, {{A, B, C, X(9785), X(12577)}}, {{A, B, C, X(10198), X(25006)}}, {{A, B, C, X(10307), X(30712)}}, {{A, B, C, X(10309), X(43972)}}, {{A, B, C, X(10390), X(36629)}}, {{A, B, C, X(10570), X(17097)}}, {{A, B, C, X(11037), X(12575)}}, {{A, B, C, X(11038), X(30331)}}, {{A, B, C, X(11109), X(19541)}}, {{A, B, C, X(14377), X(34018)}}, {{A, B, C, X(14497), X(29348)}}, {{A, B, C, X(14828), X(37658)}}, {{A, B, C, X(15173), X(56141)}}, {{A, B, C, X(15313), X(29016)}}, {{A, B, C, X(16870), X(34231)}}, {{A, B, C, X(23876), X(28845)}}, {{A, B, C, X(23884), X(28877)}}, {{A, B, C, X(24248), X(50307)}}, {{A, B, C, X(26015), X(45701)}}, {{A, B, C, X(30332), X(43180)}}, {{A, B, C, X(34917), X(36910)}}, {{A, B, C, X(37381), X(52255)}}, {{A, B, C, X(39748), X(52518)}}, {{A, B, C, X(39954), X(40131)}}
X(56144) = barycentric quotient X(i)/X(j) for these (i, j): {1, 24635}, {4, 37448}, {6, 991}, {9, 41228}

X(56145) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(10) AND X(56)

Barycentrics    (a^2+a*(-3*b+c)+b*(b+c))*(a^2+a*(b-3*c)+c*(b+c)) : :

X(56145) lies on these lines: {1, 4723}, {6, 2325}, {8, 106}, {10, 3445}, {34, 38462}, {56, 519}, {58, 145}, {86, 40018}, {269, 12629}, {292, 49458}, {522, 10912}, {937, 2901}, {977, 15955}, {998, 36846}, {1125, 41436}, {1126, 3241}, {1220, 50637}, {1411, 22837}, {1724, 20039}, {2098, 44040}, {2163, 3633}, {2334, 3635}, {3623, 41434}, {3878, 9432}, {4076, 9268}, {5697, 9457}, {20050, 37639}, {36604, 49492}, {39748, 48863}

X(56145) = isotomic conjugate of X(4398)
X(56145) = trilinear pole of line {649, 1639}
X(56145) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 4398}, {56, 3885}, {58, 3987}
X(56145) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 3885}, {2, 4398}, {10, 3987}
X(56145) = X(i)-cross conjugate of X(j) for these {i, j}: {17340, 2}
X(56145) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(6)}}, {{A, B, C, X(2), X(3244)}}, {{A, B, C, X(4), X(6553)}}, {{A, B, C, X(8), X(519)}}, {{A, B, C, X(10), X(145)}}, {{A, B, C, X(29), X(16371)}}, {{A, B, C, X(65), X(37610)}}, {{A, B, C, X(75), X(5559)}}, {{A, B, C, X(76), X(6630)}}, {{A, B, C, X(79), X(24858)}}, {{A, B, C, X(83), X(38247)}}, {{A, B, C, X(85), X(34892)}}, {{A, B, C, X(200), X(12629)}}, {{A, B, C, X(239), X(49458)}}, {{A, B, C, X(277), X(36954)}}, {{A, B, C, X(280), X(56089)}}, {{A, B, C, X(318), X(12641)}}, {{A, B, C, X(330), X(1016)}}, {{A, B, C, X(514), X(30701)}}, {{A, B, C, X(551), X(3623)}}, {{A, B, C, X(765), X(15446)}}, {{A, B, C, X(903), X(5560)}}, {{A, B, C, X(976), X(15955)}}, {{A, B, C, X(997), X(36846)}}, {{A, B, C, X(1043), X(4900)}}, {{A, B, C, X(1125), X(3241)}}, {{A, B, C, X(1193), X(50637)}}, {{A, B, C, X(1224), X(13602)}}, {{A, B, C, X(1280), X(1389)}}, {{A, B, C, X(1320), X(10570)}}, {{A, B, C, X(1392), X(56143)}}, {{A, B, C, X(1698), X(51093)}}, {{A, B, C, X(1751), X(35058)}}, {{A, B, C, X(2051), X(39696)}}, {{A, B, C, X(2985), X(13478)}}, {{A, B, C, X(3227), X(14377)}}, {{A, B, C, X(3621), X(3625)}}, {{A, B, C, X(3622), X(51071)}}, {{A, B, C, X(3626), X(20050)}}, {{A, B, C, X(3632), X(39710)}}, {{A, B, C, X(3633), X(3679)}}, {{A, B, C, X(3636), X(20057)}}, {{A, B, C, X(3680), X(5687)}}, {{A, B, C, X(3699), X(10912)}}, {{A, B, C, X(3811), X(3872)}}, {{A, B, C, X(3957), X(30143)}}, {{A, B, C, X(4373), X(43734)}}, {{A, B, C, X(4398), X(17340)}}, {{A, B, C, X(4511), X(22837)}}, {{A, B, C, X(4669), X(20014)}}, {{A, B, C, X(4701), X(20053)}}, {{A, B, C, X(4853), X(6765)}}, {{A, B, C, X(4861), X(22836)}}, {{A, B, C, X(4882), X(11519)}}, {{A, B, C, X(5485), X(36605)}}, {{A, B, C, X(5558), X(43972)}}, {{A, B, C, X(5854), X(55134)}}, {{A, B, C, X(6743), X(6764)}}, {{A, B, C, X(6757), X(34895)}}, {{A, B, C, X(7317), X(43533)}}, {{A, B, C, X(7320), X(42285)}}, {{A, B, C, X(8580), X(12127)}}, {{A, B, C, X(9797), X(12447)}}, {{A, B, C, X(13606), X(31359)}}, {{A, B, C, X(14497), X(54972)}}, {{A, B, C, X(15179), X(23617)}}, {{A, B, C, X(15315), X(46187)}}, {{A, B, C, X(17015), X(30142)}}, {{A, B, C, X(17016), X(30145)}}, {{A, B, C, X(17758), X(49536)}}, {{A, B, C, X(20037), X(50608)}}, {{A, B, C, X(20054), X(34641)}}, {{A, B, C, X(21398), X(56141)}}, {{A, B, C, X(27818), X(40509)}}, {{A, B, C, X(30144), X(38460)}}, {{A, B, C, X(30652), X(40718)}}, {{A, B, C, X(32008), X(36871)}}, {{A, B, C, X(32013), X(39736)}}, {{A, B, C, X(36479), X(49476)}}, {{A, B, C, X(36534), X(49477)}}, {{A, B, C, X(36565), X(49682)}}, {{A, B, C, X(38955), X(42471)}}, {{A, B, C, X(39720), X(53109)}}, {{A, B, C, X(49560), X(50015)}}, {{A, B, C, X(50017), X(50316)}}
X(56145) = barycentric product X(i)*X(j) for these (i, j): {40018, 6}
X(56145) = barycentric quotient X(i)/X(j) for these (i, j): {2, 4398}, {9, 3885}, {37, 3987}, {40018, 76}

X(56146) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(10) AND X(64)

Barycentrics    (a-b-c)*(a^3-b^2*c+c^3-a*b*(b+c))*(a^3+b^3-b*c^2-a*c*(b+c)) : :

X(56146) lies on these lines: {1, 1441}, {3, 34429}, {8, 2328}, {10, 55}, {20, 103}, {29, 3190}, {33, 2901}, {64, 516}, {101, 37055}, {200, 3701}, {220, 2321}, {272, 4313}, {281, 2332}, {515, 7169}, {519, 2192}, {952, 6759}, {958, 55076}, {963, 4297}, {996, 10950}, {1043, 3596}, {2310, 52387}, {2342, 38955}, {2900, 54396}, {3216, 27394}, {3294, 54359}, {3771, 52257}, {4298, 52013}, {4339, 5264}, {4347, 28850}, {5090, 21072}, {5496, 6757}, {5711, 6738}, {6284, 26942}, {8058, 23289}, {10570, 44669}, {12432, 32118}, {12575, 32941}, {13727, 15467}, {14547, 43531}, {14624, 16788}, {14942, 40011}, {15065, 52371}, {32943, 51785}, {32945, 53053}, {33937, 56098}, {37387, 49542}

X(56146) = isogonal conjugate of X(4306)
X(56146) = trilinear pole of line {657, 3700}
X(56146) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 4306}, {7, 2352}, {56, 3868}, {57, 579}, {109, 23800}, {110, 51658}, {209, 1014}, {269, 3190}, {603, 5125}, {604, 18134}, {651, 43060}, {934, 8676}, {1396, 51574}, {1407, 27396}, {1412, 22021}, {1427, 56000}, {1434, 2198}, {2217, 19367}, {7177, 41320}, {17878, 23979}
X(56146) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 3868}, {3, 4306}, {11, 23800}, {244, 51658}, {2968, 20294}, {3161, 18134}, {5452, 579}, {6600, 3190}, {7952, 5125}, {14714, 8676}, {24771, 27396}, {38991, 43060}, {40599, 22021}
X(56146) = X(i)-Ceva conjugate of X(j) for these {i, j}: {2997, 1751}
X(56146) = X(i)-cross conjugate of X(j) for these {i, j}: {2318, 9}, {3695, 44040}, {34969, 7253}, {42069, 3239}
X(56146) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(33)}}, {{A, B, C, X(2), X(6743)}}, {{A, B, C, X(4), X(346)}}, {{A, B, C, X(7), X(4314)}}, {{A, B, C, X(8), X(10)}}, {{A, B, C, X(9), X(29)}}, {{A, B, C, X(20), X(516)}}, {{A, B, C, X(21), X(5248)}}, {{A, B, C, X(28), X(294)}}, {{A, B, C, X(78), X(3811)}}, {{A, B, C, X(80), X(158)}}, {{A, B, C, X(84), X(1067)}}, {{A, B, C, X(90), X(24179)}}, {{A, B, C, X(219), X(3191)}}, {{A, B, C, X(280), X(596)}}, {{A, B, C, X(284), X(19763)}}, {{A, B, C, X(312), X(32777)}}, {{A, B, C, X(318), X(3419)}}, {{A, B, C, X(333), X(19732)}}, {{A, B, C, X(345), X(3189)}}, {{A, B, C, X(390), X(4298)}}, {{A, B, C, X(497), X(49542)}}, {{A, B, C, X(519), X(7080)}}, {{A, B, C, X(522), X(36626)}}, {{A, B, C, X(937), X(51341)}}, {{A, B, C, X(943), X(2287)}}, {{A, B, C, X(958), X(3294)}}, {{A, B, C, X(960), X(16788)}}, {{A, B, C, X(962), X(4297)}}, {{A, B, C, X(1010), X(3886)}}, {{A, B, C, X(1065), X(7160)}}, {{A, B, C, X(1098), X(15175)}}, {{A, B, C, X(1167), X(3362)}}, {{A, B, C, X(1219), X(15998)}}, {{A, B, C, X(1220), X(4866)}}, {{A, B, C, X(1222), X(4900)}}, {{A, B, C, X(1257), X(41798)}}, {{A, B, C, X(1260), X(52676)}}, {{A, B, C, X(1265), X(3239)}}, {{A, B, C, X(1320), X(8715)}}, {{A, B, C, X(1697), X(5711)}}, {{A, B, C, X(1770), X(4302)}}, {{A, B, C, X(1857), X(4082)}}, {{A, B, C, X(2318), X(3190)}}, {{A, B, C, X(2901), X(3694)}}, {{A, B, C, X(3057), X(5264)}}, {{A, B, C, X(3085), X(6737)}}, {{A, B, C, X(3100), X(4347)}}, {{A, B, C, X(3486), X(39579)}}, {{A, B, C, X(3600), X(12575)}}, {{A, B, C, X(3663), X(4339)}}, {{A, B, C, X(3671), X(4313)}}, {{A, B, C, X(3680), X(5687)}}, {{A, B, C, X(3710), X(41507)}}, {{A, B, C, X(3871), X(49492)}}, {{A, B, C, X(3900), X(29016)}}, {{A, B, C, X(4292), X(4294)}}, {{A, B, C, X(4293), X(10624)}}, {{A, B, C, X(4295), X(4304)}}, {{A, B, C, X(4301), X(5731)}}, {{A, B, C, X(4308), X(4342)}}, {{A, B, C, X(4311), X(30305)}}, {{A, B, C, X(4315), X(9785)}}, {{A, B, C, X(5255), X(10480)}}, {{A, B, C, X(5496), X(35193)}}, {{A, B, C, X(5732), X(12651)}}, {{A, B, C, X(6556), X(17895)}}, {{A, B, C, X(6735), X(49168)}}, {{A, B, C, X(6736), X(18391)}}, {{A, B, C, X(7017), X(36934)}}, {{A, B, C, X(7040), X(10395)}}, {{A, B, C, X(7319), X(23521)}}, {{A, B, C, X(8611), X(52387)}}, {{A, B, C, X(11037), X(30331)}}, {{A, B, C, X(13405), X(20007)}}, {{A, B, C, X(15315), X(40505)}}, {{A, B, C, X(15446), X(24202)}}, {{A, B, C, X(17885), X(43731)}}, {{A, B, C, X(33576), X(40446)}}, {{A, B, C, X(34919), X(43972)}}, {{A, B, C, X(36123), X(38271)}}, {{A, B, C, X(40836), X(43672)}}, {{A, B, C, X(42470), X(56140)}}
X(56146) = barycentric product X(i)*X(j) for these (i, j): {29, 40161}, {190, 23289}, {333, 41506}, {1305, 3239}, {1751, 8}, {2218, 312}, {2321, 272}, {2322, 28786}, {2997, 9}, {3710, 40574}, {15467, 220}, {40011, 55}, {51566, 650}
X(56146) = barycentric quotient X(i)/X(j) for these (i, j): {6, 4306}, {8, 18134}, {9, 3868}, {41, 2352}, {55, 579}, {200, 27396}, {210, 22021}, {220, 3190}, {272, 1434}, {281, 5125}, {573, 19367}, {650, 23800}, {657, 8676}, {661, 51658}, {663, 43060}, {1305, 658}, {1334, 209}, {1751, 7}, {2218, 57}, {2318, 51574}, {2328, 56000}, {2997, 85}, {3239, 20294}, {7071, 41320}, {23289, 514}, {24026, 17878}, {40011, 6063}, {40161, 307}, {41506, 226}, {42069, 5190}, {51566, 4554}
X(56146) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2218, 41506, 1751}, {40161, 41506, 10}

X(56147) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(10) AND X(76)

Barycentrics    a*(-b^4+a*c^3+b*c^3+a^3*(b+c))*(a*b^3+a^3*(b+c)+c*(b^3-c^3)) : :

X(56147) lies on these lines: {32, 761}, {42, 7146}, {55, 16876}, {76, 760}, {210, 3661}, {257, 54291}, {518, 51837}, {984, 1334}, {2176, 52029}, {2809, 3864}, {3212, 13576}

X(56147) = trilinear pole of line {1491, 3709}
X(56147) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 24586}
X(56147) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 24586}
X(56147) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(76)}}, {{A, B, C, X(4), X(16876)}}, {{A, B, C, X(6), X(7261)}}, {{A, B, C, X(8), X(42)}}, {{A, B, C, X(19), X(7233)}}, {{A, B, C, X(25), X(7224)}}, {{A, B, C, X(32), X(760)}}, {{A, B, C, X(56), X(2113)}}, {{A, B, C, X(85), X(105)}}, {{A, B, C, X(251), X(7357)}}, {{A, B, C, X(291), X(17743)}}, {{A, B, C, X(518), X(2176)}}, {{A, B, C, X(812), X(2809)}}, {{A, B, C, X(904), X(1469)}}, {{A, B, C, X(981), X(39712)}}, {{A, B, C, X(983), X(1581)}}, {{A, B, C, X(1390), X(31359)}}, {{A, B, C, X(1432), X(43751)}}, {{A, B, C, X(1829), X(32937)}}, {{A, B, C, X(1876), X(43750)}}, {{A, B, C, X(3907), X(10570)}}, {{A, B, C, X(4429), X(33938)}}, {{A, B, C, X(7241), X(9278)}}, {{A, B, C, X(9941), X(12194)}}, {{A, B, C, X(13476), X(41527)}}, {{A, B, C, X(35628), X(42550)}}
X(56147) = barycentric quotient X(i)/X(j) for these (i, j): {1, 24586}

X(56148) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(10) AND X(78)

Barycentrics    a*(a^6-2*a^5*b+(b-c)^4*(b+c)^2+2*a^3*b*(2*b^2-b*c-c^2)-a^4*(b^2-4*b*c+c^2)-a^2*(b-c)^2*(b^2+4*b*c+c^2)-2*a*b*(b^4-b^3*c+b^2*c^2+b*c^3-2*c^4))*(a^6-2*a^5*c+(b-c)^4*(b+c)^2-2*a^3*c*(b^2+b*c-2*c^2)-a^4*(b^2-4*b*c+c^2)-a^2*(b-c)^2*(b^2+4*b*c+c^2)-2*a*c*(-2*b^4+b^3*c+b^2*c^2-b*c^3+c^4)) : :

X(56148) lies on these lines: {1, 14257}, {3, 227}, {29, 47372}, {34, 102}, {40, 283}, {46, 1795}, {65, 1433}, {78, 515}, {219, 1766}, {282, 1826}, {284, 2331}, {322, 332}, {517, 1069}, {945, 34036}, {1482, 38248}, {2646, 8283}, {3576, 40442}, {4320, 44075}, {5691, 39990}, {20220, 51565}

X(56148) = isogonal conjugate of X(6261)
X(56148) = trilinear pole of line {652, 6588}
X(56148) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 6261}
X(56148) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 42464}
X(56148) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 6261}
X(56148) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3)}}, {{A, B, C, X(4), X(961)}}, {{A, B, C, X(28), X(3427)}}, {{A, B, C, X(34), X(84)}}, {{A, B, C, X(40), X(65)}}, {{A, B, C, X(46), X(517)}}, {{A, B, C, X(57), X(14110)}}, {{A, B, C, X(64), X(1411)}}, {{A, B, C, X(80), X(921)}}, {{A, B, C, X(280), X(36121)}}, {{A, B, C, X(937), X(30500)}}, {{A, B, C, X(944), X(34036)}}, {{A, B, C, X(963), X(38269)}}, {{A, B, C, X(972), X(1002)}}, {{A, B, C, X(1063), X(40437)}}, {{A, B, C, X(1155), X(7982)}}, {{A, B, C, X(1167), X(56101)}}, {{A, B, C, X(1385), X(3612)}}, {{A, B, C, X(1420), X(50371)}}, {{A, B, C, X(1870), X(15176)}}, {{A, B, C, X(2646), X(3576)}}, {{A, B, C, X(2804), X(2817)}}, {{A, B, C, X(3062), X(54197)}}, {{A, B, C, X(3417), X(3449)}}, {{A, B, C, X(4185), X(37422)}}, {{A, B, C, X(4320), X(10444)}}, {{A, B, C, X(5119), X(34339)}}, {{A, B, C, X(5560), X(29374)}}, {{A, B, C, X(7991), X(36279)}}, {{A, B, C, X(10309), X(36125)}}, {{A, B, C, X(14956), X(37117)}}, {{A, B, C, X(22766), X(37611)}}, {{A, B, C, X(28473), X(44661)}}, {{A, B, C, X(29056), X(40718)}}, {{A, B, C, X(30389), X(37606)}}, {{A, B, C, X(37570), X(39598)}}, {{A, B, C, X(40397), X(41514)}}
X(56148) = barycentric quotient X(i)/X(j) for these (i, j): {6, 6261}

X(56149) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(10) AND X(82)

Barycentrics    a*(a^3+a*b^2+2*b^3+b^2*c+c^3)*(a^3+b^3+a*c^2+b*c^2+2*c^3) : :

X(56149) lies on these lines: {10, 32775}, {37, 30117}, {38, 759}, {82, 758}, {994, 49454}, {2363, 3874}, {3868, 54336}, {3961, 4674}, {29656, 34895}, {49686, 53114}

X(56149) = isogonal conjugate of X(49480)
X(56149) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 49480}, {32, 30893}
X(56149) = X(i)-vertex conjugate of X(j) for these {i, j}: {58, 38813}
X(56149) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 49480}, {6376, 30893}
X(56149) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}}, {{A, B, C, X(2), X(17925)}}, {{A, B, C, X(6), X(22453)}}, {{A, B, C, X(38), X(758)}}, {{A, B, C, X(58), X(1257)}}, {{A, B, C, X(76), X(40398)}}, {{A, B, C, X(80), X(15321)}}, {{A, B, C, X(291), X(32775)}}, {{A, B, C, X(519), X(3961)}}, {{A, B, C, X(675), X(1390)}}, {{A, B, C, X(741), X(39395)}}, {{A, B, C, X(753), X(1280)}}, {{A, B, C, X(977), X(52375)}}, {{A, B, C, X(993), X(49454)}}, {{A, B, C, X(996), X(1168)}}, {{A, B, C, X(998), X(39959)}}, {{A, B, C, X(1000), X(2751)}}, {{A, B, C, X(1120), X(4360)}}, {{A, B, C, X(1126), X(38813)}}, {{A, B, C, X(1255), X(32013)}}, {{A, B, C, X(1389), X(45136)}}, {{A, B, C, X(2292), X(3874)}}, {{A, B, C, X(2334), X(7087)}}, {{A, B, C, X(3242), X(5526)}}, {{A, B, C, X(3679), X(49686)}}, {{A, B, C, X(3757), X(30116)}}, {{A, B, C, X(4492), X(15175)}}, {{A, B, C, X(5561), X(40401)}}, {{A, B, C, X(7096), X(40023)}}, {{A, B, C, X(15315), X(40436)}}, {{A, B, C, X(32779), X(33155)}}
X(56149) = barycentric quotient X(i)/X(j) for these (i, j): {6, 49480}, {75, 30893}

X(56150) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(10) AND X(87)

Barycentrics    a*(a^2*(b-c)+b*c*(b+c)+a*(b^2-5*b*c-c^2))*(a^2*(b-c)-b*c*(b+c)+a*(b^2+5*b*c-c^2)) : :

X(56150) lies on these lines: {6, 52964}, {43, 106}, {56, 50581}, {58, 25439}, {87, 519}, {145, 979}, {978, 3445}, {3244, 39969}, {3632, 39949}, {3633, 39748}, {3751, 9432}, {4083, 23345}, {16236, 37627}

X(56150) = trilinear pole of line {649, 14408}
X(56150) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 24620}
X(56150) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 24620}
X(56150) = X(i)-cross conjugate of X(j) for these {i, j}: {3241, 1}
X(56150) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(6)}}, {{A, B, C, X(8), X(50581)}}, {{A, B, C, X(43), X(519)}}, {{A, B, C, X(57), X(1016)}}, {{A, B, C, X(80), X(39742)}}, {{A, B, C, X(145), X(959)}}, {{A, B, C, X(291), X(1000)}}, {{A, B, C, X(1002), X(56142)}}, {{A, B, C, X(1219), X(43073)}}, {{A, B, C, X(1247), X(7160)}}, {{A, B, C, X(2802), X(25574)}}, {{A, B, C, X(3216), X(3633)}}, {{A, B, C, X(3244), X(21214)}}, {{A, B, C, X(3293), X(3632)}}, {{A, B, C, X(3362), X(21398)}}, {{A, B, C, X(3500), X(38247)}}, {{A, B, C, X(3551), X(39697)}}, {{A, B, C, X(3577), X(29348)}}, {{A, B, C, X(4674), X(25439)}}, {{A, B, C, X(4752), X(16236)}}, {{A, B, C, X(4866), X(52549)}}, {{A, B, C, X(4900), X(7220)}}, {{A, B, C, X(6553), X(45989)}}, {{A, B, C, X(7284), X(9282)}}, {{A, B, C, X(18793), X(53114)}}, {{A, B, C, X(30116), X(42042)}}, {{A, B, C, X(32013), X(39963)}}, {{A, B, C, X(34860), X(46187)}}, {{A, B, C, X(42285), X(52654)}}, {{A, B, C, X(42360), X(43071)}}, {{A, B, C, X(49997), X(51093)}}, {{A, B, C, X(52924), X(53115)}}
X(56150) = barycentric quotient X(i)/X(j) for these (i, j): {1, 24620}

X(56151) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(10) AND X(89)

Barycentrics    a*(2*a^2+5*b^2+a*(b-2*c)+b*c+2*c^2)*(2*a^2+2*b^2+b*c+5*c^2+a*(-2*b+c)) : :

X(56151) lies on these lines: {45, 105}, {81, 41711}, {88, 4392}, {89, 518}, {279, 5252}, {985, 49712}, {3227, 36534}, {3242, 55935}, {3617, 39724}, {3938, 39948}, {3961, 39980}, {5550, 32019}, {7174, 39963}, {16670, 39958}, {34914, 36479}, {36480, 36871}

X(56151) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(4), X(39744)}}, {{A, B, C, X(8), X(5252)}}, {{A, B, C, X(44), X(4492)}}, {{A, B, C, X(45), X(518)}}, {{A, B, C, X(899), X(36534)}}, {{A, B, C, X(984), X(49712)}}, {{A, B, C, X(2297), X(41439)}}, {{A, B, C, X(3240), X(36480)}}, {{A, B, C, X(3242), X(3246)}}, {{A, B, C, X(3617), X(3961)}}, {{A, B, C, X(3938), X(9780)}}, {{A, B, C, X(4373), X(39977)}}, {{A, B, C, X(5220), X(49515)}}, {{A, B, C, X(5297), X(36479)}}, {{A, B, C, X(7174), X(16670)}}, {{A, B, C, X(9309), X(23051)}}, {{A, B, C, X(14191), X(14947)}}, {{A, B, C, X(28370), X(29668)}}, {{A, B, C, X(29820), X(46934)}}, {{A, B, C, X(36588), X(40401)}}, {{A, B, C, X(49448), X(51297)}}

X(56152) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(10) AND X(90)

Barycentrics    a*(a^3+3*b^3-b^2*c-3*b*c^2+c^3-a^2*(3*b+c)-a*(b^2-4*b*c+c^2))*(a^3+b^3-3*b^2*c-b*c^2+3*c^3-a^2*(b+3*c)-a*(b^2-4*b*c+c^2)) : :

X(56152) lies on the Feuerbach hyperbola and on these lines: {1, 6911}, {4, 25415}, {7, 45287}, {8, 5187}, {9, 5697}, {21, 5119}, {40, 15446}, {46, 104}, {65, 7284}, {79, 3340}, {80, 7982}, {84, 5903}, {90, 517}, {515, 5553}, {519, 43740}, {952, 41688}, {1000, 3090}, {1320, 3811}, {1392, 34772}, {1420, 56036}, {1476, 3338}, {1478, 5555}, {1479, 30513}, {1697, 15175}, {2099, 17098}, {2136, 6596}, {2320, 3612}, {2802, 45393}, {3057, 7162}, {3085, 7320}, {3254, 3633}, {3296, 3476}, {3333, 15180}, {3577, 11009}, {3632, 6598}, {5557, 11529}, {5559, 7741}, {5560, 11280}, {5691, 46435}, {5902, 7091}, {6867, 10827}, {6942, 37618}, {7133, 35642}, {7280, 11279}, {7971, 37006}, {9614, 34918}, {10915, 30852}, {11491, 37518}, {11531, 38271}, {12641, 12653}, {13606, 37735}, {15179, 51816}, {15313, 23838}, {16200, 21398}, {35641, 42013}, {37356, 41687}, {38665, 56040}

X(56152) = isogonal conjugate of X(37618)
X(56152) = X(i)-cross conjugate of X(j) for these {i, j}: {1482, 1}
X(56152) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(3), X(25415)}}, {{A, B, C, X(28), X(5187)}}, {{A, B, C, X(29), X(6911)}}, {{A, B, C, X(33), X(45287)}}, {{A, B, C, X(34), X(1168)}}, {{A, B, C, X(35), X(3340)}}, {{A, B, C, X(36), X(7982)}}, {{A, B, C, X(40), X(5903)}}, {{A, B, C, X(46), X(517)}}, {{A, B, C, X(56), X(30323)}}, {{A, B, C, X(57), X(5697)}}, {{A, B, C, X(65), X(5119)}}, {{A, B, C, X(92), X(39947)}}, {{A, B, C, X(102), X(52186)}}, {{A, B, C, X(519), X(3811)}}, {{A, B, C, X(945), X(36052)}}, {{A, B, C, X(998), X(21616)}}, {{A, B, C, X(1121), X(44178)}}, {{A, B, C, X(1126), X(3422)}}, {{A, B, C, X(1222), X(11501)}}, {{A, B, C, X(1391), X(16835)}}, {{A, B, C, X(1411), X(10826)}}, {{A, B, C, X(1482), X(37618)}}, {{A, B, C, X(1697), X(5902)}}, {{A, B, C, X(1807), X(37711)}}, {{A, B, C, X(2093), X(7991)}}, {{A, B, C, X(2099), X(3612)}}, {{A, B, C, X(2334), X(52185)}}, {{A, B, C, X(2802), X(55126)}}, {{A, B, C, X(3057), X(3338)}}, {{A, B, C, X(3085), X(4853)}}, {{A, B, C, X(3090), X(17519)}}, {{A, B, C, X(3362), X(39969)}}, {{A, B, C, X(3478), X(3527)}}, {{A, B, C, X(3576), X(11009)}}, {{A, B, C, X(3632), X(34772)}}, {{A, B, C, X(3633), X(3935)}}, {{A, B, C, X(3746), X(11529)}}, {{A, B, C, X(3872), X(10039)}}, {{A, B, C, X(4674), X(14923)}}, {{A, B, C, X(4915), X(5703)}}, {{A, B, C, X(5563), X(7962)}}, {{A, B, C, X(5691), X(15500)}}, {{A, B, C, X(7095), X(39959)}}, {{A, B, C, X(7280), X(11280)}}, {{A, B, C, X(8056), X(50442)}}, {{A, B, C, X(9623), X(19843)}}, {{A, B, C, X(9957), X(51816)}}, {{A, B, C, X(10428), X(45818)}}, {{A, B, C, X(10570), X(11499)}}, {{A, B, C, X(10623), X(15337)}}, {{A, B, C, X(11502), X(14942)}}, {{A, B, C, X(11531), X(15803)}}, {{A, B, C, X(12629), X(34619)}}, {{A, B, C, X(15227), X(44760)}}, {{A, B, C, X(15617), X(18771)}}, {{A, B, C, X(16200), X(21842)}}, {{A, B, C, X(18398), X(31393)}}, {{A, B, C, X(37556), X(50190)}}
X(56152) = barycentric quotient X(i)/X(j) for these (i, j): {6, 37618}

X(56153) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(10) AND X(92)

Barycentrics    a*(-(a^3*b^2)+a^4*(b+c)-a^2*b*(b+c)^2+a*(b^4-b^2*c^2)+c*(b^4-c^4))*(-b^5-a^3*c^2+b*c^4+a^4*(b+c)-a^2*c*(b+c)^2+a*(-(b^2*c^2)+c^4)) : :

X(56153) lies on these lines: {48, 26702}, {63, 4184}, {72, 3693}, {92, 44661}, {226, 1861}, {304, 33297}, {306, 3681}, {518, 1214}, {3419, 39993}, {3868, 9436}

X(56153) = isogonal conjugate of X(51687)
X(56153) = trilinear pole of line {656, 6586}
X(56153) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 51687}, {2, 44081}, {6, 379}
X(56153) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 51687}, {9, 379}, {32664, 44081}
X(56153) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(63)}}, {{A, B, C, X(4), X(103)}}, {{A, B, C, X(6), X(15314)}}, {{A, B, C, X(8), X(2328)}}, {{A, B, C, X(9), X(75)}}, {{A, B, C, X(21), X(6063)}}, {{A, B, C, X(48), X(520)}}, {{A, B, C, X(58), X(39732)}}, {{A, B, C, X(65), X(2258)}}, {{A, B, C, X(66), X(2259)}}, {{A, B, C, X(69), X(284)}}, {{A, B, C, X(189), X(955)}}, {{A, B, C, X(253), X(2335)}}, {{A, B, C, X(291), X(1751)}}, {{A, B, C, X(313), X(22021)}}, {{A, B, C, X(405), X(1224)}}, {{A, B, C, X(909), X(5486)}}, {{A, B, C, X(928), X(2809)}}, {{A, B, C, X(943), X(1390)}}, {{A, B, C, X(951), X(34259)}}, {{A, B, C, X(956), X(18397)}}, {{A, B, C, X(960), X(11523)}}, {{A, B, C, X(984), X(10477)}}, {{A, B, C, X(994), X(2249)}}, {{A, B, C, X(1257), X(34258)}}, {{A, B, C, X(1280), X(39700)}}, {{A, B, C, X(1903), X(13476)}}, {{A, B, C, X(2334), X(7169)}}, {{A, B, C, X(2733), X(18446)}}, {{A, B, C, X(3451), X(17040)}}, {{A, B, C, X(5223), X(5728)}}, {{A, B, C, X(7018), X(40436)}}, {{A, B, C, X(8048), X(13404)}}, {{A, B, C, X(8748), X(40417)}}, {{A, B, C, X(14054), X(41229)}}, {{A, B, C, X(38883), X(41434)}}, {{A, B, C, X(41863), X(45120)}}, {{A, B, C, X(52560), X(55035)}}
X(56153) = barycentric quotient X(i)/X(j) for these (i, j): {1, 379}, {6, 51687}, {31, 44081}

X(56154) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(10) AND X(98)

Barycentrics    a*(a+b)*(a-b-c)*(a+c)*(-b^2+a*c)*(a*b-c^2) : :
X(56154) = -3*X[2]+2*X[50440]

X(56154) lies on these lines: {1, 1581}, {2, 50440}, {6, 24523}, {8, 7257}, {21, 644}, {27, 295}, {42, 81}, {55, 643}, {58, 3864}, {65, 664}, {86, 17792}, {98, 385}, {99, 3110}, {210, 333}, {261, 3688}, {270, 607}, {292, 5331}, {334, 7270}, {512, 7983}, {518, 7061}, {528, 19635}, {645, 3271}, {660, 17763}, {662, 8301}, {674, 19623}, {799, 17794}, {813, 53707}, {875, 4155}, {940, 37099}, {1002, 51563}, {1010, 40848}, {1362, 4573}, {2334, 4614}, {2357, 13138}, {2363, 18268}, {2887, 30965}, {3056, 27958}, {3124, 25819}, {3286, 51928}, {3750, 51867}, {3868, 3905}, {3873, 6742}, {4553, 25536}, {4589, 4645}, {8033, 24349}, {9025, 40882}, {9413, 9415}, {10760, 41610}, {17944, 34079}, {18206, 18788}, {20531, 31001}, {24678, 27164}, {28471, 36066}, {30995, 31126}, {36214, 48909}, {37683, 54383}

X(56154) = reflection of X(i) in X(j) for these {i,j}: {3903, 1}, {8, 40608}, {99, 3110}
X(56154) = isogonal conjugate of X(1284)
X(56154) = anticomplement of X(50440)
X(56154) = trilinear pole of line {9, 3287}
X(56154) = perspector of circumconic {{A, B, C, X(4584), X(36806)}}
X(56154) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 1284}, {3, 1874}, {6, 16609}, {7, 3747}, {10, 1428}, {12, 5009}, {37, 1429}, {42, 1447}, {56, 740}, {57, 2238}, {58, 7235}, {65, 238}, {73, 242}, {77, 862}, {85, 41333}, {101, 7212}, {108, 53556}, {109, 4010}, {181, 33295}, {213, 10030}, {225, 7193}, {226, 1914}, {239, 1400}, {269, 4433}, {349, 14599}, {350, 1402}, {604, 3948}, {651, 21832}, {659, 4551}, {664, 4455}, {741, 3027}, {804, 29055}, {812, 4559}, {874, 51641}, {1020, 4435}, {1042, 3685}, {1214, 2201}, {1397, 35544}, {1407, 3985}, {1412, 4037}, {1414, 4155}, {1417, 4783}, {1425, 14024}, {1427, 3684}, {1431, 4039}, {1441, 2210}, {1464, 36815}, {1880, 20769}, {1910, 16591}, {1918, 18033}, {2197, 31905}, {2720, 42767}, {3570, 7180}, {3573, 4017}, {3716, 53321}, {4552, 8632}, {4557, 43041}, {4564, 39786}, {4573, 46390}, {7066, 34856}, {7132, 18904}, {8850, 18793}, {12835, 43534}, {13576, 51329}, {18785, 34253}, {21859, 50456}, {24459, 32674}, {26700, 53563}
X(56154) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 740}, {3, 1284}, {9, 16609}, {10, 7235}, {11, 4010}, {1015, 7212}, {2886, 51464}, {3161, 3948}, {5452, 2238}, {6600, 4433}, {6626, 10030}, {8299, 3027}, {9470, 65}, {11672, 16591}, {24771, 3985}, {34021, 18033}, {34961, 3573}, {35072, 24459}, {35095, 46842}, {36103, 1874}, {36906, 226}, {38981, 42767}, {38983, 53556}, {38991, 21832}, {39025, 4455}, {40582, 239}, {40589, 1429}, {40592, 1447}, {40599, 4037}, {40602, 238}, {40605, 350}, {40608, 4155}, {40625, 3766}, {50440, 50440}, {52871, 4783}, {55042, 53563}, {55067, 812}, {55068, 3716}
X(56154) = X(i)-Ceva conjugate of X(j) for these {i, j}: {18827, 37128}
X(56154) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {741, 147}, {1976, 39367}, {3572, 39359}
X(56154) = X(i)-cross conjugate of X(j) for these {i, j}: {295, 1808}, {926, 5546}, {2311, 37128}, {4433, 9}, {4435, 645}, {4876, 36800}, {7077, 2311}, {35104, 8}
X(56154) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(98)}}, {{A, B, C, X(6), X(7155)}}, {{A, B, C, X(8), X(42)}}, {{A, B, C, X(9), X(4649)}}, {{A, B, C, X(21), X(27)}}, {{A, B, C, X(29), X(13588)}}, {{A, B, C, X(56), X(20359)}}, {{A, B, C, X(58), X(3794)}}, {{A, B, C, X(60), X(17187)}}, {{A, B, C, X(74), X(39768)}}, {{A, B, C, X(78), X(1999)}}, {{A, B, C, X(80), X(53873)}}, {{A, B, C, X(100), X(643)}}, {{A, B, C, X(103), X(2481)}}, {{A, B, C, X(280), X(39696)}}, {{A, B, C, X(283), X(5208)}}, {{A, B, C, X(284), X(314)}}, {{A, B, C, X(290), X(53336)}}, {{A, B, C, X(291), X(1581)}}, {{A, B, C, X(345), X(19791)}}, {{A, B, C, X(511), X(23996)}}, {{A, B, C, X(518), X(4645)}}, {{A, B, C, X(521), X(17973)}}, {{A, B, C, X(522), X(11609)}}, {{A, B, C, X(741), X(2311)}}, {{A, B, C, X(940), X(37539)}}, {{A, B, C, X(1043), X(33296)}}, {{A, B, C, X(1469), X(3056)}}, {{A, B, C, X(1793), X(19642)}}, {{A, B, C, X(1911), X(1967)}}, {{A, B, C, X(2316), X(36798)}}, {{A, B, C, X(2699), X(36051)}}, {{A, B, C, X(2983), X(31643)}}, {{A, B, C, X(2990), X(26703)}}, {{A, B, C, X(2997), X(37741)}}, {{A, B, C, X(3423), X(54128)}}, {{A, B, C, X(3680), X(7220)}}, {{A, B, C, X(3684), X(7281)}}, {{A, B, C, X(3868), X(7270)}}, {{A, B, C, X(3871), X(3996)}}, {{A, B, C, X(3873), X(35193)}}, {{A, B, C, X(4155), X(35104)}}, {{A, B, C, X(4511), X(17763)}}, {{A, B, C, X(4570), X(14616)}}, {{A, B, C, X(5148), X(5194)}}, {{A, B, C, X(9840), X(48909)}}, {{A, B, C, X(11604), X(42552)}}, {{A, B, C, X(13476), X(43749)}}, {{A, B, C, X(13577), X(43740)}}, {{A, B, C, X(14947), X(43672)}}, {{A, B, C, X(15630), X(40608)}}, {{A, B, C, X(17792), X(24349)}}, {{A, B, C, X(19628), X(56105)}}, {{A, B, C, X(28531), X(50520)}}, {{A, B, C, X(34409), X(56153)}}, {{A, B, C, X(36800), X(37128)}}, {{A, B, C, X(39933), X(39941)}}, {{A, B, C, X(39971), X(52652)}}, {{A, B, C, X(46273), X(53194)}}, {{A, B, C, X(50612), X(50635)}}, {{A, B, C, X(50615), X(50629)}}, {{A, B, C, X(50617), X(50630)}}, {{A, B, C, X(50618), X(50631)}}, {{A, B, C, X(50621), X(50626)}}, {{A, B, C, X(50622), X(50627)}}
X(56154) = barycentric product X(i)*X(j) for these (i, j): {1, 36800}, {21, 335}, {274, 7077}, {284, 334}, {291, 333}, {292, 314}, {295, 31623}, {310, 51858}, {312, 741}, {645, 876}, {1019, 36801}, {1172, 337}, {1581, 27958}, {1808, 92}, {1911, 28660}, {1922, 40072}, {2185, 43534}, {2196, 44130}, {2287, 7233}, {2311, 75}, {3056, 40834}, {3572, 7257}, {3703, 39276}, {3737, 4562}, {4444, 643}, {4518, 81}, {4560, 660}, {4583, 7252}, {4584, 522}, {4589, 650}, {4639, 663}, {4876, 86}, {17197, 5378}, {18155, 813}, {18206, 33676}, {18265, 6385}, {18268, 3596}, {18827, 9}, {18829, 3287}, {18895, 2194}, {35352, 4612}, {36066, 3700}, {36806, 512}, {37128, 8}, {37134, 3907}, {39292, 40608}, {40017, 55}
X(56154) = barycentric quotient X(i)/X(j) for these (i, j): {1, 16609}, {6, 1284}, {8, 3948}, {9, 740}, {19, 1874}, {21, 239}, {37, 7235}, {41, 3747}, {55, 2238}, {58, 1429}, {81, 1447}, {86, 10030}, {200, 3985}, {210, 4037}, {220, 4433}, {261, 30940}, {270, 31905}, {274, 18033}, {283, 20769}, {284, 238}, {291, 226}, {292, 65}, {295, 1214}, {312, 35544}, {314, 1921}, {333, 350}, {334, 349}, {335, 1441}, {337, 1231}, {511, 16591}, {513, 7212}, {521, 24459}, {607, 862}, {643, 3570}, {645, 874}, {650, 4010}, {652, 53556}, {660, 4552}, {663, 21832}, {741, 57}, {805, 37137}, {813, 4551}, {875, 7180}, {876, 7178}, {1019, 43041}, {1021, 3716}, {1043, 3975}, {1172, 242}, {1333, 1428}, {1808, 63}, {1911, 1400}, {1922, 1402}, {2150, 5009}, {2175, 41333}, {2185, 33295}, {2193, 7193}, {2194, 1914}, {2196, 73}, {2238, 3027}, {2287, 3685}, {2299, 2201}, {2311, 1}, {2325, 4783}, {2326, 14024}, {2328, 3684}, {2329, 4039}, {2341, 36815}, {3056, 18904}, {3063, 4455}, {3271, 39786}, {3286, 34253}, {3287, 804}, {3572, 4017}, {3684, 4368}, {3709, 4155}, {3737, 812}, {3786, 3797}, {3794, 33891}, {3864, 16603}, {4433, 35068}, {4444, 4077}, {4512, 4771}, {4518, 321}, {4560, 3766}, {4584, 664}, {4589, 4554}, {4639, 4572}, {4876, 10}, {4877, 4716}, {5546, 3573}, {7077, 37}, {7233, 1446}, {7252, 659}, {7257, 27853}, {9404, 53563}, {13588, 39930}, {16588, 51464}, {18191, 27918}, {18206, 39775}, {18265, 213}, {18268, 56}, {18787, 4032}, {18827, 85}, {21789, 4435}, {27958, 1966}, {28660, 18891}, {31623, 40717}, {34067, 4559}, {35104, 46842}, {36066, 4573}, {36800, 75}, {36801, 4033}, {36806, 670}, {37128, 7}, {40017, 6063}, {40072, 44169}, {40972, 4093}, {43534, 6358}, {45783, 17084}, {46393, 42767}, {51858, 42}
X(56154) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {291, 741, 37128}

X(56155) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(10) AND X(145)

Barycentrics    a*(a+b-c)*(a-b+c)*(a*(b-2*c)+b*(b+c))*(a*(2*b-c)-c*(b+c)) : :

X(56155) lies on cubic K571 and on these lines: {1, 14261}, {2, 39701}, {8, 1357}, {56, 7419}, {57, 3214}, {65, 145}, {959, 1401}, {978, 1400}, {1042, 1149}, {1388, 45247}, {1426, 1878}, {1463, 5265}, {3445, 8686}, {3485, 20615}, {3616, 55011}, {3813, 40617}, {3976, 53538}, {4307, 5045}, {4308, 17114}, {4441, 35159}, {5697, 38515}, {9309, 52541}, {23617, 25524}

X(56155) = isogonal conjugate of X(3913)
X(56155) = trilinear pole of line {4394, 7180}
X(56155) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 3913}, {2, 3217}, {6, 30568}, {8, 3915}, {9, 4383}, {21, 3214}, {41, 18135}, {55, 3875}, {78, 4186}, {100, 42312}, {284, 3175}, {312, 16946}, {643, 4139}, {644, 4498}, {2287, 28387}, {3939, 4106}, {4076, 17477}
X(56155) = X(i)-vertex conjugate of X(j) for these {i, j}: {1002, 1617}
X(56155) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 3913}, {9, 30568}, {223, 3875}, {478, 4383}, {1015, 20317}, {3160, 18135}, {8054, 42312}, {32664, 3217}, {40590, 3175}, {40611, 3214}, {40617, 4106}, {55060, 4139}
X(56155) = X(i)-Ceva conjugate of X(j) for these {i, j}: {42304, 39956}
X(56155) = X(i)-cross conjugate of X(j) for these {i, j}: {37, 57}, {2275, 279}, {3616, 959}
X(56155) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(145)}}, {{A, B, C, X(2), X(978)}}, {{A, B, C, X(3), X(840)}}, {{A, B, C, X(4), X(106)}}, {{A, B, C, X(6), X(5558)}}, {{A, B, C, X(7), X(56)}}, {{A, B, C, X(8), X(513)}}, {{A, B, C, X(9), X(12632)}}, {{A, B, C, X(10), X(28370)}}, {{A, B, C, X(21), X(2191)}}, {{A, B, C, X(28), X(4190)}}, {{A, B, C, X(34), X(1476)}}, {{A, B, C, X(37), X(3214)}}, {{A, B, C, X(43), X(26111)}}, {{A, B, C, X(54), X(41442)}}, {{A, B, C, X(57), X(3361)}}, {{A, B, C, X(58), X(1002)}}, {{A, B, C, X(60), X(3433)}}, {{A, B, C, X(64), X(38882)}}, {{A, B, C, X(78), X(28080)}}, {{A, B, C, X(79), X(957)}}, {{A, B, C, X(84), X(105)}}, {{A, B, C, X(87), X(1219)}}, {{A, B, C, X(102), X(10305)}}, {{A, B, C, X(104), X(56148)}}, {{A, B, C, X(108), X(7040)}}, {{A, B, C, X(269), X(961)}}, {{A, B, C, X(277), X(1019)}}, {{A, B, C, X(279), X(4334)}}, {{A, B, C, X(479), X(52013)}}, {{A, B, C, X(596), X(3676)}}, {{A, B, C, X(738), X(21446)}}, {{A, B, C, X(945), X(10309)}}, {{A, B, C, X(951), X(1119)}}, {{A, B, C, X(953), X(5553)}}, {{A, B, C, X(979), X(6553)}}, {{A, B, C, X(994), X(43733)}}, {{A, B, C, X(998), X(15179)}}, {{A, B, C, X(1037), X(1413)}}, {{A, B, C, X(1106), X(7248)}}, {{A, B, C, X(1126), X(18490)}}, {{A, B, C, X(1173), X(41487)}}, {{A, B, C, X(1247), X(50520)}}, {{A, B, C, X(1257), X(11851)}}, {{A, B, C, X(1319), X(1388)}}, {{A, B, C, X(1376), X(52541)}}, {{A, B, C, X(1411), X(37738)}}, {{A, B, C, X(1416), X(8817)}}, {{A, B, C, X(1434), X(42290)}}, {{A, B, C, X(1462), X(7131)}}, {{A, B, C, X(1463), X(17090)}}, {{A, B, C, X(1617), X(5045)}}, {{A, B, C, X(2163), X(5557)}}, {{A, B, C, X(2275), X(24349)}}, {{A, B, C, X(3161), X(3913)}}, {{A, B, C, X(3418), X(51496)}}, {{A, B, C, X(3435), X(38269)}}, {{A, B, C, X(3551), X(43533)}}, {{A, B, C, X(3612), X(34489)}}, {{A, B, C, X(3669), X(27818)}}, {{A, B, C, X(3742), X(4255)}}, {{A, B, C, X(3752), X(25524)}}, {{A, B, C, X(3896), X(17127)}}, {{A, B, C, X(4307), X(4350)}}, {{A, B, C, X(4719), X(37674)}}, {{A, B, C, X(5193), X(5697)}}, {{A, B, C, X(5438), X(5573)}}, {{A, B, C, X(5556), X(34434)}}, {{A, B, C, X(7320), X(41436)}}, {{A, B, C, X(8056), X(45047)}}, {{A, B, C, X(9957), X(41426)}}, {{A, B, C, X(10428), X(39267)}}, {{A, B, C, X(15337), X(38273)}}, {{A, B, C, X(16079), X(46356)}}, {{A, B, C, X(17107), X(43760)}}, {{A, B, C, X(18398), X(37583)}}, {{A, B, C, X(18771), X(42019)}}, {{A, B, C, X(20332), X(54123)}}, {{A, B, C, X(28479), X(39732)}}, {{A, B, C, X(29814), X(50590)}}, {{A, B, C, X(34860), X(39956)}}, {{A, B, C, X(35577), X(56150)}}, {{A, B, C, X(36602), X(39975)}}, {{A, B, C, X(37129), X(39702)}}, {{A, B, C, X(40436), X(46972)}}, {{A, B, C, X(44301), X(51656)}}, {{A, B, C, X(45104), X(54121)}}, {{A, B, C, X(52205), X(53146)}}
X(56155) = barycentric product X(i)*X(j) for these (i, j): {1, 42304}, {1014, 56123}, {4383, 55011}, {7178, 8690}, {34860, 57}, {39956, 7}, {40012, 56}
X(56155) = barycentric quotient X(i)/X(j) for these (i, j): {1, 30568}, {6, 3913}, {7, 18135}, {31, 3217}, {56, 4383}, {57, 3875}, {65, 3175}, {513, 20317}, {604, 3915}, {608, 4186}, {649, 42312}, {1042, 28387}, {1397, 16946}, {1400, 3214}, {3669, 4106}, {7180, 4139}, {8690, 645}, {19604, 27813}, {34860, 312}, {39956, 8}, {40012, 3596}, {42304, 75}, {43924, 4498}, {55011, 40012}, {56123, 3701}

X(56156) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(37) AND X(2)

Barycentrics    a*(b+c)*(b*c+a*(4*b+c))*(b*c+a*(b+4*c)) : :

X(56156) lies on these lines: {2, 52959}, {6, 30653}, {37, 19998}, {1218, 1278}, {2276, 39982}, {2350, 17018}, {4651, 52708}, {17314, 39983}, {17756, 39798}, {26860, 37128}

X(56156) = X(i)-isoconjugate-of-X(j) for these {i, j}: {58, 4688}, {81, 30950}, {86, 16971}, {1412, 4519}
X(56156) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 4688}, {40586, 30950}, {40599, 4519}, {40600, 16971}
X(56156) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(19998)}}, {{A, B, C, X(2), X(6)}}, {{A, B, C, X(65), X(46872)}}, {{A, B, C, X(89), X(18785)}}, {{A, B, C, X(1000), X(13576)}}, {{A, B, C, X(1002), X(4674)}}, {{A, B, C, X(1500), X(50487)}}, {{A, B, C, X(2238), X(21806)}}, {{A, B, C, X(3240), X(29822)}}, {{A, B, C, X(3995), X(17756)}}, {{A, B, C, X(4651), X(17018)}}, {{A, B, C, X(8049), X(39739)}}, {{A, B, C, X(18098), X(25417)}}, {{A, B, C, X(21805), X(31011)}}, {{A, B, C, X(30653), X(40718)}}
X(56156) = barycentric product X(i)*X(j) for these (i, j): {1, 56126}, {10, 55932}
X(56156) = barycentric quotient X(i)/X(j) for these (i, j): {37, 4688}, {42, 30950}, {210, 4519}, {213, 16971}, {55932, 86}, {56126, 75}

X(56157) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(37) AND X(7)

Barycentrics    (b+c)*(a^2+b*(b-c)-a*(2*b+c))*(a^2+c*(-b+c)-a*(b+2*c)) : :

X(56157) lies on these lines: {2, 55076}, {7, 20683}, {8, 344}, {10, 21931}, {210, 1441}, {281, 6605}, {1026, 16713}, {1170, 5772}, {1174, 10327}, {1893, 3697}, {2321, 4651}, {3596, 4441}, {3696, 3701}, {3956, 15065}, {4015, 6757}, {4298, 14626}, {4552, 21039}, {5308, 10013}, {5936, 21453}, {6606, 35141}, {7064, 13576}, {10482, 56146}, {10570, 47487}, {25001, 40659}, {31994, 42311}

X(56157) = isotomic conjugate of X(17169)
X(56157) = trilinear pole of line {3700, 4151}
X(56157) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 18164}, {28, 22053}, {31, 17169}, {32, 16708}, {48, 53238}, {56, 17194}, {58, 354}, {81, 1475}, {110, 48151}, {142, 1333}, {163, 21104}, {284, 1418}, {560, 53236}, {593, 21808}, {604, 16713}, {757, 52020}, {849, 3925}, {1014, 2293}, {1019, 35326}, {1212, 1412}, {1229, 16947}, {1408, 4847}, {1414, 2488}, {1434, 20229}, {1444, 40983}, {2150, 52023}, {2194, 10481}, {2206, 20880}, {3733, 35338}, {4565, 21127}, {4637, 10581}, {7341, 21039}
X(56157) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 17194}, {2, 17169}, {9, 18164}, {10, 354}, {37, 142}, {115, 21104}, {244, 48151}, {1214, 10481}, {1249, 53238}, {3161, 16713}, {4075, 3925}, {6374, 53236}, {6376, 16708}, {6741, 6362}, {40586, 1475}, {40590, 1418}, {40591, 22053}, {40599, 1212}, {40603, 20880}, {40607, 52020}, {40608, 2488}, {52872, 51463}, {55064, 21127}, {55065, 55282}
X(56157) = X(i)-cross conjugate of X(j) for these {i, j}: {1577, 3952}, {4171, 4552}, {22042, 190}, {46196, 2}
X(56157) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4043)}}, {{A, B, C, X(4), X(5047)}}, {{A, B, C, X(7), X(37)}}, {{A, B, C, X(8), X(10)}}, {{A, B, C, X(65), X(3303)}}, {{A, B, C, X(72), X(3697)}}, {{A, B, C, X(82), X(27807)}}, {{A, B, C, X(210), X(480)}}, {{A, B, C, X(226), X(18230)}}, {{A, B, C, X(321), X(344)}}, {{A, B, C, X(333), X(27039)}}, {{A, B, C, X(594), X(3932)}}, {{A, B, C, X(758), X(3956)}}, {{A, B, C, X(966), X(37670)}}, {{A, B, C, X(1000), X(4674)}}, {{A, B, C, X(1002), X(40504)}}, {{A, B, C, X(1654), X(3570)}}, {{A, B, C, X(1826), X(38057)}}, {{A, B, C, X(3617), X(17751)}}, {{A, B, C, X(3668), X(8236)}}, {{A, B, C, X(3678), X(4015)}}, {{A, B, C, X(3753), X(3921)}}, {{A, B, C, X(3754), X(4540)}}, {{A, B, C, X(4171), X(21039)}}, {{A, B, C, X(4373), X(41683)}}, {{A, B, C, X(4685), X(26038)}}, {{A, B, C, X(6539), X(17233)}}, {{A, B, C, X(7064), X(20683)}}, {{A, B, C, X(7319), X(41506)}}, {{A, B, C, X(8049), X(39737)}}, {{A, B, C, X(9534), X(26115)}}, {{A, B, C, X(17038), X(55035)}}, {{A, B, C, X(17169), X(46196)}}, {{A, B, C, X(18785), X(41527)}}, {{A, B, C, X(18793), X(39956)}}, {{A, B, C, X(21031), X(21677)}}, {{A, B, C, X(27809), X(39721)}}, {{A, B, C, X(28626), X(40718)}}, {{A, B, C, X(36588), X(42027)}}, {{A, B, C, X(46772), X(49460)}}
X(56157) = barycentric product X(i)*X(j) for these (i, j): {1, 56127}, {10, 32008}, {210, 31618}, {226, 56118}, {1170, 3701}, {1174, 313}, {1441, 6605}, {2346, 321}, {3696, 42310}, {3700, 6606}, {4024, 55281}, {10482, 349}, {10509, 4082}, {21453, 2321}, {42311, 4515}
X(56157) = barycentric quotient X(i)/X(j) for these (i, j): {1, 18164}, {2, 17169}, {4, 53238}, {8, 16713}, {9, 17194}, {10, 142}, {12, 52023}, {37, 354}, {42, 1475}, {65, 1418}, {71, 22053}, {75, 16708}, {76, 53236}, {210, 1212}, {226, 10481}, {313, 1233}, {321, 20880}, {523, 21104}, {594, 3925}, {661, 48151}, {756, 21808}, {1018, 35338}, {1170, 1014}, {1174, 58}, {1334, 2293}, {1446, 53242}, {1500, 52020}, {2321, 4847}, {2333, 40983}, {2346, 81}, {3700, 6362}, {3701, 1229}, {3709, 2488}, {3932, 51384}, {3943, 51463}, {3991, 15185}, {4024, 55282}, {4041, 21127}, {4069, 35341}, {4077, 23599}, {4080, 53240}, {4082, 51972}, {4171, 6608}, {4515, 3059}, {4524, 10581}, {4552, 35312}, {4557, 35326}, {6605, 21}, {6606, 4573}, {7064, 21795}, {10482, 284}, {13576, 53241}, {18082, 18087}, {20616, 43915}, {21096, 41573}, {21453, 1434}, {32008, 86}, {35309, 35335}, {39130, 13156}, {40149, 53237}, {40521, 35310}, {43534, 53239}, {47487, 1790}, {52370, 22079}, {53008, 1855}, {53243, 4565}, {55281, 4610}, {56118, 333}, {56127, 75}
X(56157) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {32008, 56118, 2346}

X(56158) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(37) AND X(42)

Barycentrics    a*(b+c)*(a*(b-2*c)-2*b*c)*(2*a*b-a*c+2*b*c) : :

X(56158) lies on these lines: {2, 3761}, {6, 750}, {37, 2229}, {42, 52959}, {43, 39961}, {111, 5251}, {672, 46018}, {941, 5750}, {1218, 4751}, {1575, 39974}, {2238, 28658}, {2998, 4699}, {3572, 4893}, {3720, 39967}, {3911, 42290}, {5235, 37128}, {16569, 39965}, {16610, 39957}, {16975, 30970}, {27809, 31025}, {29822, 56156}, {36856, 39798}

X(56158) = X(i)-isoconjugate-of-X(j) for these {i, j}: {58, 4664}, {81, 3240}, {86, 54981}, {110, 4776}, {662, 29350}
X(56158) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 4664}, {244, 4776}, {1084, 29350}, {40586, 3240}, {40600, 54981}
X(56158) = X(i)-Ceva conjugate of X(j) for these {i, j}: {36871, 56125}
X(56158) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(52716)}}, {{A, B, C, X(2), X(6)}}, {{A, B, C, X(10), X(661)}}, {{A, B, C, X(88), X(40747)}}, {{A, B, C, X(274), X(649)}}, {{A, B, C, X(291), X(53114)}}, {{A, B, C, X(650), X(1334)}}, {{A, B, C, X(750), X(3761)}}, {{A, B, C, X(1220), X(31356)}}, {{A, B, C, X(1224), X(1245)}}, {{A, B, C, X(1500), X(52708)}}, {{A, B, C, X(1575), X(31025)}}, {{A, B, C, X(2238), X(4893)}}, {{A, B, C, X(2296), X(39742)}}, {{A, B, C, X(3720), X(43223)}}, {{A, B, C, X(3911), X(21805)}}, {{A, B, C, X(4413), X(13576)}}, {{A, B, C, X(4699), X(21877)}}, {{A, B, C, X(5251), X(21839)}}, {{A, B, C, X(14474), X(21832)}}, {{A, B, C, X(17077), X(40586)}}, {{A, B, C, X(17756), X(31993)}}, {{A, B, C, X(18098), X(39962)}}, {{A, B, C, X(18785), X(39963)}}, {{A, B, C, X(28248), X(31330)}}, {{A, B, C, X(29822), X(30950)}}, {{A, B, C, X(30571), X(53034)}}, {{A, B, C, X(31002), X(42027)}}, {{A, B, C, X(37132), X(40775)}}
X(56158) = barycentric product X(i)*X(j) for these (i, j): {1, 56125}, {10, 55919}, {226, 56116}, {29351, 523}, {36871, 37}, {37209, 661}, {56077, 65}
X(56158) = barycentric quotient X(i)/X(j) for these (i, j): {37, 4664}, {42, 3240}, {213, 54981}, {512, 29350}, {661, 4776}, {29351, 99}, {36871, 274}, {37209, 799}, {55919, 86}, {56077, 314}, {56116, 333}, {56125, 75}

X(56159) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(37) AND X(65)

Barycentrics    a*(a+b-5*c)*(a-5*b+c)*(b+c) : :

X(56159) lies on these lines: {1, 3689}, {8, 39702}, {10, 48641}, {19, 1878}, {37, 4695}, {65, 21805}, {75, 4723}, {210, 4674}, {596, 4691}, {759, 6014}, {897, 15481}, {2214, 16668}, {3668, 40663}, {3696, 41683}, {3753, 21870}, {3828, 30818}, {3968, 37593}, {4002, 4868}, {4041, 55244}, {4424, 56134}, {4669, 36924}, {4678, 34860}, {4732, 42027}, {5919, 31197}, {13476, 49984}, {16602, 17460}, {18827, 53659}, {21886, 21888}, {21896, 31503}, {24620, 31145}, {31359, 46933}

X(56159) = X(i)-isoconjugate-of-X(j) for these {i, j}: {21, 13462}, {27, 23073}, {58, 3241}, {81, 16670}, {99, 8656}, {110, 6006}, {593, 4029}, {757, 21870}, {1171, 4982}, {1333, 30829}
X(56159) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 3241}, {37, 30829}, {244, 6006}, {38986, 8656}, {40586, 16670}, {40607, 21870}, {40611, 13462}
X(56159) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}}, {{A, B, C, X(4), X(16408)}}, {{A, B, C, X(12), X(3698)}}, {{A, B, C, X(72), X(16885)}}, {{A, B, C, X(210), X(1261)}}, {{A, B, C, X(226), X(4731)}}, {{A, B, C, X(321), X(1878)}}, {{A, B, C, X(1122), X(4642)}}, {{A, B, C, X(1214), X(5183)}}, {{A, B, C, X(3696), X(43037)}}, {{A, B, C, X(3701), X(3893)}}, {{A, B, C, X(3753), X(40587)}}, {{A, B, C, X(3983), X(4848)}}, {{A, B, C, X(3987), X(4647)}}, {{A, B, C, X(4058), X(21896)}}, {{A, B, C, X(4413), X(13576)}}, {{A, B, C, X(4424), X(4714)}}, {{A, B, C, X(4651), X(49984)}}, {{A, B, C, X(4669), X(31855)}}, {{A, B, C, X(4709), X(21868)}}, {{A, B, C, X(4732), X(20691)}}, {{A, B, C, X(6539), X(26745)}}, {{A, B, C, X(9709), X(15232)}}, {{A, B, C, X(15481), X(21839)}}, {{A, B, C, X(30818), X(31025)}}, {{A, B, C, X(36588), X(41436)}}, {{A, B, C, X(39956), X(43533)}}, {{A, B, C, X(39963), X(40029)}}, {{A, B, C, X(43534), X(48641)}}
X(56159) = barycentric product X(i)*X(j) for these (i, j): {10, 39963}, {226, 4900}, {321, 41436}, {1577, 6014}, {30575, 36924}, {36588, 37}, {36915, 4674}, {40029, 42}, {53659, 661}, {56075, 65}
X(56159) = barycentric quotient X(i)/X(j) for these (i, j): {10, 30829}, {37, 3241}, {42, 16670}, {228, 23073}, {661, 6006}, {756, 4029}, {798, 8656}, {1400, 13462}, {1500, 21870}, {1962, 4982}, {4770, 52593}, {4900, 333}, {6014, 662}, {36588, 274}, {36915, 30939}, {36924, 16729}, {39963, 86}, {40029, 310}, {41436, 81}, {53659, 799}, {56075, 314}
X(56159) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4900, 39963, 41436}

X(56160) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(37) AND X(75)

Barycentrics    a*(b+c)*(-(b*(b-2*c)*c)+2*a^2*(b+c)-a*(b^2-2*c^2))*(b*(2*b-c)*c+2*a^2*(b+c)+a*(2*b^2-c^2)) : :

X(56160) lies on these lines: {37, 22294}, {75, 21805}, {596, 49499}, {872, 4674}, {4687, 42285}, {4850, 13476}, {19998, 56125}, {31025, 46772}, {39697, 49490}, {50487, 55244}

X(56160) = X(i)-isoconjugate-of-X(j) for these {i, j}: {58, 31136}
X(56160) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 31136}
X(56160) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}}, {{A, B, C, X(749), X(18082)}}, {{A, B, C, X(751), X(13576)}}, {{A, B, C, X(872), X(21805)}}, {{A, B, C, X(3240), X(19998)}}, {{A, B, C, X(4043), X(4850)}}, {{A, B, C, X(4687), X(31025)}}, {{A, B, C, X(22294), X(30575)}}
X(56160) = barycentric quotient X(i)/X(j) for these (i, j): {37, 31136}

X(56161) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(42) AND X(4)

Barycentrics    (-(a^2*b*c)+a^3*(b+c)+b*c*(b^2-c^2)+a*(b^3-b^2*c-3*b*c^2-c^3))*(-(a^2*b*c)-b^3*c+b*c^3+a^3*(b+c)-a*(b^3+3*b^2*c+b*c^2-c^3)) : :

X(56161) lies on the Kiepert hyperbola and on these lines: {2, 37502}, {4, 2238}, {10, 3208}, {30, 54793}, {43, 226}, {69, 40017}, {76, 9534}, {321, 27538}, {376, 54497}, {377, 6625}, {386, 17758}, {443, 37632}, {573, 43672}, {656, 4444}, {1446, 3212}, {2550, 40718}, {3545, 54728}, {3949, 43534}, {4251, 43531}, {5082, 54291}, {5084, 32022}, {5138, 14534}, {6685, 38204}, {6821, 37676}, {7235, 40149}, {13329, 13478}, {13584, 37191}, {14956, 55944}, {24624, 30943}, {30962, 40031}, {37193, 54119}

X(56161) = isogonal conjugate of X(37507)
X(56161) = isotomic conjugate of X(30962)
X(56161) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 37507}, {31, 30962}
X(56161) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 30962}, {3, 37507}
X(56161) = X(i)-cross conjugate of X(j) for these {i, j}: {37673, 2}
X(56161) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(39741)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(37502)}}, {{A, B, C, X(7), X(17038)}}, {{A, B, C, X(8), X(43)}}, {{A, B, C, X(19), X(40422)}}, {{A, B, C, X(25), X(1244)}}, {{A, B, C, X(37), X(1246)}}, {{A, B, C, X(42), X(9534)}}, {{A, B, C, X(65), X(39967)}}, {{A, B, C, X(69), X(656)}}, {{A, B, C, X(80), X(52654)}}, {{A, B, C, X(277), X(18031)}}, {{A, B, C, X(314), X(8769)}}, {{A, B, C, X(330), X(56138)}}, {{A, B, C, X(377), X(4213)}}, {{A, B, C, X(386), X(4251)}}, {{A, B, C, X(406), X(6817)}}, {{A, B, C, X(443), X(4207)}}, {{A, B, C, X(475), X(6818)}}, {{A, B, C, X(573), X(13329)}}, {{A, B, C, X(740), X(2998)}}, {{A, B, C, X(860), X(30943)}}, {{A, B, C, X(966), X(37632)}}, {{A, B, C, X(985), X(41527)}}, {{A, B, C, X(994), X(1000)}}, {{A, B, C, X(1738), X(3596)}}, {{A, B, C, X(1929), X(54128)}}, {{A, B, C, X(2092), X(5138)}}, {{A, B, C, X(2321), X(9307)}}, {{A, B, C, X(2478), X(4212)}}, {{A, B, C, X(2481), X(39954)}}, {{A, B, C, X(3144), X(37193)}}, {{A, B, C, X(3296), X(8049)}}, {{A, B, C, X(3617), X(6685)}}, {{A, B, C, X(3696), X(39957)}}, {{A, B, C, X(4194), X(6821)}}, {{A, B, C, X(4196), X(5084)}}, {{A, B, C, X(4200), X(6822)}}, {{A, B, C, X(4441), X(26242)}}, {{A, B, C, X(5936), X(55035)}}, {{A, B, C, X(6048), X(10453)}}, {{A, B, C, X(10482), X(11578)}}, {{A, B, C, X(14555), X(37676)}}, {{A, B, C, X(15320), X(39983)}}, {{A, B, C, X(15474), X(17982)}}, {{A, B, C, X(16606), X(41506)}}, {{A, B, C, X(17889), X(43740)}}, {{A, B, C, X(19853), X(26037)}}, {{A, B, C, X(25612), X(40027)}}, {{A, B, C, X(29822), X(48852)}}, {{A, B, C, X(30962), X(37673)}}, {{A, B, C, X(31359), X(40418)}}, {{A, B, C, X(36695), X(37276)}}, {{A, B, C, X(39734), X(43733)}}, {{A, B, C, X(40399), X(45137)}}
X(56161) = barycentric product X(i)*X(j) for these (i, j): {10, 55968}
X(56161) = barycentric quotient X(i)/X(j) for these (i, j): {2, 30962}, {6, 37507}, {55968, 86}

X(56162) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(42) AND X(6)

Barycentrics    a*(a*b^3+b^2*c*(b+c)+a^2*(b^2-c^2))*(-(a*c^3)-b*c^2*(b+c)+a^2*(b^2-c^2)) : :

X(56162) lies on these lines: {6, 2229}, {37, 4009}, {42, 4116}, {899, 1400}, {1150, 37128}, {1427, 43037}, {1575, 28658}, {2238, 46018}, {4671, 27809}, {16606, 31330}, {16704, 39952}, {16975, 30970}, {37660, 39981}

X(56162) = isotomic conjugate of X(30964)
X(56162) = trilinear pole of line {4526, 512}
X(56162) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 30964}, {4588, 27773}
X(56162) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 30964}, {55045, 27773}
X(56162) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}}, {{A, B, C, X(4), X(16405)}}, {{A, B, C, X(8), X(650)}}, {{A, B, C, X(31), X(30710)}}, {{A, B, C, X(43), X(31330)}}, {{A, B, C, X(76), X(661)}}, {{A, B, C, X(87), X(31002)}}, {{A, B, C, X(291), X(994)}}, {{A, B, C, X(310), X(3223)}}, {{A, B, C, X(330), X(649)}}, {{A, B, C, X(1150), X(2238)}}, {{A, B, C, X(1575), X(4671)}}, {{A, B, C, X(2162), X(35058)}}, {{A, B, C, X(3240), X(30970)}}, {{A, B, C, X(5291), X(5692)}}, {{A, B, C, X(7241), X(55035)}}, {{A, B, C, X(16704), X(37673)}}, {{A, B, C, X(16975), X(36871)}}, {{A, B, C, X(27810), X(40024)}}, {{A, B, C, X(37657), X(37660)}}, {{A, B, C, X(38955), X(56161)}}, {{A, B, C, X(39694), X(40148)}}
X(56162) = barycentric product X(i)*X(j) for these (i, j): {1, 56128}, {36873, 75}
X(56162) = barycentric quotient X(i)/X(j) for these (i, j): {2, 30964}, {4893, 27773}, {36873, 1}, {56128, 75}

X(56163) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(42) AND X(7)

Barycentrics    (b*(b-c)*c+a^2*(b+c)+a*(b^2-5*b*c-c^2))*(b*c*(-b+c)+a^2*(b+c)+a*(-b^2-5*b*c+c^2)) : :

X(56163) lies on these lines: {7, 899}, {8, 31002}, {75, 4009}, {86, 4413}, {310, 26038}, {335, 24620}, {903, 30946}, {1088, 43037}, {6650, 31018}, {10453, 40027}, {16569, 39741}, {16610, 27475}, {17484, 39720}, {30598, 52638}

X(56163) = isotomic conjugate of X(30947)
X(56163) = trilinear pole of line {4526, 514}
X(56163) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(7)}}, {{A, B, C, X(8), X(650)}}, {{A, B, C, X(42), X(26038)}}, {{A, B, C, X(80), X(52654)}}, {{A, B, C, X(88), X(41527)}}, {{A, B, C, X(291), X(1000)}}, {{A, B, C, X(330), X(7035)}}, {{A, B, C, X(350), X(24620)}}, {{A, B, C, X(2481), X(39963)}}, {{A, B, C, X(3911), X(30946)}}, {{A, B, C, X(4413), X(13576)}}, {{A, B, C, X(4441), X(16610)}}, {{A, B, C, X(7045), X(38250)}}, {{A, B, C, X(8056), X(54128)}}, {{A, B, C, X(10453), X(16569)}}, {{A, B, C, X(18490), X(30571)}}, {{A, B, C, X(20347), X(31188)}}, {{A, B, C, X(21448), X(52030)}}, {{A, B, C, X(26745), X(27807)}}
X(56163) = barycentric quotient X(i)/X(j) for these (i, j): {2, 30947}

X(56164) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(42) AND X(8)

Barycentrics    (a^2*b*(-2*b+c)+a^3*(b+c)+b*c*(b^2-c^2)+a*(b^3+b^2*c+b*c^2-c^3))*(-(b^3*c)+a^2*(b-2*c)*c+b*c^3+a^3*(b+c)+a*(-b^3+b^2*c+b*c^2+c^3)) : :

X(56164) lies on these lines: {2, 1458}, {6, 14942}, {7, 18031}, {8, 672}, {85, 3812}, {92, 1876}, {257, 3177}, {312, 518}, {333, 1376}, {958, 32008}, {1212, 31359}, {3252, 4518}, {4651, 30711}, {4997, 30947}, {5554, 54120}, {9309, 13576}, {14626, 17135}, {17947, 18391}, {26103, 38255}, {28660, 30941}, {28850, 52517}, {29824, 56075}, {39741, 54128}, {41245, 52013}

X(56164) = isotomic conjugate of X(30946)
X(56164) = trilinear pole of line {665, 21348}
X(56164) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 37555}, {31, 30946}
X(56164) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 30946}, {9, 37555}
X(56164) = X(i)-cross conjugate of X(j) for these {i, j}: {17754, 2}
X(56164) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10453)}}, {{A, B, C, X(2), X(8)}}, {{A, B, C, X(4), X(291)}}, {{A, B, C, X(6), X(7)}}, {{A, B, C, X(9), X(31643)}}, {{A, B, C, X(65), X(36854)}}, {{A, B, C, X(80), X(52654)}}, {{A, B, C, X(310), X(1219)}}, {{A, B, C, X(314), X(2297)}}, {{A, B, C, X(519), X(30947)}}, {{A, B, C, X(749), X(1246)}}, {{A, B, C, X(958), X(1212)}}, {{A, B, C, X(959), X(2350)}}, {{A, B, C, X(1000), X(30571)}}, {{A, B, C, X(1016), X(40031)}}, {{A, B, C, X(1222), X(6384)}}, {{A, B, C, X(1376), X(3967)}}, {{A, B, C, X(1390), X(41527)}}, {{A, B, C, X(2481), X(39959)}}, {{A, B, C, X(2995), X(7155)}}, {{A, B, C, X(3177), X(7196)}}, {{A, B, C, X(3241), X(29824)}}, {{A, B, C, X(3427), X(24247)}}, {{A, B, C, X(3616), X(17135)}}, {{A, B, C, X(3617), X(26038)}}, {{A, B, C, X(3621), X(26103)}}, {{A, B, C, X(4441), X(44798)}}, {{A, B, C, X(4651), X(9780)}}, {{A, B, C, X(4998), X(56144)}}, {{A, B, C, X(5222), X(41245)}}, {{A, B, C, X(5331), X(5558)}}, {{A, B, C, X(5556), X(8049)}}, {{A, B, C, X(6063), X(43672)}}, {{A, B, C, X(7123), X(56154)}}, {{A, B, C, X(8048), X(43749)}}, {{A, B, C, X(12649), X(29839)}}, {{A, B, C, X(15909), X(34399)}}, {{A, B, C, X(17754), X(30946)}}, {{A, B, C, X(20028), X(39975)}}, {{A, B, C, X(30701), X(40017)}}, {{A, B, C, X(34434), X(39966)}}, {{A, B, C, X(38955), X(40718)}}, {{A, B, C, X(39749), X(40030)}}, {{A, B, C, X(39956), X(55035)}}, {{A, B, C, X(39967), X(46187)}}
X(56164) = barycentric quotient X(i)/X(j) for these (i, j): {1, 37555}, {2, 30946}

X(56165) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(42) AND X(57)

Barycentrics    a*(a^2*(b-c)+a*(b^2-b*c-c^2)+b*(2*b^2+b*c+c^2))*(a^2*(b-c)+a*(b^2+b*c-c^2)-c*(b^2+b*c+2*c^2)) : :

X(56165) lies on these lines: {2, 21101}, {43, 985}, {57, 1575}, {81, 17754}, {105, 748}, {274, 17308}, {279, 43040}, {312, 32020}, {330, 3661}, {982, 52654}, {1422, 52089}, {1929, 16569}, {3227, 17294}, {3676, 20515}, {3795, 5269}, {6542, 38247}, {7243, 34018}, {7308, 39954}, {17397, 39738}, {29591, 39740}, {29603, 32009}, {29608, 39736}, {43928, 47828}, {45782, 53678}

X(56165) = trilinear pole of line {21349, 513}
X(56165) = X(i)-cross conjugate of X(j) for these {i, j}: {49509, 1}
X(56165) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(42), X(17308)}}, {{A, B, C, X(43), X(3661)}}, {{A, B, C, X(75), X(39979)}}, {{A, B, C, X(76), X(979)}}, {{A, B, C, X(87), X(335)}}, {{A, B, C, X(223), X(52089)}}, {{A, B, C, X(226), X(16606)}}, {{A, B, C, X(257), X(39969)}}, {{A, B, C, X(312), X(650)}}, {{A, B, C, X(321), X(18793)}}, {{A, B, C, X(596), X(3500)}}, {{A, B, C, X(673), X(7241)}}, {{A, B, C, X(748), X(4382)}}, {{A, B, C, X(749), X(39957)}}, {{A, B, C, X(899), X(17294)}}, {{A, B, C, X(2051), X(7350)}}, {{A, B, C, X(2254), X(40217)}}, {{A, B, C, X(2258), X(2276)}}, {{A, B, C, X(3223), X(18795)}}, {{A, B, C, X(3551), X(20332)}}, {{A, B, C, X(3676), X(6384)}}, {{A, B, C, X(3720), X(29603)}}, {{A, B, C, X(6542), X(16569)}}, {{A, B, C, X(7153), X(34860)}}, {{A, B, C, X(7261), X(8817)}}, {{A, B, C, X(14621), X(39742)}}, {{A, B, C, X(17038), X(39971)}}, {{A, B, C, X(17397), X(26102)}}, {{A, B, C, X(25502), X(29586)}}, {{A, B, C, X(27475), X(39798)}}, {{A, B, C, X(29591), X(42043)}}, {{A, B, C, X(29608), X(42042)}}, {{A, B, C, X(36807), X(39981)}}, {{A, B, C, X(39749), X(39956)}}, {{A, B, C, X(39966), X(40746)}}, {{A, B, C, X(40029), X(47915)}}, {{A, B, C, X(40098), X(51844)}}
X(56165) = barycentric product X(i)*X(j) for these (i, j): {1, 56124}
X(56165) = barycentric quotient X(i)/X(j) for these (i, j): {56124, 75}

X(56166) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(42) AND X(75)

Barycentrics    (a*b*(b-c)+b^2*c+a^2*(b+c))*(b*c^2+a*c*(-b+c)+a^2*(b+c)) : :

X(56166) lies on these lines: {1, 31002}, {2, 3230}, {42, 6384}, {43, 310}, {75, 899}, {86, 750}, {335, 4850}, {649, 3758}, {903, 37678}, {1240, 3875}, {2229, 27447}, {2296, 6685}, {2382, 50300}, {3720, 40027}, {17393, 40010}, {17495, 27494}, {21759, 37677}, {26037, 56052}, {30963, 40039}, {37632, 39704}

X(56166) = isotomic conjugate of X(30942)
X(56166) = trilinear pole of line {3768, 514}
X(56166) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 16975}, {31, 30942}
X(56166) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 30942}, {9, 16975}
X(56166) = X(i)-cross conjugate of X(j) for these {i, j}: {29350, 190}
X(56166) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(649)}}, {{A, B, C, X(2), X(7)}}, {{A, B, C, X(42), X(43)}}, {{A, B, C, X(57), X(3112)}}, {{A, B, C, X(81), X(7033)}}, {{A, B, C, X(83), X(4998)}}, {{A, B, C, X(88), X(870)}}, {{A, B, C, X(89), X(3226)}}, {{A, B, C, X(190), X(3758)}}, {{A, B, C, X(291), X(994)}}, {{A, B, C, X(350), X(4850)}}, {{A, B, C, X(537), X(50300)}}, {{A, B, C, X(561), X(2051)}}, {{A, B, C, X(749), X(18082)}}, {{A, B, C, X(750), X(3761)}}, {{A, B, C, X(873), X(8056)}}, {{A, B, C, X(1002), X(1120)}}, {{A, B, C, X(2229), X(2295)}}, {{A, B, C, X(2279), X(37132)}}, {{A, B, C, X(2350), X(3223)}}, {{A, B, C, X(3720), X(16569)}}, {{A, B, C, X(3771), X(29850)}}, {{A, B, C, X(3875), X(54308)}}, {{A, B, C, X(4600), X(17743)}}, {{A, B, C, X(4664), X(46922)}}, {{A, B, C, X(4672), X(32935)}}, {{A, B, C, X(5235), X(37632)}}, {{A, B, C, X(6685), X(31330)}}, {{A, B, C, X(6686), X(30957)}}, {{A, B, C, X(10455), X(25590)}}, {{A, B, C, X(14554), X(39712)}}, {{A, B, C, X(16606), X(40504)}}, {{A, B, C, X(16704), X(37678)}}, {{A, B, C, X(17495), X(30963)}}, {{A, B, C, X(25430), X(40439)}}, {{A, B, C, X(25453), X(29846)}}, {{A, B, C, X(26037), X(43223)}}, {{A, B, C, X(29663), X(32783)}}, {{A, B, C, X(29678), X(33138)}}, {{A, B, C, X(29825), X(30970)}}
X(56166) = barycentric product X(i)*X(j) for these (i, j): {1, 56129}
X(56166) = barycentric quotient X(i)/X(j) for these (i, j): {1, 16975}, {2, 30942}, {56129, 75}

X(56167) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(42) AND X(76)

Barycentrics    (b^3*c+a^3*(b+c)+a*(b^3-b*c^2))*(b*c^3+a^3*(b+c)+a*(-(b^2*c)+c^3)) : :

X(56167) lies on the Kiepert hyperbola and on these lines: {2, 41333}, {6, 40017}, {10, 54291}, {76, 2238}, {798, 4444}, {872, 43534}, {1916, 40729}, {4429, 40718}, {6625, 17680}, {17758, 37632}, {24512, 40031}, {37657, 40030}, {37673, 40024}, {37676, 40012}

X(56167) = isotomic conjugate of X(30945)
X(56167) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(798)}}, {{A, B, C, X(19), X(38810)}}, {{A, B, C, X(25), X(39276)}}, {{A, B, C, X(43), X(17033)}}, {{A, B, C, X(239), X(985)}}, {{A, B, C, X(291), X(17743)}}, {{A, B, C, X(717), X(3402)}}, {{A, B, C, X(899), X(30114)}}, {{A, B, C, X(941), X(40409)}}, {{A, B, C, X(1002), X(1016)}}, {{A, B, C, X(1218), X(18082)}}, {{A, B, C, X(2296), X(32009)}}, {{A, B, C, X(3223), X(39970)}}, {{A, B, C, X(4213), X(17680)}}, {{A, B, C, X(4383), X(37676)}}, {{A, B, C, X(6383), X(55035)}}, {{A, B, C, X(14377), X(39925)}}, {{A, B, C, X(14621), X(30571)}}, {{A, B, C, X(16606), X(40516)}}, {{A, B, C, X(17277), X(37632)}}, {{A, B, C, X(18793), X(39797)}}, {{A, B, C, X(24512), X(37673)}}, {{A, B, C, X(29846), X(30165)}}, {{A, B, C, X(29850), X(30149)}}, {{A, B, C, X(30701), X(39741)}}, {{A, B, C, X(32008), X(40418)}}, {{A, B, C, X(39961), X(40408)}}
X(56167) = barycentric quotient X(i)/X(j) for these (i, j): {2, 30945}

X(56168) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(42) AND X(81)

Barycentrics    a*(a^2*(b-c)+a*(2*b^2-c^2)+b*(2*b^2+2*b*c+c^2))*(a^2*(b-c)+a*(b^2-2*c^2)-c*(b^2+2*b*c+2*c^2)) : :

X(56168) lies on these lines: {2, 56130}, {38, 52654}, {81, 1575}, {89, 37676}, {274, 29610}, {321, 32020}, {330, 29593}, {985, 32911}, {3227, 29615}, {20055, 38247}, {24512, 25417}, {29609, 32009}, {30966, 39747}, {43928, 47827}

X(56168) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 49477}
X(56168) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 49477}
X(56168) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(42), X(29610)}}, {{A, B, C, X(43), X(29593)}}, {{A, B, C, X(75), X(20332)}}, {{A, B, C, X(87), X(27494)}}, {{A, B, C, X(321), X(661)}}, {{A, B, C, X(335), X(39798)}}, {{A, B, C, X(899), X(29615)}}, {{A, B, C, X(1268), X(39971)}}, {{A, B, C, X(3720), X(29609)}}, {{A, B, C, X(5235), X(37676)}}, {{A, B, C, X(5333), X(24512)}}, {{A, B, C, X(6539), X(18793)}}, {{A, B, C, X(7241), X(14621)}}, {{A, B, C, X(16569), X(20055)}}, {{A, B, C, X(27483), X(39979)}}, {{A, B, C, X(30965), X(33854)}}, {{A, B, C, X(30966), X(32911)}}, {{A, B, C, X(32018), X(39748)}}, {{A, B, C, X(41836), X(41839)}}
X(56168) = barycentric product X(i)*X(j) for these (i, j): {1, 56130}
X(56168) = barycentric quotient X(i)/X(j) for these (i, j): {1, 49477}, {56130, 75}

X(56169) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(42) AND X(86)

Barycentrics    b*c*(b*c+a*(4*b+c))*(b*c+a*(b+4*c)) : :

X(56169) lies on these lines: {2, 52959}, {10, 31002}, {75, 3994}, {86, 899}, {310, 6381}, {335, 24589}, {350, 55955}, {871, 40089}, {2296, 16569}, {4358, 27483}, {6384, 26037}, {14621, 37680}, {31330, 40027}

X(56169) = isotomic conjugate of X(30950)
X(56169) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 16971}, {31, 30950}, {32, 4688}, {1397, 4519}
X(56169) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 30950}, {9, 16971}, {6376, 4688}
X(56169) = X(i)-cross conjugate of X(j) for these {i, j}: {4776, 1978}
X(56169) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(7)}}, {{A, B, C, X(10), X(661)}}, {{A, B, C, X(43), X(26037)}}, {{A, B, C, X(88), X(39717)}}, {{A, B, C, X(274), X(7035)}}, {{A, B, C, X(291), X(41434)}}, {{A, B, C, X(350), X(24589)}}, {{A, B, C, X(3226), X(39706)}}, {{A, B, C, X(4600), X(32008)}}, {{A, B, C, X(6686), X(31241)}}, {{A, B, C, X(16569), X(31330)}}, {{A, B, C, X(18031), X(20569)}}, {{A, B, C, X(18827), X(40434)}}, {{A, B, C, X(20568), X(40024)}}, {{A, B, C, X(30571), X(39697)}}, {{A, B, C, X(30966), X(37680)}}, {{A, B, C, X(32010), X(39962)}}
X(56169) = barycentric product X(i)*X(j) for these (i, j): {274, 56126}, {310, 56156}, {55932, 76}
X(56169) = barycentric quotient X(i)/X(j) for these (i, j): {1, 16971}, {2, 30950}, {75, 4688}, {312, 4519}, {55932, 6}, {56126, 37}, {56156, 42}

X(56170) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(42) AND X(88)

Barycentrics    a*(a^2*(b-c)-a*c*(2*b+c)+b*(2*b^2+c^2))*(a^2*(b-c)+a*b*(b+2*c)-c*(b^2+2*c^2)) : :

X(56170) lies on these lines: {1, 3799}, {2, 3807}, {88, 1575}, {89, 20331}, {100, 985}, {105, 37680}, {244, 52654}, {274, 17292}, {291, 17449}, {330, 17230}, {1390, 3315}, {3227, 17310}, {4358, 32020}, {24183, 41836}, {27805, 40738}, {29614, 32009}, {30965, 39747}, {40833, 46795}, {43928, 48244}

X(56170) = trilinear pole of line {984, 513}
X(56170) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 50023}
X(56170) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 50023}
X(56170) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(42), X(17292)}}, {{A, B, C, X(43), X(17230)}}, {{A, B, C, X(100), X(1978)}}, {{A, B, C, X(312), X(8851)}}, {{A, B, C, X(335), X(513)}}, {{A, B, C, X(593), X(28574)}}, {{A, B, C, X(739), X(52205)}}, {{A, B, C, X(899), X(17310)}}, {{A, B, C, X(1126), X(10159)}}, {{A, B, C, X(1575), X(1635)}}, {{A, B, C, X(2051), X(15323)}}, {{A, B, C, X(3720), X(29614)}}, {{A, B, C, X(4080), X(18793)}}, {{A, B, C, X(4674), X(32012)}}, {{A, B, C, X(4893), X(4945)}}, {{A, B, C, X(4997), X(56154)}}, {{A, B, C, X(4998), X(9075)}}, {{A, B, C, X(6186), X(39966)}}, {{A, B, C, X(6187), X(39967)}}, {{A, B, C, X(16606), X(30588)}}, {{A, B, C, X(17449), X(18109)}}, {{A, B, C, X(21297), X(30941)}}, {{A, B, C, X(24625), X(31002)}}, {{A, B, C, X(27475), X(36494)}}, {{A, B, C, X(30575), X(30866)}}, {{A, B, C, X(30965), X(32911)}}, {{A, B, C, X(36807), X(37128)}}, {{A, B, C, X(40735), X(52660)}}
X(56170) = barycentric quotient X(i)/X(j) for these (i, j): {1, 50023}

X(56171) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(42) AND X(98)

Barycentrics    (b^2-a*c)*(a*b-c^2)*(a^3*c-a*c*(b+c)^2-a^2*b*(2*b+c)+b*c*(b^2-c^2))*(-(a^3*b)+a*b*(b+c)^2+a^2*c*(b+2*c)+b*c*(b^2-c^2)) : :

X(56171) lies on the Kiepert hyperbola and on these lines: {2, 50440}, {10, 4876}, {76, 52257}, {83, 1009}, {98, 2238}, {226, 291}, {321, 4518}, {325, 40017}, {598, 11355}, {694, 53425}, {1446, 7233}, {2311, 6998}, {6054, 19635}

X(56171) = trilinear pole of line {49509, 523}
X(56171) = X(i)-isoconjugate-of-X(j) for these {i, j}: {238, 37609}
X(56171) = X(i)-Dao conjugate of X(j) for these {i, j}: {9470, 37609}
X(56171) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(52257)}}, {{A, B, C, X(100), X(4583)}}, {{A, B, C, X(291), X(1581)}}, {{A, B, C, X(305), X(43698)}}, {{A, B, C, X(325), X(2238)}}, {{A, B, C, X(427), X(1009)}}, {{A, B, C, X(1390), X(53707)}}, {{A, B, C, X(5094), X(11355)}}, {{A, B, C, X(7095), X(52654)}}, {{A, B, C, X(7249), X(30571)}}
X(56171) = barycentric quotient X(i)/X(j) for these (i, j): {292, 37609}

X(56172) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(65) AND X(4)

Barycentrics    (b+c)*(a^3+a^2*b+b^3-b*c^2+a*(b^2-4*b*c-c^2))*(a^3+a^2*c-b^2*c+c^3+a*(-b^2-4*b*c+c^2)) : :

X(56172) lies on the Kiepert hyperbola and on these lines:: {2, 496}, {8, 40013}, {40, 43672}, {76, 42696}, {226, 3293}, {321, 3697}, {2550, 43531}, {3436, 54775}, {4000, 17758}, {9614, 14554}, {21896, 54933}, {40149, 53861}

X(56172) = X(i)-isoconjugate-of-X(j) for these {i, j}: {58, 3555}
X(56172) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 3555}
X(56172) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(8), X(3293)}}, {{A, B, C, X(37), X(3296)}}, {{A, B, C, X(65), X(1000)}}, {{A, B, C, X(210), X(11578)}}, {{A, B, C, X(225), X(1058)}}, {{A, B, C, X(496), X(52383)}}, {{A, B, C, X(1002), X(4651)}}, {{A, B, C, X(1247), X(39768)}}, {{A, B, C, X(2321), X(15998)}}, {{A, B, C, X(3696), X(3931)}}, {{A, B, C, X(3701), X(6601)}}, {{A, B, C, X(4000), X(4043)}}, {{A, B, C, X(4373), X(42471)}}, {{A, B, C, X(4646), X(5295)}}, {{A, B, C, X(5082), X(41013)}}, {{A, B, C, X(5687), X(38955)}}, {{A, B, C, X(9709), X(15232)}}, {{A, B, C, X(15170), X(52382)}}, {{A, B, C, X(15320), X(43733)}}, {{A, B, C, X(24298), X(24390)}}, {{A, B, C, X(31419), X(51870)}}, {{A, B, C, X(39708), X(55035)}}, {{A, B, C, X(40504), X(51223)}}
X(56172) = barycentric quotient X(i)/X(j) for these (i, j): {37, 3555}

X(56173) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(65) AND X(8)

Barycentrics    (a+b-c)*(a-b+c)*(b+c)*(a^2+a*(-2*b+c)+b*(b+c))*(a^2+a*(b-2*c)+c*(b+c)) : :

X(56173) lies on these lines: {1, 40451}, {7, 3596}, {8, 56}, {10, 1042}, {65, 3701}, {281, 608}, {388, 20615}, {938, 27394}, {959, 32017}, {1400, 2321}, {1426, 3753}, {1441, 3698}, {1837, 40528}, {2295, 21049}, {2475, 39270}, {3617, 55076}, {3754, 15065}, {3918, 6757}, {4339, 5264}, {4358, 13601}, {4552, 4642}, {5554, 10570}, {6613, 35141}, {6740, 14584}, {11545, 48877}, {12709, 52353}, {17539, 23703}, {21677, 56157}, {24806, 26030}

X(56173) = isotomic conjugate of X(17183)
X(56173) = trilinear pole of line {3700, 7180}
X(56173) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 18163}, {21, 1201}, {28, 22072}, {29, 22344}, {31, 17183}, {41, 18600}, {58, 3057}, {60, 4642}, {81, 2347}, {110, 6615}, {163, 21120}, {283, 1828}, {284, 3752}, {333, 20228}, {593, 21809}, {643, 6363}, {849, 21031}, {1122, 2328}, {1333, 3452}, {1408, 6736}, {1444, 40982}, {2150, 4415}, {2185, 21796}, {2194, 3663}, {2206, 20895}, {3737, 23845}, {5546, 48334}, {7252, 21362}, {7256, 42336}, {38832, 52195}
X(56173) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 17183}, {9, 18163}, {10, 3057}, {37, 3452}, {115, 21120}, {244, 6615}, {1214, 3663}, {3160, 18600}, {4075, 21031}, {6741, 42337}, {36908, 1122}, {40586, 2347}, {40590, 3752}, {40591, 22072}, {40603, 20895}, {40611, 1201}, {55060, 6363}
X(56173) = X(i)-cross conjugate of X(j) for these {i, j}: {661, 4552}, {4404, 3952}, {51662, 4551}
X(56173) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4581)}}, {{A, B, C, X(2), X(11109)}}, {{A, B, C, X(4), X(404)}}, {{A, B, C, X(7), X(56)}}, {{A, B, C, X(8), X(10)}}, {{A, B, C, X(12), X(14584)}}, {{A, B, C, X(37), X(7320)}}, {{A, B, C, X(72), X(3753)}}, {{A, B, C, X(75), X(55036)}}, {{A, B, C, X(189), X(321)}}, {{A, B, C, X(210), X(3698)}}, {{A, B, C, X(225), X(3476)}}, {{A, B, C, X(226), X(4848)}}, {{A, B, C, X(279), X(18097)}}, {{A, B, C, X(307), X(5749)}}, {{A, B, C, X(377), X(7412)}}, {{A, B, C, X(523), X(38455)}}, {{A, B, C, X(661), X(4642)}}, {{A, B, C, X(758), X(3754)}}, {{A, B, C, X(1376), X(3967)}}, {{A, B, C, X(1427), X(8051)}}, {{A, B, C, X(2295), X(2533)}}, {{A, B, C, X(2475), X(4242)}}, {{A, B, C, X(2994), X(6539)}}, {{A, B, C, X(3427), X(23604)}}, {{A, B, C, X(3617), X(4651)}}, {{A, B, C, X(3668), X(4308)}}, {{A, B, C, X(3678), X(3918)}}, {{A, B, C, X(3696), X(31994)}}, {{A, B, C, X(3697), X(4002)}}, {{A, B, C, X(3919), X(4084)}}, {{A, B, C, X(3922), X(3962)}}, {{A, B, C, X(3925), X(21677)}}, {{A, B, C, X(3932), X(21049)}}, {{A, B, C, X(3968), X(4015)}}, {{A, B, C, X(3983), X(4731)}}, {{A, B, C, X(4004), X(4018)}}, {{A, B, C, X(5423), X(53013)}}, {{A, B, C, X(5558), X(53114)}}, {{A, B, C, X(6553), X(41683)}}, {{A, B, C, X(8256), X(51870)}}, {{A, B, C, X(10449), X(19874)}}, {{A, B, C, X(10944), X(52383)}}, {{A, B, C, X(17097), X(31643)}}, {{A, B, C, X(20683), X(53110)}}, {{A, B, C, X(21739), X(27797)}}, {{A, B, C, X(34265), X(43533)}}, {{A, B, C, X(40420), X(40446)}}
X(56173) = barycentric product X(i)*X(j) for these (i, j): {10, 40420}, {306, 40446}, {313, 3451}, {349, 51476}, {1222, 226}, {1261, 1446}, {1441, 23617}, {1476, 321}, {3668, 52549}, {3700, 6613}, {7178, 8706}, {32017, 65}
X(56173) = barycentric quotient X(i)/X(j) for these (i, j): {1, 18163}, {2, 17183}, {7, 18600}, {10, 3452}, {12, 4415}, {37, 3057}, {42, 2347}, {65, 3752}, {71, 22072}, {181, 21796}, {226, 3663}, {321, 20895}, {523, 21120}, {594, 21031}, {661, 6615}, {756, 21809}, {1222, 333}, {1261, 2287}, {1400, 1201}, {1402, 20228}, {1409, 22344}, {1427, 1122}, {1441, 26563}, {1476, 81}, {1880, 1828}, {2171, 4642}, {2321, 6736}, {2333, 40982}, {2533, 28006}, {3451, 58}, {3668, 52563}, {3700, 42337}, {3950, 12640}, {3952, 25268}, {4017, 48334}, {4551, 21362}, {4552, 21272}, {4559, 23845}, {4848, 45204}, {6613, 4573}, {7180, 6363}, {8706, 645}, {14321, 14284}, {16606, 52195}, {18082, 18086}, {23067, 23113}, {23617, 21}, {32017, 314}, {40420, 86}, {40446, 27}, {40451, 17197}, {40663, 51415}, {51476, 284}, {52384, 42549}, {52549, 1043}
X(56173) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1222, 40420, 1476}

X(56174) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(65) AND X(65)

Barycentrics    a*(a+b-3*c)*(a-3*b+c)*(b+c) : :

X(56174) lies on cubic K372 and on these lines: {1, 474}, {8, 21342}, {10, 3967}, {19, 44}, {37, 3698}, {42, 3922}, {43, 10107}, {72, 4674}, {75, 3617}, {158, 38462}, {165, 52183}, {225, 40663}, {244, 3893}, {513, 23835}, {517, 14261}, {518, 39742}, {596, 3626}, {656, 55244}, {759, 1293}, {876, 29226}, {897, 11684}, {899, 34434}, {942, 50575}, {994, 50193}, {1054, 11260}, {1086, 6736}, {1104, 54286}, {1155, 2217}, {1247, 5302}, {1575, 2186}, {1738, 8256}, {1910, 34080}, {2214, 16666}, {2218, 37568}, {2292, 4731}, {3057, 16602}, {3125, 4515}, {3212, 27818}, {3293, 4004}, {3621, 3999}, {3625, 39697}, {3634, 42285}, {3668, 4848}, {3679, 39711}, {3696, 42027}, {3697, 56135}, {3754, 50587}, {3756, 21627}, {3918, 3931}, {3959, 44798}, {3983, 56159}, {4002, 4424}, {4018, 31855}, {4301, 51415}, {4420, 31343}, {4663, 13610}, {4689, 40430}, {4952, 11851}, {5121, 13463}, {5220, 8769}, {5221, 40151}, {5295, 42471}, {6048, 44663}, {6557, 9780}, {7991, 37679}, {8286, 34895}, {9588, 31187}, {11278, 45763}, {12640, 24175}, {14923, 16610}, {15854, 22837}, {16605, 18785}, {16945, 32636}, {17751, 41683}, {18827, 53647}, {19604, 24471}, {20331, 45202}, {24880, 50821}, {27827, 39739}, {33963, 52429}, {46032, 51844}, {46187, 49537}

X(56174) = midpoint of X(i) and X(j) for these {i,j}: {8, 34860}
X(56174) = isogonal conjugate of X(16948)
X(56174) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 16948}, {2, 33628}, {3, 4248}, {6, 41629}, {21, 1420}, {27, 20818}, {28, 4855}, {56, 52352}, {58, 145}, {60, 4848}, {81, 1743}, {86, 3052}, {99, 8643}, {110, 3667}, {163, 4462}, {249, 21950}, {284, 5435}, {593, 3950}, {643, 51656}, {662, 4394}, {757, 4849}, {759, 4881}, {765, 18211}, {849, 52353}, {1014, 3158}, {1171, 4856}, {1333, 18743}, {1408, 44720}, {1412, 3161}, {1414, 4162}, {2194, 39126}, {3285, 31227}, {3733, 43290}, {3756, 4570}, {4521, 4565}, {4534, 52378}, {4556, 14321}, {4591, 14425}, {4729, 52935}, {5546, 30719}, {7419, 54237}, {16947, 44723}
X(56174) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 52352}, {3, 16948}, {9, 41629}, {10, 145}, {37, 18743}, {115, 4462}, {244, 3667}, {513, 18211}, {1084, 4394}, {1214, 39126}, {3739, 4891}, {4075, 52353}, {24151, 86}, {32664, 33628}, {34586, 4881}, {36103, 4248}, {38986, 8643}, {40586, 1743}, {40590, 5435}, {40591, 4855}, {40599, 3161}, {40600, 3052}, {40607, 4849}, {40608, 4162}, {40611, 1420}, {50330, 3756}, {52872, 4487}, {55060, 51656}, {55064, 4521}, {55065, 4404}
X(56174) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4373, 4052}
X(56174) = X(i)-cross conjugate of X(j) for these {i, j}: {210, 37}, {21809, 226}, {21963, 513}, {53540, 523}
X(56174) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}}, {{A, B, C, X(2), X(4214)}}, {{A, B, C, X(4), X(474)}}, {{A, B, C, X(6), X(4255)}}, {{A, B, C, X(8), X(3214)}}, {{A, B, C, X(12), X(3753)}}, {{A, B, C, X(28), X(16052)}}, {{A, B, C, X(42), X(3617)}}, {{A, B, C, X(44), X(72)}}, {{A, B, C, X(88), X(321)}}, {{A, B, C, X(89), X(6539)}}, {{A, B, C, X(105), X(4906)}}, {{A, B, C, X(201), X(21866)}}, {{A, B, C, X(210), X(3158)}}, {{A, B, C, X(213), X(49515)}}, {{A, B, C, X(226), X(3698)}}, {{A, B, C, X(291), X(4096)}}, {{A, B, C, X(313), X(24440)}}, {{A, B, C, X(512), X(28582)}}, {{A, B, C, X(523), X(3701)}}, {{A, B, C, X(594), X(1254)}}, {{A, B, C, X(650), X(6598)}}, {{A, B, C, X(740), X(21868)}}, {{A, B, C, X(758), X(4926)}}, {{A, B, C, X(860), X(15952)}}, {{A, B, C, X(896), X(11684)}}, {{A, B, C, X(899), X(17751)}}, {{A, B, C, X(959), X(4492)}}, {{A, B, C, X(1042), X(4346)}}, {{A, B, C, X(1089), X(3987)}}, {{A, B, C, X(1156), X(43703)}}, {{A, B, C, X(1214), X(37567)}}, {{A, B, C, X(1242), X(51499)}}, {{A, B, C, X(1245), X(28658)}}, {{A, B, C, X(1257), X(2161)}}, {{A, B, C, X(1334), X(10005)}}, {{A, B, C, X(1376), X(3967)}}, {{A, B, C, X(1426), X(40085)}}, {{A, B, C, X(1441), X(5836)}}, {{A, B, C, X(1575), X(42711)}}, {{A, B, C, X(1706), X(1826)}}, {{A, B, C, X(1739), X(24006)}}, {{A, B, C, X(1824), X(4696)}}, {{A, B, C, X(1888), X(40149)}}, {{A, B, C, X(1903), X(5438)}}, {{A, B, C, X(2136), X(2321)}}, {{A, B, C, X(2292), X(4719)}}, {{A, B, C, X(2996), X(39981)}}, {{A, B, C, X(3212), X(3696)}}, {{A, B, C, X(3293), X(3626)}}, {{A, B, C, X(3445), X(4373)}}, {{A, B, C, X(3596), X(35634)}}, {{A, B, C, X(3625), X(31855)}}, {{A, B, C, X(3649), X(4002)}}, {{A, B, C, X(3671), X(4731)}}, {{A, B, C, X(3679), X(50587)}}, {{A, B, C, X(3694), X(43708)}}, {{A, B, C, X(3714), X(19582)}}, {{A, B, C, X(3742), X(7249)}}, {{A, B, C, X(3754), X(4792)}}, {{A, B, C, X(3842), X(25614)}}, {{A, B, C, X(3931), X(5221)}}, {{A, B, C, X(3932), X(16605)}}, {{A, B, C, X(4041), X(4515)}}, {{A, B, C, X(4052), X(8056)}}, {{A, B, C, X(4424), X(4647)}}, {{A, B, C, X(4663), X(21879)}}, {{A, B, C, X(4682), X(52208)}}, {{A, B, C, X(4714), X(16666)}}, {{A, B, C, X(5220), X(21874)}}, {{A, B, C, X(5295), X(21858)}}, {{A, B, C, X(5297), X(27714)}}, {{A, B, C, X(5551), X(35576)}}, {{A, B, C, X(5556), X(15320)}}, {{A, B, C, X(5687), X(38955)}}, {{A, B, C, X(8688), X(56155)}}, {{A, B, C, X(9353), X(39946)}}, {{A, B, C, X(10308), X(17614)}}, {{A, B, C, X(10914), X(24297)}}, {{A, B, C, X(14624), X(31356)}}, {{A, B, C, X(17063), X(21951)}}, {{A, B, C, X(17122), X(32011)}}, {{A, B, C, X(17490), X(22034)}}, {{A, B, C, X(17898), X(40933)}}, {{A, B, C, X(18211), X(21963)}}, {{A, B, C, X(21677), X(41539)}}, {{A, B, C, X(24174), X(43677)}}, {{A, B, C, X(31993), X(44417)}}, {{A, B, C, X(32635), X(34893)}}, {{A, B, C, X(39970), X(40023)}}, {{A, B, C, X(39974), X(51223)}}, {{A, B, C, X(49468), X(52959)}}, {{A, B, C, X(52371), X(53013)}}, {{A, B, C, X(52389), X(52391)}}
X(56174) = barycentric product X(i)*X(j) for these (i, j): {1, 4052}, {10, 8056}, {37, 4373}, {65, 6557}, {210, 27818}, {226, 3680}, {313, 38266}, {321, 3445}, {1293, 1577}, {1427, 6556}, {2415, 55244}, {3120, 5382}, {3701, 40151}, {16945, 30713}, {17958, 34899}, {19604, 2321}, {27823, 7241}, {27832, 53008}, {27834, 523}, {31343, 7178}, {34080, 850}, {38828, 4086}, {40014, 42}, {53647, 661}
X(56174) = barycentric quotient X(i)/X(j) for these (i, j): {1, 41629}, {6, 16948}, {9, 52352}, {10, 18743}, {19, 4248}, {31, 33628}, {37, 145}, {42, 1743}, {65, 5435}, {71, 4855}, {210, 3161}, {213, 3052}, {226, 39126}, {228, 20818}, {512, 4394}, {523, 4462}, {594, 52353}, {661, 3667}, {756, 3950}, {798, 8643}, {1015, 18211}, {1018, 43290}, {1293, 662}, {1334, 3158}, {1400, 1420}, {1500, 4849}, {1962, 4856}, {2171, 4848}, {2245, 4881}, {2321, 44720}, {2415, 55243}, {2643, 21950}, {3125, 3756}, {3445, 81}, {3680, 333}, {3694, 44722}, {3701, 44723}, {3709, 4162}, {3930, 4899}, {3943, 4487}, {3949, 52354}, {3954, 4884}, {4017, 30719}, {4024, 4404}, {4041, 4521}, {4052, 75}, {4069, 30720}, {4079, 4729}, {4171, 4546}, {4373, 274}, {4515, 6555}, {4516, 4534}, {4642, 45204}, {4674, 31227}, {4705, 14321}, {4729, 31182}, {4730, 14425}, {5382, 4600}, {6557, 314}, {7180, 51656}, {8056, 86}, {16589, 4891}, {16945, 1412}, {17958, 37792}, {19604, 1434}, {21044, 4939}, {21796, 45219}, {21801, 51433}, {21809, 12640}, {21810, 4918}, {21832, 53580}, {24290, 4925}, {27834, 99}, {27837, 17218}, {31343, 645}, {34080, 110}, {36042, 4591}, {36197, 4953}, {38266, 58}, {38828, 1414}, {40014, 310}, {40151, 1014}, {42027, 27496}, {48005, 4949}, {53540, 40617}, {53647, 799}, {55244, 2403}
X(56174) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 11512, 8688}, {65, 21896, 4849}, {65, 4695, 21896}, {1739, 10914, 52541}, {3698, 4642, 37}, {3753, 3987, 4646}, {5836, 24440, 3752}, {8056, 10563, 3680}, {14923, 16610, 45219}, {16605, 21888, 21872}

X(56175) = KIMBERLING-PAVLOV X(37)-CONJUGATE OF X(65) AND X(75)

Barycentrics    (b+c)*(b*c*(b+c)+a^2*(2*b+c)+a*(2*b^2-2*b*c+c^2))*(b*c*(b+c)+a^2*(b+2*c)+a*(b^2-2*b*c+2*c^2)) : :

X(56175) lies on these lines: {1, 4434}, {65, 22294}, {75, 4695}, {876, 48249}, {982, 39697}, {1215, 4674}, {2533, 55244}, {4972, 52383}, {13476, 51055}, {17038, 50094}, {26030, 34434}, {30829, 42285}, {31025, 56159}, {46895, 56135}

X(56175) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1333, 30818}
X(56175) = X(i)-Dao conjugate of X(j) for these {i, j}: {37, 30818}
X(56175) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}}, {{A, B, C, X(756), X(4695)}}, {{A, B, C, X(1215), X(2533)}}, {{A, B, C, X(2292), X(4642)}}, {{A, B, C, X(4080), X(40029)}}, {{A, B, C, X(17751), X(26030)}}, {{A, B, C, X(18082), X(38955)}}, {{A, B, C, X(30829), X(31025)}}, {{A, B, C, X(40014), X(40515)}}
X(56175) = barycentric quotient X(i)/X(j) for these (i, j): {10, 30818}

X(56176) = KP2(X(9)) OF X(1) AND X(37)

Barycentrics    a*(a-b-c)*(2*a^2-b^2-c^2+a*(b+c)) : :
X(56176) = 3*X[2]+X[3189], -X[40]+3*X[4421], 3*X[165]+X[11523], -3*X[551]+X[21627], X[962]+3*X[34607], -5*X[1698]+X[12625], -7*X[3523]+3*X[24477], 3*X[3576]+X[6765], 7*X[3622]+X[12632], -7*X[3624]+3*X[24392], -3*X[3928]+7*X[16192], -X[5691]+3*X[11236] and many others

X(56176) lies on these lines: {1, 474}, {2, 3189}, {3, 518}, {6, 37552}, {8, 2320}, {9, 4258}, {10, 6675}, {11, 27385}, {20, 12678}, {21, 210}, {30, 21077}, {35, 72}, {36, 3555}, {37, 1247}, {40, 4421}, {41, 3693}, {42, 37539}, {43, 1104}, {44, 54354}, {55, 78}, {56, 3870}, {58, 3939}, {63, 5217}, {65, 100}, {101, 3991}, {140, 10916}, {145, 1319}, {165, 11523}, {200, 958}, {214, 3244}, {224, 11509}, {284, 3694}, {354, 404}, {355, 33596}, {377, 17718}, {386, 1386}, {389, 34372}, {392, 3746}, {405, 2900}, {411, 7957}, {480, 7675}, {484, 4018}, {495, 17647}, {497, 25681}, {498, 3419}, {515, 12607}, {516, 5763}, {517, 6796}, {519, 549}, {521, 33649}, {522, 3159}, {524, 48893}, {527, 12512}, {528, 946}, {529, 4297}, {536, 24315}, {537, 8720}, {540, 48926}, {551, 21627}, {581, 9025}, {612, 16352}, {674, 970}, {740, 8669}, {758, 3579}, {908, 6284}, {912, 26285}, {936, 1001}, {942, 25440}, {944, 32049}, {950, 1329}, {952, 10915}, {954, 15587}, {956, 3612}, {962, 34607}, {975, 15569}, {976, 3666}, {978, 1279}, {984, 37574}, {993, 34790}, {997, 3295}, {1012, 17857}, {1043, 3714}, {1071, 2077}, {1100, 3169}, {1125, 3813}, {1155, 3868}, {1191, 3749}, {1193, 3744}, {1201, 3722}, {1210, 3035}, {1212, 3684}, {1215, 50054}, {1259, 10391}, {1260, 10393}, {1320, 33176}, {1324, 40660}, {1331, 1399}, {1388, 4917}, {1410, 2283}, {1479, 5087}, {1490, 15726}, {1621, 25917}, {1697, 5289}, {1698, 12625}, {1792, 2330}, {1818, 30621}, {1837, 5123}, {1858, 51379}, {1897, 1940}, {2098, 3895}, {2177, 37548}, {2223, 54300}, {2264, 27396}, {2268, 3965}, {2292, 4689}, {2329, 4515}, {2348, 25082}, {2550, 5703}, {2551, 4313}, {2801, 34862}, {2802, 10222}, {2886, 13411}, {2975, 3935}, {3052, 54386}, {3057, 3871}, {3058, 41012}, {3085, 5794}, {3149, 37569}, {3208, 6603}, {3214, 12642}, {3219, 4005}, {3241, 20323}, {3243, 3361}, {3256, 12709}, {3303, 10179}, {3304, 35262}, {3333, 42871}, {3336, 24473}, {3338, 16371}, {3421, 4305}, {3434, 11375}, {3452, 4314}, {3475, 6904}, {3485, 17784}, {3486, 7080}, {3487, 5880}, {3523, 24477}, {3576, 6765}, {3584, 47033}, {3585, 13272}, {3616, 3748}, {3622, 12632}, {3624, 24392}, {3625, 51111}, {3632, 37525}, {3633, 21842}, {3647, 4134}, {3678, 15481}, {3679, 33595}, {3681, 4189}, {3683, 3876}, {3697, 5251}, {3699, 52352}, {3710, 3712}, {3739, 25500}, {3745, 19767}, {3751, 4252}, {3769, 20018}, {3772, 36573}, {3816, 6700}, {3825, 18527}, {3838, 11374}, {3848, 16408}, {3869, 37568}, {3872, 34471}, {3873, 4188}, {3874, 37582}, {3885, 5048}, {3893, 4861}, {3894, 37524}, {3901, 37572}, {3916, 5010}, {3921, 5426}, {3928, 16192}, {3931, 30115}, {3940, 12514}, {3957, 5253}, {3961, 36529}, {3967, 7283}, {3970, 35342}, {3976, 4864}, {3983, 5260}, {3998, 36559}, {4004, 5425}, {4097, 35104}, {4104, 49728}, {4190, 10404}, {4201, 33126}, {4251, 25066}, {4256, 37592}, {4294, 24703}, {4304, 21075}, {4413, 54392}, {4428, 31435}, {4430, 37307}, {4661, 17548}, {4847, 4999}, {4849, 5247}, {4850, 36565}, {4853, 8168}, {4863, 10527}, {4867, 11010}, {4870, 49719}, {4882, 53054}, {4981, 16347}, {4995, 21677}, {5013, 16973}, {5022, 51194}, {5044, 5248}, {5045, 15570}, {5057, 20066}, {5080, 11015}, {5119, 5730}, {5172, 16465}, {5175, 10588}, {5204, 41711}, {5220, 31424}, {5221, 11520}, {5225, 5748}, {5227, 37504}, {5252, 10528}, {5281, 20007}, {5288, 37616}, {5432, 6734}, {5433, 26015}, {5436, 8580}, {5534, 12114}, {5541, 11009}, {5554, 37724}, {5563, 15015}, {5691, 11236}, {5719, 12609}, {5720, 11496}, {5722, 26364}, {5745, 6743}, {5752, 9047}, {5855, 11362}, {5856, 24470}, {5882, 38455}, {5887, 11849}, {5901, 49600}, {6001, 11248}, {6244, 12520}, {6261, 10306}, {6265, 23340}, {6326, 12672}, {6601, 17582}, {6691, 11019}, {6692, 6744}, {6708, 56146}, {6735, 10950}, {6762, 7987}, {6764, 54445}, {6769, 52026}, {6906, 14872}, {6909, 12680}, {6911, 13374}, {6921, 17728}, {7288, 36845}, {7674, 17580}, {7686, 11499}, {8069, 11517}, {8227, 11235}, {8583, 10389}, {8666, 13624}, {8951, 15601}, {9037, 37482}, {9052, 15489}, {9709, 54318}, {9780, 12536}, {9844, 18236}, {9943, 10310}, {9945, 18990}, {9957, 25439}, {10107, 54286}, {10164, 24391}, {10178, 10884}, {10382, 18227}, {10448, 54387}, {10477, 19760}, {10525, 37713}, {10543, 21031}, {10572, 17757}, {10595, 34640}, {10609, 45287}, {10679, 45770}, {10896, 30852}, {11011, 14923}, {11112, 13407}, {11115, 46897}, {11230, 24387}, {11281, 49732}, {11491, 14110}, {11500, 37531}, {11519, 30392}, {11698, 16160}, {12433, 47742}, {12436, 25557}, {12521, 18241}, {12526, 35445}, {12541, 38314}, {12559, 36279}, {12631, 22754}, {12648, 37738}, {12649, 24914}, {12701, 20075}, {12738, 16138}, {12740, 13278}, {13405, 25466}, {13462, 45036}, {13463, 13464}, {14054, 36152}, {15071, 17613}, {15171, 21616}, {15178, 22837}, {15325, 49627}, {15347, 51577}, {15803, 41863}, {15823, 15837}, {15829, 53053}, {16370, 41229}, {16610, 28082}, {16616, 18491}, {16783, 25068}, {16866, 51572}, {17100, 17660}, {17201, 25585}, {17243, 40530}, {17351, 24850}, {17558, 38057}, {17605, 52367}, {17606, 27529}, {17619, 37702}, {17689, 27495}, {17715, 21214}, {17724, 23536}, {17733, 28581}, {17735, 21874}, {17765, 49613}, {17768, 28645}, {17780, 52353}, {17792, 52544}, {18178, 20359}, {18360, 35281}, {18391, 37828}, {19785, 36578}, {19862, 24386}, {21937, 51050}, {21949, 24161}, {24299, 26446}, {24475, 33814}, {24953, 25006}, {25973, 37722}, {26877, 34474}, {27399, 30812}, {28609, 34626}, {31660, 44782}, {31837, 32613}, {33956, 37727}, {34379, 48929}, {34707, 48661}, {35242, 54422}, {36745, 45728}, {36746, 45729}, {37176, 38047}, {37284, 45120}, {37540, 54421}, {37562, 37733}, {37583, 41539}, {37605, 54391}, {37607, 49478}, {37608, 49490}, {40663, 41575}, {41239, 44798}, {49467, 50608}, {51071, 51714}

X(56176) = midpoint of X(i) and X(j) for these {i,j}: {1, 3913}, {10, 12437}, {1001, 3174}, {11236, 34701}, {11248, 37700}, {11500, 37531}, {2136, 10912}, {28609, 34626}, {3, 3811}, {3244, 12640}, {34607, 34647}, {37727, 49169}, {40, 12635}, {5534, 12114}, {6261, 10306}, {6265, 25438}, {6326, 13205}, {6765, 12513}, {8715, 22836}, {944, 32049}, {997, 52804}
X(56176) = reflection of X(i) in X(j) for these {i,j}: {10916, 140}, {11260, 1385}, {11362, 32157}, {13463, 13464}, {22837, 15178}, {3813, 1125}, {32537, 10915}, {33895, 1}, {49600, 5901}, {8666, 13624}
X(56176) = perspector of circumconic {{A, B, C, X(27834), X(53629)}}
X(56176) = X(i)-Dao conjugate of X(j) for these {i, j}: {3686, 4359}, {17058, 693}
X(56176) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1255, 9}, {3879, 4641}, {40406, 219}
X(56176) = intersection, other than A, B, C, of circumconics {{A, B, C, X(145), X(10912)}}, {{A, B, C, X(1036), X(2320)}}, {{A, B, C, X(1247), X(2339)}}, {{A, B, C, X(3680), X(3879)}}, {{A, B, C, X(3812), X(23617)}}, {{A, B, C, X(9309), X(17054)}}, {{A, B, C, X(32635), X(34893)}}, {{A, B, C, X(34195), X(44669)}}
X(56176) = barycentric product X(i)*X(j) for these (i, j): {1, 56078}, {3879, 9}, {4641, 8}, {4897, 644}, {11363, 345}, {27820, 3158}
X(56176) = barycentric quotient X(i)/X(j) for these (i, j): {3879, 85}, {4641, 7}, {4897, 24002}, {11363, 278}, {17476, 53545}, {56078, 75}
X(56176) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1376, 3812}, {1, 2136, 10912}, {1, 3158, 3913}, {1, 3880, 33895}, {1, 3913, 3880}, {1, 4255, 4719}, {1, 474, 3742}, {1, 48696, 10914}, {1, 5438, 25524}, {1, 5687, 5836}, {2, 37080, 51715}, {8, 5218, 26066}, {10, 12437, 44669}, {21, 210, 5302}, {21, 4420, 210}, {35, 72, 4640}, {40, 12635, 44663}, {41, 3693, 30618}, {55, 78, 960}, {56, 3870, 34791}, {100, 34772, 65}, {200, 3601, 958}, {200, 958, 4662}, {214, 3244, 24928}, {386, 5266, 1386}, {484, 41696, 4018}, {497, 27383, 25681}, {519, 1385, 11260}, {950, 6745, 1329}, {952, 10915, 32537}, {1043, 7081, 3714}, {1125, 5853, 3813}, {1837, 5552, 5123}, {2550, 5703, 28628}, {2646, 3689, 8}, {3295, 52804, 8668}, {3303, 19861, 10179}, {3678, 31445, 15481}, {3870, 4855, 56}, {3871, 4511, 3057}, {3873, 4188, 32636}, {3957, 5253, 17609}, {4421, 12635, 40}, {5010, 5904, 3916}, {5044, 5248, 15254}, {5293, 37573, 37}, {5855, 32157, 11362}, {6762, 7987, 11194}, {8715, 22836, 517}, {10310, 18446, 9943}, {10679, 45770, 45776}, {11248, 37700, 6001}, {11499, 37533, 7686}, {25439, 30144, 9957}, {30115, 33771, 3931}

X(56177) = KP2(X(9)) OF X(1) AND X(45)

Barycentrics    a*(a-b-c)*(3*a^2+a*(b+c)-2*(b^2-b*c+c^2)) : :
X(56177) = -4*X[140]+X[49168], X[3189]+5*X[3616], -7*X[3624]+X[12625], -4*X[3636]+X[21627], 11*X[5550]+X[12536], -X[6762]+7*X[30389], 5*X[7987]+X[11523], -5*X[10595]+2*X[13463], -4*X[11729]+X[13271], -X[12245]+4*X[32157], -X[24392]+3*X[25055], -X[24477]+3*X[54445]

X(56177) lies on these lines: {1, 474}, {2, 44669}, {3, 758}, {6, 5429}, {8, 4999}, {9, 53054}, {10, 37739}, {35, 3899}, {36, 3894}, {55, 3877}, {56, 3873}, {63, 37600}, {65, 4855}, {72, 3612}, {78, 210}, {100, 2099}, {106, 41457}, {140, 49168}, {165, 44663}, {191, 19535}, {200, 4711}, {214, 999}, {224, 17616}, {354, 35262}, {376, 17768}, {392, 4428}, {405, 5426}, {443, 11281}, {480, 30284}, {498, 38058}, {515, 11236}, {516, 34626}, {517, 4421}, {518, 3576}, {519, 3653}, {522, 47040}, {528, 5603}, {529, 5731}, {551, 5853}, {938, 6691}, {944, 12607}, {950, 25681}, {952, 34717}, {956, 37525}, {960, 3601}, {968, 54387}, {993, 3940}, {995, 40499}, {997, 1001}, {1012, 6326}, {1125, 12437}, {1259, 22768}, {1317, 12648}, {1319, 3870}, {1329, 3486}, {1385, 3811}, {1420, 34791}, {1470, 12739}, {1478, 10609}, {1482, 8715}, {1483, 49169}, {1699, 34701}, {1837, 27385}, {1962, 19765}, {2096, 38759}, {2098, 3871}, {2320, 3711}, {2478, 10543}, {2802, 10247}, {2900, 8167}, {2975, 4661}, {3035, 18391}, {3061, 4258}, {3161, 30728}, {3169, 16884}, {3174, 42819}, {3189, 3616}, {3241, 5854}, {3242, 37617}, {3243, 13462}, {3295, 3898}, {3303, 8668}, {3306, 44840}, {3336, 19537}, {3361, 45036}, {3434, 15950}, {3488, 3816}, {3555, 37618}, {3586, 5087}, {3617, 51683}, {3624, 12625}, {3632, 24926}, {3635, 12640}, {3636, 21627}, {3649, 4190}, {3684, 34522}, {3689, 3872}, {3794, 4267}, {3868, 5204}, {3869, 5217}, {3895, 5048}, {3897, 4420}, {3919, 25440}, {3927, 4525}, {3956, 9708}, {3962, 4652}, {3968, 9709}, {3976, 8572}, {4188, 5221}, {4302, 51409}, {4304, 24703}, {4361, 25523}, {4539, 41229}, {4640, 30282}, {4731, 19860}, {4744, 36279}, {4867, 5010}, {5123, 5727}, {5131, 19705}, {5433, 12649}, {5529, 37679}, {5538, 7580}, {5550, 12536}, {5552, 10950}, {5657, 5855}, {5692, 16370}, {5703, 25466}, {5790, 34700}, {5794, 13411}, {5851, 54052}, {5882, 32049}, {5883, 16417}, {5886, 11235}, {5902, 15015}, {5904, 37616}, {5905, 15326}, {6265, 10679}, {6282, 11495}, {6735, 37740}, {6737, 26066}, {6762, 30389}, {6765, 11260}, {6767, 52804}, {6910, 21677}, {6911, 22935}, {6932, 54193}, {7223, 17136}, {7280, 41696}, {7483, 39783}, {7967, 34619}, {7987, 11523}, {8583, 51715}, {9668, 11813}, {9945, 39542}, {10072, 34123}, {10176, 16418}, {10179, 10389}, {10200, 12433}, {10306, 40257}, {10310, 21740}, {10528, 10944}, {10595, 13463}, {10915, 37727}, {11015, 12953}, {11041, 35023}, {11108, 35016}, {11321, 30135}, {11374, 17647}, {11415, 15338}, {11496, 33596}, {11517, 22766}, {11520, 32636}, {11682, 37568}, {11684, 17548}, {11729, 13271}, {12114, 37700}, {12245, 32157}, {12559, 37582}, {12738, 18519}, {12943, 31053}, {14882, 38901}, {15174, 17527}, {15624, 37620}, {16126, 37524}, {16137, 17563}, {16408, 30143}, {16486, 17715}, {16761, 37285}, {17318, 24324}, {17532, 37701}, {17558, 45085}, {17595, 49454}, {17619, 37721}, {18185, 18465}, {18446, 50371}, {18481, 21077}, {19538, 41872}, {19582, 52352}, {19861, 37080}, {19907, 25438}, {20007, 30478}, {22753, 37533}, {22837, 37624}, {24392, 25055}, {24473, 35271}, {24477, 54445}, {24914, 41575}, {24982, 37724}, {26364, 37730}, {26725, 44217}, {28160, 34739}, {28234, 34743}, {30115, 30903}, {31165, 35258}, {33126, 48801}, {33135, 48842}, {35227, 46943}, {37531, 37837}, {38028, 45700}, {38202, 50839}, {41711, 54391}, {50194, 54286}, {53037, 54423}

X(56177) = midpoint of X(i) and X(j) for these {i,j}: {1, 3158}, {1699, 34701}, {12437, 24386}, {5731, 25568}, {7967, 34619}
X(56177) = reflection of X(i) in X(j) for these {i,j}: {11194, 3576}, {11235, 5886}, {24386, 1125}, {3158, 56176}, {3913, 3158}, {34700, 5790}, {34706, 1699}, {45700, 38028}
X(56177) = X(i)-Dao conjugate of X(j) for these {i, j}: {3707, 24589}
X(56177) = X(i)-Ceva conjugate of X(j) for these {i, j}: {40434, 9}
X(56177) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 2136, 33895}, {1, 3158, 3880}, {1, 3913, 10912}, {1, 5438, 3812}, {1, 5440, 1376}, {1, 56176, 3913}, {3, 22836, 12635}, {55, 4511, 5289}, {78, 2646, 958}, {354, 35262, 40726}, {993, 3940, 5220}, {997, 24929, 1001}, {1385, 3811, 12513}, {3189, 3616, 3813}, {3486, 27383, 1329}, {3689, 3872, 8168}, {3873, 4881, 56}, {3880, 56176, 3158}, {3940, 37606, 993}, {4188, 34195, 5221}, {4881, 34772, 3873}, {5731, 25568, 529}, {5902, 15015, 16371}, {7967, 34619, 38455}, {33596, 45770, 11496}

X(56178) = KP2(X(9)) OF X(1) AND X(72)

Barycentrics    a*(a-b-c)*(2*a^4-a^3*(b+c)-(b^2-c^2)^2-a^2*(b^2+c^2)+a*(b^3+b^2*c+b*c^2+c^3)) : :

X(56178) lies on these lines: {1, 474}, {6, 2900}, {8, 27407}, {31, 15733}, {33, 1260}, {40, 10606}, {55, 39943}, {56, 15954}, {65, 951}, {72, 3465}, {100, 1214}, {200, 219}, {210, 2328}, {278, 17784}, {387, 3189}, {517, 53815}, {518, 1754}, {612, 6600}, {1104, 12625}, {1172, 3694}, {1279, 24392}, {1498, 17857}, {1723, 3052}, {1998, 52424}, {3174, 5269}, {3190, 3689}, {3198, 5285}, {3332, 25568}, {3434, 37695}, {3744, 5853}, {3811, 5706}, {3870, 37543}, {4030, 4847}, {4640, 53388}, {4689, 25080}, {5927, 23693}, {6244, 30265}, {6737, 50366}, {6745, 40960}, {7322, 47375}, {8715, 37528}, {12437, 37539}, {12664, 38857}, {21949, 37887}, {22308, 52139}, {34381, 49127}

X(56178) = X(i)-Dao conjugate of X(j) for these {i, j}: {950, 17863}
X(56178) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1257, 9}
X(56178) = intersection, other than A, B, C, of circumconics {{A, B, C, X(282), X(2341)}}, {{A, B, C, X(2192), X(3445)}}, {{A, B, C, X(52371), X(53013)}}
X(56178) = barycentric product X(i)*X(j) for these (i, j): {44409, 644}
X(56178) = barycentric quotient X(i)/X(j) for these (i, j): {44409, 24002}
X(56178) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {200, 7070, 219}

X(56179) = KP2(X(9)) OF X(8) AND X(2)

Barycentrics    a*(a^2-2*a*b+b^2+c^2)*(a^2+b^2-2*a*c+c^2) : :

X(56179) lies on these lines: {1, 344}, {2, 2191}, {6, 3692}, {8, 34}, {9, 1438}, {33, 30688}, {42, 52396}, {43, 7194}, {46, 34378}, {55, 30676}, {56, 78}, {58, 1792}, {63, 12329}, {69, 200}, {72, 12410}, {75, 28043}, {86, 612}, {87, 3961}, {100, 7289}, {106, 997}, {190, 4319}, {193, 3935}, {271, 1413}, {292, 16973}, {326, 2340}, {519, 998}, {522, 1027}, {613, 42019}, {614, 17352}, {937, 6765}, {977, 54418}, {1026, 53996}, {1126, 16475}, {1253, 4712}, {1386, 2334}, {1411, 3872}, {1431, 3779}, {1474, 2287}, {1809, 36819}, {2261, 4579}, {2263, 32850}, {2279, 51194}, {2346, 25082}, {3056, 9432}, {3174, 51190}, {3226, 54967}, {3242, 3445}, {3416, 52372}, {3589, 4666}, {3619, 8580}, {3912, 8271}, {3957, 51171}, {3979, 39972}, {4327, 49499}, {4384, 55076}, {4385, 8747}, {4437, 25930}, {4578, 26669}, {4737, 36123}, {4855, 22769}, {5287, 10013}, {5531, 39878}, {5534, 6776}, {5687, 34381}, {5720, 39898}, {6600, 25083}, {6769, 51212}, {7172, 54303}, {8816, 20007}, {9001, 16504}, {9053, 36846}, {9277, 42042}, {10382, 30702}, {12651, 51538}, {14872, 39877}, {15624, 16728}, {16491, 41434}, {16713, 26227}, {16972, 25426}, {17962, 49509}, {19860, 49524}, {22836, 49536}, {25050, 51210}, {25992, 38047}, {26924, 43146}, {34249, 53146}, {37782, 53661}, {41436, 49465}

X(56179) = isogonal conjugate of X(614)
X(56179) = isotomic conjugate of X(3673)
X(56179) = trilinear pole of line {649, 3309}
X(56179) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 614}, {2, 16502}, {3, 1851}, {4, 1473}, {6, 4000}, {7, 7083}, {9, 28017}, {19, 7289}, {21, 40961}, {25, 17170}, {27, 23620}, {28, 17441}, {31, 3673}, {34, 1040}, {55, 7195}, {56, 497}, {57, 2082}, {58, 3914}, {65, 5324}, {72, 4211}, {77, 40987}, {81, 16583}, {86, 40934}, {99, 50490}, {101, 48398}, {110, 48403}, {112, 21107}, {213, 16750}, {269, 4319}, {274, 21750}, {278, 7124}, {279, 30706}, {286, 22363}, {513, 1633}, {608, 27509}, {649, 3732}, {738, 28070}, {934, 17115}, {1014, 40965}, {1333, 53510}, {1407, 6554}, {1438, 51400}, {1474, 18589}, {1509, 21813}, {1790, 52577}, {1863, 7053}, {2203, 20235}, {2221, 5286}, {4012, 7023}, {7290, 21450}, {7386, 51686}, {8020, 17206}, {8747, 22057}, {15487, 40188}, {17060, 41934}
X(56179) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 497}, {2, 3673}, {3, 614}, {6, 7289}, {9, 4000}, {10, 3914}, {37, 53510}, {223, 7195}, {244, 48403}, {478, 28017}, {1015, 48398}, {5375, 3732}, {5452, 2082}, {6184, 51400}, {6505, 17170}, {6600, 4319}, {6626, 16750}, {11517, 1040}, {14714, 17115}, {23050, 1863}, {24771, 6554}, {32664, 16502}, {34591, 21107}, {36033, 1473}, {36103, 1851}, {38986, 50490}, {39026, 1633}, {40181, 5286}, {40586, 16583}, {40591, 17441}, {40600, 40934}, {40602, 5324}, {40611, 40961}, {51574, 18589}
X(56179) = X(i)-Ceva conjugate of X(j) for these {i, j}: {8817, 7131}, {40403, 7123}
X(56179) = X(i)-cross conjugate of X(j) for these {i, j}: {657, 190}, {905, 100}, {3938, 1}, {7123, 7131}, {14523, 7}, {17658, 8}, {22131, 63}, {25066, 2}, {53583, 1026}
X(56179) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(6)}}, {{A, B, C, X(2), X(344)}}, {{A, B, C, X(4), X(56137)}}, {{A, B, C, X(7), X(1280)}}, {{A, B, C, X(8), X(69)}}, {{A, B, C, X(9), X(75)}}, {{A, B, C, X(10), X(3811)}}, {{A, B, C, X(19), X(291)}}, {{A, B, C, X(21), X(1219)}}, {{A, B, C, X(28), X(13742)}}, {{A, B, C, X(29), X(37282)}}, {{A, B, C, X(33), X(7033)}}, {{A, B, C, X(37), X(3751)}}, {{A, B, C, X(42), X(612)}}, {{A, B, C, X(43), X(3961)}}, {{A, B, C, X(44), X(9353)}}, {{A, B, C, X(57), X(82)}}, {{A, B, C, X(59), X(77)}}, {{A, B, C, X(63), X(28739)}}, {{A, B, C, X(65), X(989)}}, {{A, B, C, X(66), X(80)}}, {{A, B, C, X(67), X(43731)}}, {{A, B, C, X(72), X(4385)}}, {{A, B, C, X(79), X(43726)}}, {{A, B, C, X(81), X(3618)}}, {{A, B, C, X(84), X(34860)}}, {{A, B, C, X(90), X(596)}}, {{A, B, C, X(95), X(52133)}}, {{A, B, C, X(105), X(39956)}}, {{A, B, C, X(145), X(19861)}}, {{A, B, C, X(190), X(3729)}}, {{A, B, C, X(200), X(480)}}, {{A, B, C, X(219), X(326)}}, {{A, B, C, X(238), X(16973)}}, {{A, B, C, X(256), X(23051)}}, {{A, B, C, X(257), X(31360)}}, {{A, B, C, X(264), X(4518)}}, {{A, B, C, X(281), X(34894)}}, {{A, B, C, X(282), X(14942)}}, {{A, B, C, X(284), X(36741)}}, {{A, B, C, X(319), X(3416)}}, {{A, B, C, X(320), X(49688)}}, {{A, B, C, X(321), X(3681)}}, {{A, B, C, X(341), X(44692)}}, {{A, B, C, X(517), X(4737)}}, {{A, B, C, X(519), X(997)}}, {{A, B, C, X(611), X(3553)}}, {{A, B, C, X(613), X(3554)}}, {{A, B, C, X(614), X(3938)}}, {{A, B, C, X(657), X(4319)}}, {{A, B, C, X(751), X(49527)}}, {{A, B, C, X(757), X(39958)}}, {{A, B, C, X(897), X(41441)}}, {{A, B, C, X(903), X(3062)}}, {{A, B, C, X(905), X(7289)}}, {{A, B, C, X(936), X(6765)}}, {{A, B, C, X(941), X(1390)}}, {{A, B, C, X(969), X(1002)}}, {{A, B, C, X(1000), X(17040)}}, {{A, B, C, X(1001), X(51194)}}, {{A, B, C, X(1014), X(39975)}}, {{A, B, C, X(1016), X(40405)}}, {{A, B, C, X(1023), X(16504)}}, {{A, B, C, X(1037), X(1041)}}, {{A, B, C, X(1038), X(12410)}}, {{A, B, C, X(1100), X(16475)}}, {{A, B, C, X(1156), X(4373)}}, {{A, B, C, X(1252), X(37741)}}, {{A, B, C, X(1253), X(2340)}}, {{A, B, C, X(1268), X(41712)}}, {{A, B, C, X(1320), X(35262)}}, {{A, B, C, X(1386), X(1449)}}, {{A, B, C, X(1476), X(6553)}}, {{A, B, C, X(1743), X(3242)}}, {{A, B, C, X(1757), X(49509)}}, {{A, B, C, X(1807), X(6391)}}, {{A, B, C, X(1814), X(40399)}}, {{A, B, C, X(1909), X(2330)}}, {{A, B, C, X(1911), X(1974)}}, {{A, B, C, X(1961), X(42042)}}, {{A, B, C, X(1992), X(24557)}}, {{A, B, C, X(2161), X(7241)}}, {{A, B, C, X(2209), X(9288)}}, {{A, B, C, X(2827), X(9041)}}, {{A, B, C, X(3247), X(4663)}}, {{A, B, C, X(3422), X(43725)}}, {{A, B, C, X(3467), X(39711)}}, {{A, B, C, X(3551), X(9282)}}, {{A, B, C, X(3673), X(25066)}}, {{A, B, C, X(3869), X(4696)}}, {{A, B, C, X(3872), X(4511)}}, {{A, B, C, X(3920), X(5256)}}, {{A, B, C, X(3957), X(4666)}}, {{A, B, C, X(3979), X(26102)}}, {{A, B, C, X(4384), X(17277)}}, {{A, B, C, X(4570), X(56139)}}, {{A, B, C, X(4649), X(16972)}}, {{A, B, C, X(4659), X(17336)}}, {{A, B, C, X(5223), X(50995)}}, {{A, B, C, X(5287), X(17018)}}, {{A, B, C, X(5293), X(50581)}}, {{A, B, C, X(5486), X(5559)}}, {{A, B, C, X(5557), X(38005)}}, {{A, B, C, X(5560), X(15321)}}, {{A, B, C, X(6339), X(54123)}}, {{A, B, C, X(6601), X(52663)}}, {{A, B, C, X(7091), X(39702)}}, {{A, B, C, X(7093), X(34250)}}, {{A, B, C, X(7131), X(30676)}}, {{A, B, C, X(7155), X(18816)}}, {{A, B, C, X(7160), X(31359)}}, {{A, B, C, X(7161), X(39708)}}, {{A, B, C, X(7163), X(34207)}}, {{A, B, C, X(7284), X(39697)}}, {{A, B, C, X(8270), X(37577)}}, {{A, B, C, X(9309), X(40400)}}, {{A, B, C, X(10390), X(39704)}}, {{A, B, C, X(13476), X(40401)}}, {{A, B, C, X(14191), X(52556)}}, {{A, B, C, X(15180), X(24858)}}, {{A, B, C, X(16491), X(16666)}}, {{A, B, C, X(16667), X(38315)}}, {{A, B, C, X(16670), X(49465)}}, {{A, B, C, X(16774), X(43734)}}, {{A, B, C, X(17792), X(24524)}}, {{A, B, C, X(18743), X(25067)}}, {{A, B, C, X(19604), X(46972)}}, {{A, B, C, X(19860), X(34772)}}, {{A, B, C, X(20880), X(25082)}}, {{A, B, C, X(21446), X(36807)}}, {{A, B, C, X(22277), X(47373)}}, {{A, B, C, X(22336), X(43732)}}, {{A, B, C, X(25237), X(25244)}}, {{A, B, C, X(25430), X(39737)}}, {{A, B, C, X(26893), X(26924)}}, {{A, B, C, X(30648), X(56142)}}, {{A, B, C, X(32635), X(43533)}}, {{A, B, C, X(34399), X(44184)}}, {{A, B, C, X(34525), X(51567)}}, {{A, B, C, X(36101), X(39749)}}, {{A, B, C, X(36404), X(49490)}}, {{A, B, C, X(39798), X(39954)}}, {{A, B, C, X(42301), X(44327)}}, {{A, B, C, X(47595), X(49698)}}, {{A, B, C, X(51565), X(56101)}}
X(56179) = barycentric product X(i)*X(j) for these (i, j): {1, 30701}, {10, 40403}, {100, 48070}, {200, 30705}, {514, 52778}, {1037, 312}, {1041, 345}, {1459, 42384}, {3239, 8269}, {7084, 76}, {7123, 75}, {7131, 8}, {8817, 9}, {40411, 72}, {54967, 649}
X(56179) = barycentric quotient X(i)/X(j) for these (i, j): {1, 4000}, {2, 3673}, {3, 7289}, {6, 614}, {9, 497}, {10, 53510}, {19, 1851}, {31, 16502}, {37, 3914}, {41, 7083}, {42, 16583}, {48, 1473}, {55, 2082}, {56, 28017}, {57, 7195}, {63, 17170}, {71, 17441}, {72, 18589}, {78, 27509}, {86, 16750}, {100, 3732}, {101, 1633}, {200, 6554}, {212, 7124}, {213, 40934}, {219, 1040}, {220, 4319}, {228, 23620}, {284, 5324}, {306, 20235}, {480, 28070}, {513, 48398}, {518, 51400}, {607, 40987}, {612, 5286}, {656, 21107}, {657, 17115}, {661, 48403}, {728, 4012}, {798, 50490}, {872, 21813}, {1037, 57}, {1041, 278}, {1253, 30706}, {1334, 40965}, {1400, 40961}, {1474, 4211}, {1824, 52577}, {1918, 21750}, {2200, 22363}, {3681, 17671}, {3870, 41785}, {3949, 21015}, {3990, 22057}, {4712, 17060}, {5227, 7386}, {7079, 1863}, {7084, 6}, {7123, 1}, {7131, 7}, {8269, 658}, {8270, 41786}, {8817, 85}, {12329, 15487}, {13577, 41788}, {14935, 2170}, {17742, 11677}, {17784, 41787}, {30701, 75}, {30705, 1088}, {40403, 86}, {40411, 286}, {48070, 693}, {52778, 190}, {54967, 1978}

X(56180) = KP2(X(9)) OF X(8) AND X(55)

Barycentrics    (a^2-a*b+b^2)*(a-b-c)*(a^2-a*c+c^2) : :

X(56180) lies on these lines: {8, 238}, {75, 183}, {87, 1911}, {200, 4451}, {242, 318}, {341, 3685}, {346, 3217}, {390, 6556}, {1043, 3790}, {1219, 7132}, {1222, 49688}, {2220, 17281}, {2370, 8685}, {2726, 8684}, {3705, 17279}, {7155, 19589}, {17786, 24820}, {36815, 52409}

X(56180) = isogonal conjugate of X(7248)
X(56180) = isotomic conjugate of X(7185)
X(56180) = trilinear pole of line {3239, 4435}
X(56180) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 7248}, {6, 41777}, {7, 7032}, {31, 7185}, {34, 3784}, {56, 982}, {57, 2275}, {109, 3777}, {269, 3056}, {279, 20665}, {604, 3662}, {664, 50514}, {1014, 3778}, {1042, 3794}, {1106, 3705}, {1119, 20753}, {1333, 16888}, {1396, 20727}, {1397, 33930}, {1402, 33947}, {1407, 3061}, {1408, 2887}, {1409, 31917}, {1412, 3721}, {1415, 3776}, {1431, 7184}, {1434, 16584}, {3863, 7175}, {3888, 43924}, {4073, 7023}, {7153, 20284}, {7186, 52372}, {7237, 7341}, {16947, 20234}, {40499, 43932}
X(56180) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 982}, {2, 7185}, {3, 7248}, {9, 41777}, {11, 3777}, {37, 16888}, {1146, 3776}, {2968, 3810}, {3161, 3662}, {5452, 2275}, {6552, 3705}, {6600, 3056}, {6741, 3801}, {11517, 3784}, {24771, 3061}, {39025, 50514}, {40599, 3721}, {40605, 33947}, {51402, 53533}
X(56180) = X(i)-Ceva conjugate of X(j) for these {i, j}: {7033, 17743}
X(56180) = X(i)-cross conjugate of X(j) for these {i, j}: {4147, 3699}, {8641, 644}
X(56180) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(37588)}}, {{A, B, C, X(2), X(26685)}}, {{A, B, C, X(6), X(8851)}}, {{A, B, C, X(8), X(75)}}, {{A, B, C, X(9), X(87)}}, {{A, B, C, X(21), X(3217)}}, {{A, B, C, X(29), X(17697)}}, {{A, B, C, X(55), X(1403)}}, {{A, B, C, X(183), X(2287)}}, {{A, B, C, X(200), X(7081)}}, {{A, B, C, X(281), X(4518)}}, {{A, B, C, X(312), X(17280)}}, {{A, B, C, X(314), X(32941)}}, {{A, B, C, X(333), X(17349)}}, {{A, B, C, X(390), X(3161)}}, {{A, B, C, X(522), X(17765)}}, {{A, B, C, X(1253), X(51928)}}, {{A, B, C, X(1261), X(1376)}}, {{A, B, C, X(2220), X(3871)}}, {{A, B, C, X(2321), X(3773)}}, {{A, B, C, X(2325), X(49700)}}, {{A, B, C, X(2329), X(3208)}}, {{A, B, C, X(3596), X(33165)}}, {{A, B, C, X(4183), X(37099)}}, {{A, B, C, X(4433), X(4517)}}, {{A, B, C, X(7071), X(34247)}}, {{A, B, C, X(7155), X(14942)}}, {{A, B, C, X(14621), X(36799)}}, {{A, B, C, X(15742), X(56179)}}, {{A, B, C, X(20895), X(49688)}}, {{A, B, C, X(30479), X(36916)}}, {{A, B, C, X(36630), X(39972)}}, {{A, B, C, X(43749), X(49704)}}, {{A, B, C, X(49693), X(55076)}}
X(56180) = barycentric product X(i)*X(j) for these (i, j): {41, 7034}, {210, 38810}, {261, 43265}, {312, 983}, {341, 7132}, {2321, 40415}, {3114, 4517}, {3407, 3790}, {4621, 522}, {7033, 9}, {7064, 7307}, {17743, 8}, {30713, 38813}, {30730, 7255}, {40834, 4433}, {52622, 8685}
X(56180) = barycentric quotient X(i)/X(j) for these (i, j): {1, 41777}, {2, 7185}, {6, 7248}, {8, 3662}, {9, 982}, {10, 16888}, {29, 31917}, {41, 7032}, {55, 2275}, {200, 3061}, {210, 3721}, {219, 3784}, {220, 3056}, {312, 33930}, {333, 33947}, {346, 3705}, {522, 3776}, {644, 3888}, {650, 3777}, {728, 4073}, {983, 57}, {1253, 20665}, {1334, 3778}, {1639, 53533}, {1802, 20753}, {2287, 3794}, {2318, 20727}, {2321, 2887}, {2329, 7184}, {3063, 50514}, {3208, 41886}, {3239, 3810}, {3685, 33891}, {3699, 33946}, {3700, 3801}, {3701, 20234}, {3790, 3314}, {4069, 7239}, {4082, 4136}, {4433, 18904}, {4435, 3808}, {4517, 3094}, {4621, 664}, {6057, 16886}, {7033, 85}, {7034, 20567}, {7081, 7187}, {7132, 269}, {7255, 17096}, {8685, 1461}, {16886, 41291}, {17743, 7}, {27538, 33890}, {38813, 1412}, {40415, 1434}, {43265, 12}, {52405, 7186}

X(56181) = KP2(X(9)) OF X(21) AND X(41)

Barycentrics    a*(a+b)*(a-b-c)*(a+c)*(-(b*c)+a*(b+c)) : :

X(56181) lies on these lines: {1, 25059}, {2, 37502}, {3, 20018}, {6, 4203}, {8, 21}, {27, 11406}, {41, 7075}, {42, 81}, {43, 2209}, {58, 3550}, {69, 37467}, {86, 1376}, {145, 4225}, {149, 14008}, {165, 18206}, {192, 20760}, {193, 37400}, {200, 3786}, {228, 1999}, {284, 2319}, {314, 7081}, {385, 4220}, {387, 37030}, {404, 940}, {497, 27518}, {519, 4276}, {581, 50579}, {612, 25058}, {643, 2194}, {740, 11688}, {846, 3728}, {851, 17778}, {941, 5275}, {956, 37303}, {1010, 5687}, {1011, 37652}, {1014, 5933}, {1030, 50252}, {1333, 6043}, {1350, 7411}, {1403, 3212}, {1444, 17731}, {1621, 5235}, {1654, 4199}, {1697, 46877}, {1778, 17735}, {1816, 1936}, {1817, 37581}, {2177, 10458}, {2269, 2287}, {2303, 4386}, {2328, 7220}, {2651, 26893}, {2975, 32853}, {3158, 3794}, {3185, 49470}, {3214, 27660}, {3286, 4421}, {3295, 11110}, {3434, 14009}, {3651, 48917}, {3685, 20967}, {3750, 10459}, {3769, 15624}, {3779, 41610}, {3868, 18673}, {3870, 5208}, {3920, 25060}, {3961, 35623}, {3971, 52923}, {4038, 5253}, {4184, 16704}, {4191, 37684}, {4204, 26044}, {4210, 37639}, {4219, 56014}, {4229, 6244}, {4278, 50590}, {4281, 5255}, {4413, 25507}, {4427, 25294}, {4511, 21334}, {4653, 25439}, {4658, 25440}, {4921, 4954}, {5047, 19732}, {5132, 14829}, {5281, 16713}, {5284, 30970}, {5331, 5710}, {5440, 18465}, {5552, 14011}, {6745, 17182}, {6765, 10461}, {7580, 56020}, {8025, 35983}, {9709, 14007}, {10306, 37422}, {10434, 49495}, {10449, 19763}, {11322, 37685}, {11358, 17379}, {11502, 31631}, {14005, 26115}, {14459, 40592}, {14552, 37175}, {14942, 46880}, {14956, 20075}, {15149, 38300}, {16056, 17300}, {16058, 17349}, {16678, 54391}, {16830, 37870}, {16858, 48862}, {17139, 25568}, {17232, 50199}, {17594, 40773}, {18178, 20359}, {20009, 27652}, {20077, 37425}, {20691, 51319}, {20805, 41835}, {21319, 37759}, {25254, 53349}, {27639, 30947}, {27653, 34772}, {30984, 32948}, {32863, 35984}, {32911, 35992}, {35206, 35633}, {35978, 37540}, {37329, 37653}

X(56181) = perspector of circumconic {{A, B, C, X(645), X(4584)}}
X(56181) = X(i)-isoconjugate-of-X(j) for these {i, j}: {7, 23493}, {37, 7153}, {56, 42027}, {57, 16606}, {65, 87}, {85, 21759}, {213, 7209}, {225, 23086}, {226, 2162}, {273, 22381}, {330, 1400}, {932, 4017}, {961, 45197}, {1014, 7148}, {1042, 7155}, {1402, 6384}, {1427, 2319}, {1434, 6378}, {1441, 7121}, {2053, 3668}, {4032, 51974}, {4551, 43931}, {4598, 7180}, {7178, 34071}, {15373, 40149}, {18830, 51641}
X(56181) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 42027}, {75, 349}, {3061, 16888}, {3835, 53540}, {5452, 16606}, {6377, 4077}, {6626, 7209}, {17063, 48643}, {20257, 21927}, {34961, 932}, {40582, 330}, {40589, 7153}, {40598, 1441}, {40602, 87}, {40605, 6384}, {40610, 7178}, {55062, 523}
X(56181) = X(i)-Ceva conjugate of X(j) for these {i, j}: {284, 21}, {33296, 27644}
X(56181) = X(i)-cross conjugate of X(j) for these {i, j}: {4147, 52923}
X(56181) = intersection, other than A, B, C, of circumconics {{A, B, C, X(8), X(43)}}, {{A, B, C, X(9), X(38275)}}, {{A, B, C, X(21), X(741)}}, {{A, B, C, X(42), X(4433)}}, {{A, B, C, X(55), X(1403)}}, {{A, B, C, X(171), X(3684)}}, {{A, B, C, X(192), X(345)}}, {{A, B, C, X(333), X(27644)}}, {{A, B, C, X(893), X(3685)}}, {{A, B, C, X(958), X(2176)}}, {{A, B, C, X(1036), X(41526)}}, {{A, B, C, X(1043), X(33296)}}, {{A, B, C, X(1259), X(20760)}}, {{A, B, C, X(1320), X(49492)}}, {{A, B, C, X(1423), X(5273)}}, {{A, B, C, X(1792), X(1808)}}, {{A, B, C, X(2269), X(18235)}}, {{A, B, C, X(3486), X(20287)}}, {{A, B, C, X(3704), X(20691)}}, {{A, B, C, X(3971), X(4147)}}, {{A, B, C, X(4083), X(44669)}}, {{A, B, C, X(4600), X(13588)}}, {{A, B, C, X(7081), X(45216)}}, {{A, B, C, X(27527), X(31008)}}
X(56181) = barycentric product X(i)*X(j) for these (i, j): {100, 27527}, {192, 21}, {210, 7304}, {284, 6376}, {312, 38832}, {333, 43}, {1043, 1423}, {2176, 314}, {2185, 3971}, {2194, 6382}, {2209, 28660}, {2287, 3212}, {2328, 30545}, {3208, 86}, {3737, 4595}, {3786, 52136}, {3835, 643}, {4083, 645}, {4110, 58}, {4147, 662}, {4560, 52923}, {4631, 50491}, {16695, 646}, {16742, 4076}, {17217, 644}, {17921, 4571}, {18197, 3699}, {20691, 261}, {20760, 31623}, {20906, 5546}, {20979, 7257}, {21051, 4612}, {22370, 29}, {25098, 36797}, {27538, 81}, {27644, 8}, {30584, 4603}, {31008, 55}, {33296, 9}, {36860, 663}, {36863, 7252}, {43051, 7256}
X(56181) = barycentric quotient X(i)/X(j) for these (i, j): {9, 42027}, {21, 330}, {41, 23493}, {43, 226}, {55, 16606}, {58, 7153}, {86, 7209}, {192, 1441}, {284, 87}, {314, 6383}, {333, 6384}, {643, 4598}, {645, 18830}, {1043, 27424}, {1334, 7148}, {1403, 1427}, {1423, 3668}, {2175, 21759}, {2176, 65}, {2193, 23086}, {2194, 2162}, {2209, 1400}, {2269, 45197}, {2287, 7155}, {2328, 2319}, {3123, 53545}, {3208, 10}, {3212, 1446}, {3786, 51837}, {3835, 4077}, {3913, 27432}, {3971, 6358}, {4083, 7178}, {4110, 313}, {4147, 1577}, {4267, 27455}, {4612, 56053}, {5546, 932}, {6376, 349}, {6377, 53540}, {7252, 43931}, {8640, 7180}, {14408, 30572}, {16695, 3669}, {16742, 1358}, {17217, 24002}, {18197, 3676}, {20691, 12}, {20760, 1214}, {20967, 45218}, {20979, 4017}, {22090, 51664}, {22370, 307}, {25098, 17094}, {27527, 693}, {27538, 321}, {27644, 7}, {31008, 6063}, {33296, 85}, {36860, 4572}, {38832, 57}, {41526, 1042}, {41886, 16888}, {45216, 45208}, {51902, 4032}, {52352, 27496}, {52425, 22381}, {52923, 4552}, {52964, 40663}
X(56181) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {43, 38832, 27644}, {81, 100, 13588}, {200, 17185, 3786}, {1043, 4267, 21}, {1376, 18185, 86}, {3913, 4267, 1043}

X(56182) = KP2(X(9)) OF X(21) AND X(78)

Barycentrics    a*(a+b)*(a-b-c)^3*(a+c) : :

X(56182) lies on these lines: {3, 37655}, {8, 21}, {27, 17784}, {28, 5687}, {29, 7080}, {58, 6765}, {69, 7411}, {78, 7070}, {81, 3870}, {86, 10578}, {92, 32929}, {99, 15731}, {100, 306}, {200, 1253}, {284, 3158}, {314, 2346}, {332, 1014}, {346, 1260}, {391, 13615}, {404, 18141}, {461, 27522}, {480, 5423}, {643, 1812}, {644, 2318}, {728, 6602}, {740, 26000}, {943, 5295}, {968, 23668}, {1005, 5739}, {1172, 3694}, {1261, 2194}, {1330, 33557}, {1441, 32932}, {1621, 3886}, {1778, 3052}, {2352, 49687}, {2895, 35989}, {3198, 5279}, {3295, 47512}, {3651, 41014}, {3695, 30733}, {3719, 41228}, {3935, 40571}, {3936, 35990}, {4082, 4578}, {4233, 10327}, {4417, 36002}, {4571, 42033}, {4651, 40435}, {4653, 9623}, {4869, 37270}, {5082, 25516}, {5174, 54340}, {5208, 7672}, {5235, 25006}, {5281, 37265}, {5327, 25568}, {6600, 7172}, {6745, 17188}, {6986, 10449}, {7256, 28071}, {7283, 52345}, {7677, 10453}, {8822, 9778}, {9709, 17581}, {11239, 51669}, {11491, 37418}, {12410, 27652}, {14552, 20835}, {16704, 20015}, {18139, 35985}, {19860, 25059}, {23079, 50423}, {23600, 27404}, {26872, 35981}, {32863, 36003}, {34409, 37741}, {35613, 52769}, {37224, 43533}, {37292, 49718}, {37442, 37580}

X(56182) = perspector of circumconic {{A, B, C, X(645), X(7259)}}
X(56182) = X(i)-isoconjugate-of-X(j) for these {i, j}: {7, 1042}, {10, 7023}, {34, 1439}, {37, 738}, {42, 479}, {56, 3668}, {57, 1427}, {58, 6046}, {65, 269}, {73, 1119}, {77, 1426}, {81, 7147}, {86, 7143}, {213, 23062}, {225, 7053}, {226, 1407}, {273, 1410}, {278, 52373}, {279, 1400}, {307, 1398}, {321, 7366}, {349, 52410}, {512, 4626}, {523, 6614}, {604, 1446}, {651, 7216}, {658, 7180}, {661, 4617}, {664, 7250}, {669, 52937}, {798, 36838}, {934, 4017}, {1014, 1254}, {1020, 3669}, {1088, 1402}, {1106, 1441}, {1214, 1435}, {1245, 7197}, {1262, 53545}, {1396, 37755}, {1409, 1847}, {1412, 6354}, {1461, 7178}, {1474, 20618}, {1880, 7177}, {2333, 30682}, {3120, 7339}, {3676, 53321}, {4516, 24013}, {4551, 43932}, {4566, 43924}, {4569, 51641}, {6611, 8808}, {7045, 53540}, {7099, 40149}, {8809, 40933}, {21044, 23971}, {32714, 51664}
X(56182) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 3668}, {10, 6046}, {2968, 4077}, {3161, 1446}, {3900, 4516}, {5452, 1427}, {6552, 1441}, {6600, 65}, {6608, 3120}, {6626, 23062}, {7358, 17094}, {11517, 1439}, {14714, 4017}, {17115, 53540}, {23050, 225}, {24771, 226}, {31998, 36838}, {34961, 934}, {35508, 7178}, {36830, 4617}, {38991, 7216}, {39025, 7250}, {39054, 4626}, {40582, 279}, {40586, 7147}, {40589, 738}, {40592, 479}, {40599, 6354}, {40600, 7143}, {40602, 269}, {40605, 1088}, {51574, 20618}, {55068, 3676}
X(56182) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1043, 2287}
X(56182) = X(i)-cross conjugate of X(j) for these {i, j}: {4163, 4578}
X(56182) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4313)}}, {{A, B, C, X(8), X(200)}}, {{A, B, C, X(9), X(5273)}}, {{A, B, C, X(21), X(2328)}}, {{A, B, C, X(33), X(3486)}}, {{A, B, C, X(55), X(480)}}, {{A, B, C, X(92), X(41798)}}, {{A, B, C, X(210), X(21677)}}, {{A, B, C, X(220), X(958)}}, {{A, B, C, X(333), X(2287)}}, {{A, B, C, X(345), X(346)}}, {{A, B, C, X(413), X(4206)}}, {{A, B, C, X(1014), X(2299)}}, {{A, B, C, X(1156), X(7008)}}, {{A, B, C, X(1259), X(1260)}}, {{A, B, C, X(1441), X(53013)}}, {{A, B, C, X(1476), X(2192)}}, {{A, B, C, X(3263), X(45791)}}, {{A, B, C, X(3680), X(12536)}}, {{A, B, C, X(3704), X(4515)}}, {{A, B, C, X(3712), X(4130)}}, {{A, B, C, X(3870), X(28057)}}, {{A, B, C, X(3900), X(44669)}}, {{A, B, C, X(4082), X(4163)}}, {{A, B, C, X(4105), X(4433)}}, {{A, B, C, X(4267), X(23609)}}, {{A, B, C, X(6060), X(7070)}}, {{A, B, C, X(6559), X(6605)}}, {{A, B, C, X(7072), X(22760)}}, {{A, B, C, X(7073), X(10543)}}, {{A, B, C, X(10950), X(52371)}}
X(56182) = barycentric product X(i)*X(j) for these (i, j): {21, 346}, {28, 30681}, {29, 3692}, {200, 333}, {210, 7058}, {220, 314}, {261, 4515}, {274, 480}, {283, 7101}, {284, 341}, {310, 6602}, {321, 6061}, {332, 7079}, {345, 4183}, {522, 7259}, {644, 7253}, {650, 7256}, {657, 7257}, {663, 7258}, {728, 86}, {1021, 3699}, {1043, 9}, {1098, 2321}, {1172, 1265}, {1253, 28660}, {1260, 31623}, {1792, 281}, {1802, 44130}, {1812, 7046}, {2185, 4082}, {2287, 8}, {2299, 52406}, {2322, 78}, {2326, 3710}, {2327, 318}, {2328, 312}, {2332, 3718}, {3022, 4601}, {3119, 4600}, {3239, 643}, {3701, 7054}, {3737, 6558}, {3900, 645}, {4012, 40403}, {4081, 4567}, {4105, 799}, {4130, 99}, {4163, 662}, {4397, 5546}, {4524, 4631}, {4560, 4578}, {5423, 81}, {14827, 40072}, {17926, 4571}, {21789, 646}, {23609, 28654}, {24010, 4620}, {30693, 58}, {36197, 6064}
X(56182) = barycentric quotient X(i)/X(j) for these (i, j): {8, 1446}, {9, 3668}, {21, 279}, {29, 1847}, {37, 6046}, {41, 1042}, {42, 7147}, {55, 1427}, {58, 738}, {72, 20618}, {81, 479}, {86, 23062}, {99, 36838}, {110, 4617}, {163, 6614}, {200, 226}, {210, 6354}, {212, 52373}, {213, 7143}, {219, 1439}, {220, 65}, {283, 7177}, {284, 269}, {333, 1088}, {341, 349}, {346, 1441}, {480, 37}, {607, 1426}, {643, 658}, {644, 4566}, {645, 4569}, {657, 4017}, {662, 4626}, {663, 7216}, {728, 10}, {762, 7314}, {799, 52937}, {1021, 3676}, {1043, 85}, {1098, 1434}, {1172, 1119}, {1253, 1400}, {1260, 1214}, {1265, 1231}, {1333, 7023}, {1334, 1254}, {1444, 30682}, {1792, 348}, {1802, 73}, {1812, 7056}, {2193, 7053}, {2194, 1407}, {2204, 1398}, {2206, 7366}, {2287, 7}, {2299, 1435}, {2303, 7197}, {2310, 53545}, {2318, 37755}, {2322, 273}, {2327, 77}, {2328, 57}, {2332, 34}, {3022, 3125}, {3059, 52023}, {3063, 7250}, {3119, 3120}, {3239, 4077}, {3692, 307}, {3694, 6356}, {3900, 7178}, {3939, 1020}, {3965, 41003}, {4012, 53510}, {4069, 4605}, {4073, 16888}, {4081, 16732}, {4082, 6358}, {4105, 661}, {4130, 523}, {4163, 1577}, {4183, 278}, {4515, 12}, {4578, 4552}, {4612, 4616}, {4620, 24011}, {4636, 4637}, {4936, 4848}, {5423, 321}, {5546, 934}, {6061, 81}, {6602, 42}, {7046, 40149}, {7054, 1014}, {7070, 36908}, {7071, 1880}, {7079, 225}, {7252, 43932}, {7253, 24002}, {7256, 4554}, {7257, 46406}, {7258, 4572}, {7259, 664}, {7367, 52384}, {7368, 227}, {8551, 52020}, {8641, 7180}, {14427, 30572}, {14827, 1402}, {14936, 53540}, {16713, 53242}, {16726, 41292}, {21789, 3669}, {23609, 593}, {24010, 21044}, {28070, 3914}, {30681, 20336}, {30693, 313}, {30706, 40961}, {35508, 4516}, {36197, 1365}, {36797, 13149}, {45791, 3925}, {46877, 3674}, {46889, 24471}, {52370, 1425}, {52378, 24013}, {52425, 1410}, {52614, 53551}, {53013, 13853}, {54416, 10376}
X(56182) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {200, 2328, 2287}, {1043, 1792, 21}

X(56183) = KP2(X(9)) OF X(21) AND X(100)

Barycentrics    a*(a-b)*(a-c)*(a-b-c)*(a^2+b^2-c^2)*(a^2-b^2+c^2) : :

X(56183) lies on these lines: {4, 528}, {19, 3174}, {20, 38687}, {25, 23858}, {28, 12437}, {33, 3158}, {34, 2136}, {55, 4081}, {100, 108}, {101, 40117}, {105, 34337}, {153, 10731}, {162, 4606}, {200, 40971}, {281, 1863}, {318, 3871}, {480, 55116}, {519, 37305}, {521, 651}, {522, 1633}, {646, 4571}, {648, 4238}, {664, 8269}, {692, 3900}, {728, 7156}, {1018, 1783}, {1119, 8730}, {1172, 4876}, {1260, 44695}, {1292, 26706}, {1295, 38554}, {1634, 7463}, {1753, 6765}, {1785, 48696}, {1826, 4097}, {1845, 5541}, {1861, 5853}, {1870, 3880}, {2356, 19589}, {2766, 9058}, {3189, 41227}, {3270, 52663}, {3813, 52252}, {4183, 36910}, {4200, 12632}, {4231, 36898}, {4249, 52604}, {4421, 37441}, {4551, 31511}, {4557, 6135}, {4578, 30730}, {4605, 8058}, {4953, 16686}, {5440, 15500}, {5687, 7952}, {6174, 23711}, {6198, 56176}, {6335, 15742}, {6606, 18026}, {7079, 47375}, {7412, 8715}, {10310, 18283}, {11248, 38870}, {12331, 21664}, {12536, 54343}, {13138, 36059}, {16578, 36122}, {17314, 38860}, {20344, 20621}, {24028, 36121}, {30236, 32704}, {32714, 35338}, {35994, 41803}

X(56183) = reflection of X(i) in X(j) for these {i,j}: {28071, 6600}
X(56183) = trilinear pole of line {33, 210}
X(56183) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 3676}, {7, 1459}, {34, 4131}, {48, 24002}, {56, 4025}, {57, 905}, {58, 17094}, {63, 3669}, {69, 43924}, {71, 17096}, {72, 7203}, {73, 7192}, {77, 513}, {78, 43932}, {81, 51664}, {85, 22383}, {109, 1565}, {184, 52621}, {222, 514}, {226, 7254}, {244, 6516}, {269, 521}, {273, 23224}, {278, 4091}, {279, 652}, {286, 51640}, {295, 43041}, {307, 3733}, {326, 43923}, {332, 7250}, {348, 649}, {522, 7053}, {525, 1412}, {552, 55230}, {603, 693}, {604, 15413}, {608, 30805}, {647, 1434}, {650, 7177}, {651, 3942}, {656, 1014}, {657, 30682}, {658, 7117}, {663, 7056}, {664, 3937}, {667, 7182}, {934, 7004}, {1019, 1214}, {1086, 1813}, {1088, 1946}, {1106, 35518}, {1111, 36059}, {1331, 1358}, {1332, 53538}, {1357, 4561}, {1364, 36118}, {1396, 24018}, {1398, 52616}, {1400, 15419}, {1407, 6332}, {1408, 14208}, {1409, 7199}, {1410, 18155}, {1414, 18210}, {1437, 4077}, {1439, 3737}, {1444, 4017}, {1461, 26932}, {1509, 55234}, {1790, 7178}, {1796, 30724}, {1797, 30725}, {1803, 21104}, {1804, 7649}, {1812, 7216}, {1814, 53544}, {1818, 43930}, {1847, 36054}, {2968, 6614}, {2969, 6517}, {3121, 55205}, {3261, 52411}, {3267, 16947}, {3270, 4626}, {3668, 23189}, {4064, 7341}, {4391, 7099}, {4394, 27832}, {4466, 4565}, {4558, 53545}, {4560, 52373}, {4572, 22096}, {4592, 53540}, {4617, 34591}, {4637, 53560}, {6545, 44717}, {6591, 7183}, {7125, 17924}, {7153, 25098}, {7180, 17206}, {7215, 36127}, {7233, 22384}, {7249, 22093}, {7335, 46107}, {7366, 15416}, {14837, 55117}, {17107, 24562}, {17197, 52610}, {17205, 23067}, {17219, 53321}, {17925, 40152}, {18815, 22379}, {23696, 34855}, {23727, 56005}, {23989, 32660}, {31637, 53539}, {36057, 43042}, {40443, 48151}, {43052, 55979}, {43925, 52565}, {52392, 53314}, {53532, 56049}
X(56183) = X(i)-vertex conjugate of X(j) for these {i, j}: {1461, 37141}
X(56183) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 4025}, {10, 17094}, {11, 1565}, {220, 24562}, {1249, 24002}, {2968, 17880}, {3161, 15413}, {3162, 3669}, {5139, 53540}, {5375, 348}, {5452, 905}, {5521, 1358}, {6552, 35518}, {6600, 521}, {6631, 7182}, {7952, 693}, {11517, 4131}, {13999, 4089}, {14714, 7004}, {15259, 43923}, {20620, 1111}, {20621, 43042}, {23050, 522}, {24771, 6332}, {34822, 23732}, {34961, 1444}, {35508, 26932}, {36103, 3676}, {38966, 11}, {38991, 3942}, {39025, 3937}, {39026, 77}, {39052, 1434}, {39053, 1088}, {40582, 15419}, {40586, 51664}, {40596, 1014}, {40599, 525}, {40608, 18210}, {53990, 40615}, {55064, 4466}, {55068, 17219}
X(56183) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1897, 1783}, {7012, 9}, {15742, 281}
X(56183) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {26706, 33650}
X(56183) = X(i)-cross conjugate of X(j) for these {i, j}: {3900, 7046}, {4130, 9}, {4557, 3939}, {18344, 33}
X(56183) = intersection, other than A, B, C, of circumconics {{A, B, C, X(9), X(651)}}, {{A, B, C, X(21), X(14074)}}, {{A, B, C, X(55), X(692)}}, {{A, B, C, X(100), X(677)}}, {{A, B, C, X(108), X(8750)}}, {{A, B, C, X(281), X(6335)}}, {{A, B, C, X(521), X(4130)}}, {{A, B, C, X(522), X(47695)}}, {{A, B, C, X(528), X(15733)}}, {{A, B, C, X(644), X(646)}}, {{A, B, C, X(653), X(1783)}}, {{A, B, C, X(943), X(44059)}}, {{A, B, C, X(1292), X(40576)}}, {{A, B, C, X(2310), X(46041)}}, {{A, B, C, X(2321), X(4605)}}, {{A, B, C, X(2328), X(43347)}}, {{A, B, C, X(2804), X(3900)}}, {{A, B, C, X(3699), X(14594)}}, {{A, B, C, X(4183), X(4242)}}, {{A, B, C, X(4238), X(28044)}}, {{A, B, C, X(4557), X(4571)}}, {{A, B, C, X(4569), X(6601)}}, {{A, B, C, X(6065), X(46649)}}, {{A, B, C, X(6558), X(36147)}}, {{A, B, C, X(7046), X(53151)}}, {{A, B, C, X(7070), X(31511)}}, {{A, B, C, X(8693), X(33635)}}, {{A, B, C, X(42069), X(44426)}}
X(56183) = barycentric product X(i)*X(j) for these (i, j): {4, 644}, {19, 3699}, {25, 646}, {27, 4069}, {28, 30730}, {34, 6558}, {55, 6335}, {100, 281}, {101, 318}, {107, 3694}, {108, 346}, {109, 7101}, {112, 3701}, {158, 4587}, {162, 2321}, {190, 33}, {200, 653}, {210, 648}, {225, 7259}, {270, 4103}, {278, 4578}, {312, 8750}, {393, 4571}, {607, 668}, {651, 7046}, {664, 7079}, {692, 7017}, {1016, 18344}, {1018, 29}, {1110, 46110}, {1172, 3952}, {1252, 44426}, {1253, 46404}, {1260, 54240}, {1261, 17906}, {1332, 1857}, {1334, 811}, {1783, 8}, {1802, 52938}, {1824, 645}, {1826, 643}, {1880, 7256}, {1896, 4574}, {1897, 9}, {1978, 2212}, {2201, 36801}, {2204, 27808}, {2299, 4033}, {2318, 823}, {2322, 4551}, {2333, 7257}, {3064, 765}, {3239, 7012}, {3700, 5379}, {3900, 46102}, {3939, 92}, {3949, 52921}, {4076, 6591}, {4163, 7128}, {4183, 4552}, {4397, 7115}, {4554, 7071}, {4600, 55206}, {4606, 461}, {4612, 7140}, {13138, 55116}, {13149, 480}, {15742, 650}, {17924, 6065}, {18026, 220}, {24019, 3710}, {28044, 32041}, {30713, 32676}, {30731, 36125}, {31615, 42069}, {31623, 4557}, {32674, 341}, {32714, 5423}, {34080, 44721}, {36099, 3974}, {36118, 728}, {36127, 3692}, {36147, 46878}, {36797, 37}, {36802, 5089}, {36804, 52427}, {36910, 4242}, {38462, 5548}, {40117, 7080}, {40521, 46103}, {40971, 44327}, {41013, 5546}, {41320, 51566}, {42384, 7083}, {46108, 52927}, {52370, 6528}, {52607, 56182}, {52663, 53151}, {52914, 594}, {53008, 662}, {55231, 7064}, {55233, 872}
X(56183) = barycentric quotient X(i)/X(j) for these (i, j): {4, 24002}, {8, 15413}, {9, 4025}, {19, 3676}, {21, 15419}, {25, 3669}, {28, 17096}, {29, 7199}, {33, 514}, {37, 17094}, {41, 1459}, {42, 51664}, {55, 905}, {78, 30805}, {92, 52621}, {100, 348}, {101, 77}, {108, 279}, {109, 7177}, {112, 1014}, {162, 1434}, {190, 7182}, {200, 6332}, {210, 525}, {212, 4091}, {219, 4131}, {220, 521}, {281, 693}, {318, 3261}, {346, 35518}, {461, 4801}, {607, 513}, {608, 43932}, {643, 17206}, {644, 69}, {646, 305}, {650, 1565}, {651, 7056}, {653, 1088}, {657, 7004}, {663, 3942}, {692, 222}, {862, 7212}, {872, 55234}, {906, 1804}, {934, 30682}, {1018, 307}, {1021, 17219}, {1110, 1813}, {1172, 7192}, {1252, 6516}, {1253, 652}, {1293, 27832}, {1331, 7183}, {1332, 7055}, {1334, 656}, {1415, 7053}, {1474, 7203}, {1783, 7}, {1824, 7178}, {1826, 4077}, {1827, 21104}, {1857, 17924}, {1897, 85}, {1973, 43924}, {2175, 22383}, {2194, 7254}, {2200, 51640}, {2201, 43041}, {2204, 3733}, {2207, 43923}, {2212, 649}, {2299, 1019}, {2318, 24018}, {2321, 14208}, {2322, 18155}, {2332, 3737}, {2333, 4017}, {2355, 30724}, {2356, 53544}, {2489, 53540}, {3063, 3937}, {3064, 1111}, {3239, 17880}, {3692, 52616}, {3694, 3265}, {3699, 304}, {3701, 3267}, {3709, 18210}, {3711, 49280}, {3900, 26932}, {3939, 63}, {3952, 1231}, {4041, 4466}, {4069, 306}, {4105, 34591}, {4130, 2968}, {4183, 4560}, {4242, 17078}, {4336, 23727}, {4433, 24459}, {4515, 52355}, {4524, 53560}, {4557, 1214}, {4559, 1439}, {4571, 3926}, {4574, 52385}, {4578, 345}, {4587, 326}, {4600, 55205}, {5089, 43042}, {5338, 30723}, {5379, 4573}, {5423, 15416}, {5546, 1444}, {6059, 6591}, {6065, 1332}, {6066, 906}, {6335, 6063}, {6558, 3718}, {6591, 1358}, {6600, 24562}, {7012, 658}, {7017, 40495}, {7046, 4391}, {7064, 55232}, {7071, 650}, {7079, 522}, {7101, 35519}, {7115, 934}, {7128, 4626}, {7156, 21172}, {7259, 332}, {7719, 31605}, {8611, 17216}, {8641, 7117}, {8750, 57}, {8751, 43930}, {11107, 16755}, {13138, 34400}, {14006, 16737}, {14776, 34051}, {14827, 1946}, {15742, 4554}, {16283, 22091}, {18344, 1086}, {20310, 23732}, {21859, 6356}, {23990, 36059}, {28044, 4762}, {30730, 20336}, {31623, 52619}, {32652, 55117}, {32656, 7125}, {32674, 269}, {32676, 1412}, {32713, 1396}, {32714, 479}, {32739, 603}, {36054, 7215}, {36118, 23062}, {36127, 1847}, {36797, 274}, {40116, 43736}, {40117, 1440}, {40521, 26942}, {40965, 21107}, {40971, 14837}, {40976, 48131}, {40982, 48334}, {40987, 48398}, {41320, 23800}, {41339, 39470}, {42069, 40166}, {44100, 4790}, {44426, 23989}, {46102, 4569}, {46878, 4509}, {52370, 520}, {52425, 23224}, {52426, 22379}, {52427, 3960}, {52914, 1509}, {52927, 1814}, {53008, 1577}, {54416, 51644}, {55116, 17896}, {55206, 3120}, {55232, 1367}, {56182, 15411}
X(56183) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 1897, 108}

X(56184) = KP2(X(10)) OF X(2) AND X(12)

Barycentrics    (a^3+b^3-2*a^2*c+c^3-a*c*(3*b+2*c))*(a^3-2*a^2*b+b^3+c^3-a*b*(2*b+3*c)) : :

X(56184) lies on these lines: {192, 15474}, {274, 27272}, {277, 3210}, {278, 41839}, {330, 17776}, {344, 39694}, {1929, 29653}, {3995, 21907}, {19822, 39736}, {28606, 39724}, {29641, 39954}, {29642, 52654}, {32849, 39747}, {33157, 39722}, {33168, 39706}, {37759, 37887}

X(56184) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(42), X(27272)}}, {{A, B, C, X(192), X(17776)}}, {{A, B, C, X(226), X(1016)}}, {{A, B, C, X(335), X(40435)}}, {{A, B, C, X(344), X(3210)}}, {{A, B, C, X(345), X(41839)}}, {{A, B, C, X(2985), X(17758)}}, {{A, B, C, X(3995), X(32849)}}, {{A, B, C, X(4393), X(29642)}}, {{A, B, C, X(5382), X(33116)}}, {{A, B, C, X(6542), X(29653)}}, {{A, B, C, X(6625), X(40394)}}, {{A, B, C, X(6630), X(30690)}}, {{A, B, C, X(17280), X(28606)}}, {{A, B, C, X(17302), X(33157)}}, {{A, B, C, X(17316), X(29641)}}, {{A, B, C, X(19822), X(27268)}}, {{A, B, C, X(25453), X(29570)}}, {{A, B, C, X(29569), X(29673)}}, {{A, B, C, X(29586), X(29654)}}, {{A, B, C, X(31035), X(33168)}}, {{A, B, C, X(36954), X(55090)}}

X(56185) = KP2(X(10)) OF X(2) AND X(43)

Barycentrics    (b+c)*(-(b^2*c^2)+a^3*(b+c)+a^2*(b^2-b*c+c^2)) : :

X(56185) lies on these lines: {2, 37}, {6, 17148}, {9, 31036}, {42, 25295}, {43, 22024}, {72, 20036}, {190, 27644}, {194, 213}, {239, 21061}, {310, 1221}, {313, 26772}, {330, 37677}, {335, 20028}, {518, 20040}, {714, 872}, {726, 1193}, {730, 23659}, {740, 4642}, {894, 54308}, {978, 3159}, {1258, 33296}, {1269, 26976}, {1400, 4552}, {2092, 3963}, {2205, 7766}, {2229, 6378}, {2269, 40886}, {2998, 17486}, {3187, 54373}, {3294, 16827}, {3662, 22008}, {3728, 4651}, {3764, 21278}, {3831, 28522}, {3875, 21371}, {3879, 31061}, {3896, 22294}, {3922, 49462}, {3948, 21796}, {3952, 21080}, {3971, 28248}, {4033, 21858}, {4442, 21927}, {4670, 16710}, {10455, 16826}, {13731, 51046}, {14923, 49470}, {16584, 22218}, {17033, 17489}, {17038, 26037}, {17053, 27166}, {17157, 17165}, {17178, 37596}, {17262, 27623}, {18044, 27095}, {20245, 49518}, {20352, 24478}, {21330, 29824}, {21935, 27713}, {22003, 27678}, {22028, 53675}, {24067, 27646}, {25059, 30710}, {25124, 29822}, {25250, 41240}, {25268, 56079}, {25271, 47894}, {25302, 34063}, {26756, 52043}, {29010, 51558}, {32925, 53676}, {34020, 34086}, {40504, 41683}, {45222, 46720}

X(56185) = reflection of X(i) in X(j) for these {i,j}: {4043, 37}
X(56185) = anticomplement of X(20891)
X(56185) = X(i)-Dao conjugate of X(j) for these {i, j}: {6378, 42027}, {20891, 20891}, {21025, 3840}
X(56185) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1258, 2}, {32011, 10}, {33296, 42}
X(56185) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {1221, 21275}, {1258, 6327}, {40409, 17138}, {40418, 315}
X(56185) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(34020)}}, {{A, B, C, X(75), X(34063)}}, {{A, B, C, X(312), X(27809)}}, {{A, B, C, X(350), X(20028)}}, {{A, B, C, X(536), X(40504)}}, {{A, B, C, X(1278), X(4674)}}, {{A, B, C, X(1400), X(1575)}}, {{A, B, C, X(3263), X(25302)}}, {{A, B, C, X(18137), X(41683)}}, {{A, B, C, X(20891), X(42027)}}, {{A, B, C, X(45988), X(46838)}}
X(56185) = barycentric product X(i)*X(j) for these (i, j): {10, 34063}, {13576, 25302}, {25305, 38955}, {34020, 37}, {34086, 42}
X(56185) = barycentric quotient X(i)/X(j) for these (i, j): {25300, 17217}, {25302, 30941}, {25305, 17139}, {34020, 274}, {34063, 86}, {34086, 310}
X(56185) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {37, 192, 3995}, {37, 536, 4043}, {42, 42027, 25295}, {192, 3210, 1278}, {3210, 4850, 17495}, {3995, 17495, 31025}, {17790, 24530, 27102}

X(56186) = KP2(X(10)) OF X(2) AND X(75)

Barycentrics    b*(a^2+b^2)*c*(b+c)*(a^2+c^2) : :

X(56186) lies on these lines: {1, 18050}, {8, 18088}, {10, 16889}, {37, 308}, {72, 42299}, {75, 16549}, {76, 17489}, {83, 213}, {100, 39427}, {242, 4222}, {257, 668}, {274, 292}, {335, 18167}, {514, 1909}, {689, 2375}, {718, 40936}, {740, 872}, {762, 56122}, {1215, 23629}, {1237, 16600}, {1500, 3948}, {2295, 21412}, {3294, 39044}, {3405, 21061}, {3770, 40085}, {4075, 56131}, {6358, 16609}, {6378, 52538}, {14839, 18101}, {18003, 18010}, {18083, 22010}, {18104, 31330}, {21814, 31622}, {27005, 27070}, {27040, 27808}, {28594, 35544}, {28615, 32018}, {29418, 29534}, {30710, 52376}

X(56186) = isotomic conjugate of X(16696)
X(56186) = trilinear pole of line {4010, 4036}
X(56186) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 17187}, {27, 20775}, {28, 4020}, {31, 16696}, {32, 16887}, {38, 1333}, {39, 58}, {81, 1964}, {86, 3051}, {110, 21123}, {141, 2206}, {163, 2530}, {184, 17171}, {274, 1923}, {284, 1401}, {310, 41331}, {560, 16703}, {593, 21035}, {649, 1634}, {662, 50521}, {688, 4610}, {757, 21814}, {849, 3954}, {1014, 40972}, {1408, 33299}, {1412, 3688}, {1437, 17442}, {1459, 35325}, {1474, 3917}, {1509, 41267}, {1576, 16892}, {1790, 1843}, {1914, 46159}, {1919, 4576}, {1980, 55239}, {2084, 52935}, {3005, 4556}, {3285, 46150}, {3703, 16947}, {3733, 46148}, {6629, 41272}, {7113, 46160}, {7252, 46153}, {7303, 21752}, {9247, 16747}, {9494, 52612}, {17206, 27369}, {17209, 51869}, {21108, 32661}
X(56186) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 16696}, {9, 17187}, {10, 39}, {37, 38}, {115, 2530}, {244, 21123}, {1084, 50521}, {4075, 3954}, {4858, 16892}, {5375, 1634}, {6374, 16703}, {6376, 16887}, {9296, 4576}, {36901, 48084}, {36906, 46159}, {37891, 18182}, {40586, 1964}, {40590, 1401}, {40591, 4020}, {40599, 3688}, {40600, 3051}, {40603, 141}, {40607, 21814}, {41884, 81}, {51574, 3917}, {55065, 8061}
X(56186) = X(i)-Ceva conjugate of X(j) for these {i, j}: {3112, 18082}
X(56186) = X(i)-cross conjugate of X(j) for these {i, j}: {37, 18098}, {4705, 668}, {21021, 10}, {21901, 1018}, {27067, 83}
X(56186) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(27809)}}, {{A, B, C, X(2), X(3293)}}, {{A, B, C, X(10), X(239)}}, {{A, B, C, X(37), X(213)}}, {{A, B, C, X(42), X(27020)}}, {{A, B, C, X(65), X(3227)}}, {{A, B, C, X(75), X(4043)}}, {{A, B, C, X(81), X(27041)}}, {{A, B, C, X(83), X(308)}}, {{A, B, C, X(226), X(27064)}}, {{A, B, C, X(313), X(33941)}}, {{A, B, C, X(321), X(1089)}}, {{A, B, C, X(330), X(4674)}}, {{A, B, C, X(335), X(40515)}}, {{A, B, C, X(668), X(1909)}}, {{A, B, C, X(671), X(40827)}}, {{A, B, C, X(762), X(4037)}}, {{A, B, C, X(1215), X(39929)}}, {{A, B, C, X(1222), X(53194)}}, {{A, B, C, X(3112), X(18833)}}, {{A, B, C, X(3175), X(31993)}}, {{A, B, C, X(3228), X(40408)}}, {{A, B, C, X(3701), X(36796)}}, {{A, B, C, X(3954), X(4705)}}, {{A, B, C, X(3963), X(17741)}}, {{A, B, C, X(4080), X(41242)}}, {{A, B, C, X(4103), X(22011)}}, {{A, B, C, X(4183), X(27053)}}, {{A, B, C, X(4651), X(29433)}}, {{A, B, C, X(6539), X(39708)}}, {{A, B, C, X(6543), X(40085)}}, {{A, B, C, X(11611), X(51870)}}, {{A, B, C, X(14624), X(27810)}}, {{A, B, C, X(16748), X(17163)}}, {{A, B, C, X(17277), X(41681)}}, {{A, B, C, X(20691), X(40844)}}, {{A, B, C, X(27067), X(52376)}}, {{A, B, C, X(29418), X(52358)}}, {{A, B, C, X(30588), X(36805)}}, {{A, B, C, X(30713), X(31623)}}, {{A, B, C, X(31008), X(52538)}}, {{A, B, C, X(32020), X(40718)}}, {{A, B, C, X(40504), X(42328)}}
X(56186) = barycentric product X(i)*X(j) for these (i, j): {10, 3112}, {100, 52618}, {213, 40016}, {251, 27801}, {308, 37}, {313, 82}, {321, 83}, {1089, 52394}, {1799, 41013}, {1978, 55240}, {4024, 4593}, {4036, 4577}, {4580, 6335}, {4599, 52623}, {4705, 689}, {10566, 4033}, {16889, 7033}, {18070, 190}, {18082, 75}, {18087, 56127}, {18097, 312}, {18098, 76}, {18099, 7018}, {18105, 6386}, {18108, 27808}, {18833, 42}, {20336, 32085}, {20948, 4628}, {21094, 37221}, {21807, 41488}, {27067, 30710}, {28654, 52376}, {34294, 4601}, {37204, 4079}, {42299, 42711}, {42371, 50487}, {46104, 72}
X(56186) = barycentric quotient X(i)/X(j) for these (i, j): {1, 17187}, {2, 16696}, {10, 38}, {37, 39}, {42, 1964}, {65, 1401}, {71, 4020}, {72, 3917}, {75, 16887}, {76, 16703}, {80, 46160}, {82, 58}, {83, 81}, {92, 17171}, {100, 1634}, {210, 3688}, {213, 3051}, {228, 20775}, {251, 1333}, {264, 16747}, {291, 46159}, {308, 274}, {313, 1930}, {321, 141}, {512, 50521}, {523, 2530}, {594, 3954}, {661, 21123}, {668, 4576}, {689, 4623}, {756, 21035}, {850, 48084}, {872, 41267}, {1018, 46148}, {1089, 15523}, {1176, 1437}, {1334, 40972}, {1441, 3665}, {1500, 21814}, {1577, 16892}, {1783, 35325}, {1799, 1444}, {1824, 1843}, {1826, 17442}, {1918, 1923}, {1978, 55239}, {2205, 41331}, {2321, 33299}, {3112, 86}, {3405, 17209}, {3434, 41582}, {3701, 3703}, {3952, 4553}, {3954, 8041}, {3963, 16720}, {4024, 8061}, {4033, 4568}, {4036, 826}, {4039, 2236}, {4079, 2084}, {4086, 48278}, {4103, 35309}, {4463, 3313}, {4551, 46153}, {4577, 52935}, {4580, 905}, {4593, 4610}, {4599, 4556}, {4628, 163}, {4674, 46150}, {4705, 3005}, {4972, 18183}, {5380, 36827}, {6335, 41676}, {6656, 18182}, {10566, 1019}, {13576, 46149}, {16889, 982}, {16890, 18167}, {17500, 18180}, {17907, 16715}, {18070, 514}, {18082, 1}, {18083, 18161}, {18084, 7289}, {18085, 18162}, {18086, 18163}, {18087, 18164}, {18088, 18165}, {18089, 18166}, {18090, 18168}, {18091, 18169}, {18093, 18170}, {18094, 18171}, {18095, 18176}, {18096, 18179}, {18097, 57}, {18098, 6}, {18099, 171}, {18100, 18189}, {18101, 18191}, {18102, 18192}, {18103, 18205}, {18104, 18195}, {18105, 667}, {18106, 18196}, {18107, 18197}, {18108, 3733}, {18109, 18198}, {18110, 18199}, {18111, 18200}, {18112, 18201}, {18113, 18211}, {18700, 18723}, {18701, 18724}, {18702, 18725}, {18703, 18726}, {18704, 18727}, {18705, 18728}, {18706, 18729}, {18707, 18730}, {18708, 18731}, {18709, 18732}, {18710, 18733}, {18711, 18734}, {18712, 18735}, {18833, 310}, {20022, 51369}, {20336, 3933}, {21021, 16587}, {21067, 40585}, {21094, 18715}, {21802, 11205}, {21803, 40936}, {21832, 46387}, {21874, 3787}, {22105, 14419}, {22322, 8711}, {24006, 21108}, {27067, 3666}, {27801, 8024}, {28724, 18604}, {32085, 28}, {34055, 1790}, {34294, 3125}, {37204, 52612}, {40016, 6385}, {41013, 427}, {42703, 51371}, {42711, 14994}, {42713, 7813}, {46104, 286}, {46289, 2206}, {50487, 688}, {51906, 3121}, {52353, 4884}, {52376, 593}, {52394, 757}, {52395, 52376}, {52570, 16707}, {52618, 693}, {52893, 52961}, {52898, 16702}, {55240, 649}

X(56187) = KP2(X(10)) OF X(2) AND X(78)

Barycentrics    (b+c)*(a^5+a^2*b*c*(b+c)-b*(b-c)^2*c*(b+c)-a^3*(2*b^2+b*c+2*c^2)+a*(b^4+b^3*c+b*c^3+c^4)) : :

X(56187) lies on these lines: {2, 37}, {33, 32929}, {72, 944}, {190, 1812}, {200, 22027}, {201, 17751}, {306, 4552}, {329, 21078}, {860, 3695}, {997, 3159}, {1824, 17784}, {1897, 56182}, {2318, 3952}, {2324, 28950}, {2406, 7364}, {2901, 18391}, {3187, 8557}, {3191, 4511}, {3553, 26223}, {3687, 18662}, {3694, 40149}, {3936, 6354}, {3969, 51367}, {4651, 40967}, {7080, 41013}, {17479, 33077}, {17742, 36023}, {21061, 22002}, {21933, 25003}, {22003, 22022}, {25241, 27184}, {25254, 26580}, {28654, 52386}, {30713, 52609}

X(56187) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1474, 43724}
X(56187) = X(i)-Dao conjugate of X(j) for these {i, j}: {21933, 1210}, {51574, 43724}
X(56187) = X(i)-Ceva conjugate of X(j) for these {i, j}: {40424, 10}
X(56187) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(7412)}}, {{A, B, C, X(350), X(46400)}}, {{A, B, C, X(4552), X(42718)}}, {{A, B, C, X(17862), X(40149)}}, {{A, B, C, X(20171), X(27809)}}, {{A, B, C, X(28654), X(42698)}}
X(56187) = barycentric product X(i)*X(j) for these (i, j): {3952, 46400}, {20336, 7412}, {27808, 39199}
X(56187) = barycentric quotient X(i)/X(j) for these (i, j): {72, 43724}, {7412, 28}, {39199, 3733}, {46400, 7192}
X(56187) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {321, 42700, 2}, {321, 42710, 42698}, {3995, 45744, 321}, {21078, 22001, 329}

X(56188) = TRILINEAR POLE OF LINE {5, 10}

Barycentrics    (a-b)*(a-c)*(-b^3+b*c^2+a*c*(-b+c)+a^2*(b+c))*(a*b*(b-c)+a^2*(b+c)+c*(b^2-c^2)) : :
X(56188) = -3*X[2]+2*X[40624]

X(56188) lies on these lines: {2, 40624}, {101, 44765}, {145, 25048}, {190, 14570}, {192, 54121}, {335, 20028}, {345, 34267}, {651, 17496}, {835, 1331}, {1897, 4246}, {1978, 55258}, {1999, 39698}, {2051, 4080}, {2397, 4033}, {2398, 4613}, {3661, 25243}, {3882, 4552}, {3952, 25268}, {3995, 18359}, {9058, 53702}, {22003, 54118}, {23978, 23980}, {25245, 53245}

X(56188) = isotomic conjugate of X(17496)
X(56188) = anticomplement of X(40624)
X(56188) = KP2(X(10)) of X(2) and X(100)
X(56188) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 21173}, {19, 23187}, {31, 17496}, {108, 38344}, {109, 11998}, {163, 53566}, {284, 51662}, {513, 572}, {514, 20986}, {649, 2975}, {663, 17074}, {667, 14829}, {692, 24237}, {1019, 52139}, {1415, 34589}, {3733, 21061}, {7121, 27346}, {7252, 37558}, {7649, 22118}, {11109, 22383}
X(56188) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 17496}, {6, 23187}, {9, 21173}, {11, 11998}, {115, 53566}, {1086, 24237}, {1146, 34589}, {5375, 2975}, {6631, 14829}, {38983, 38344}, {39026, 572}, {40590, 51662}, {40598, 27346}, {40624, 40624}
X(56188) = X(i)-cross conjugate of X(j) for these {i, j}: {4391, 2}, {12607, 4998}, {21859, 100}, {41883, 46102}, {55182, 34527}
X(56188) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(651)}}, {{A, B, C, X(94), X(648)}}, {{A, B, C, X(100), X(646)}}, {{A, B, C, X(110), X(43069)}}, {{A, B, C, X(145), X(23891)}}, {{A, B, C, X(190), X(335)}}, {{A, B, C, X(192), X(42720)}}, {{A, B, C, X(321), X(4605)}}, {{A, B, C, X(330), X(42408)}}, {{A, B, C, X(645), X(51562)}}, {{A, B, C, X(653), X(43190)}}, {{A, B, C, X(662), X(36804)}}, {{A, B, C, X(664), X(21272)}}, {{A, B, C, X(692), X(941)}}, {{A, B, C, X(1331), X(52609)}}, {{A, B, C, X(2398), X(3661)}}, {{A, B, C, X(2804), X(23978)}}, {{A, B, C, X(3257), X(15455)}}, {{A, B, C, X(4373), X(4569)}}, {{A, B, C, X(4391), X(17496)}}, {{A, B, C, X(4554), X(27834)}}, {{A, B, C, X(4582), X(6648)}}, {{A, B, C, X(4606), X(13138)}}, {{A, B, C, X(4625), X(53208)}}, {{A, B, C, X(6606), X(51568)}}, {{A, B, C, X(9295), X(53213)}}, {{A, B, C, X(17147), X(24004)}}, {{A, B, C, X(17906), X(38828)}}, {{A, B, C, X(21907), X(46119)}}, {{A, B, C, X(25243), X(42719)}}, {{A, B, C, X(25245), X(42717)}}, {{A, B, C, X(26856), X(46041)}}, {{A, B, C, X(32040), X(42357)}}, {{A, B, C, X(35058), X(42362)}}, {{A, B, C, X(35147), X(54458)}}, {{A, B, C, X(36037), X(37212)}}
X(56188) = barycentric product X(i)*X(j) for these (i, j): {100, 54121}, {190, 2051}, {3262, 53702}, {4033, 53083}, {4552, 46880}, {20028, 3952}, {27808, 52150}, {34434, 668}, {51870, 99}
X(56188) = barycentric quotient X(i)/X(j) for these (i, j): {1, 21173}, {2, 17496}, {3, 23187}, {65, 51662}, {100, 2975}, {101, 572}, {190, 14829}, {192, 27346}, {514, 24237}, {522, 34589}, {523, 53566}, {650, 11998}, {651, 17074}, {652, 38344}, {692, 20986}, {906, 22118}, {1018, 21061}, {1897, 11109}, {2051, 514}, {3952, 17751}, {4391, 40624}, {4551, 37558}, {4552, 52358}, {4557, 52139}, {17494, 26847}, {20028, 7192}, {21011, 52322}, {34434, 513}, {40521, 14973}, {46880, 4560}, {51870, 523}, {52150, 3733}, {53083, 1019}, {53702, 104}, {54121, 693}

X(56189) = KP2(X(10)) OF X(75) AND X(8)

Barycentrics    b*c*(b+c)*(a^4+b^4-b^2*c^2-a^2*(2*b^2+c^2))*(a^4-b^2*c^2+c^4-a^2*(b^2+2*c^2)) : :

X(56189) lies on these lines: {37, 42300}, {72, 8795}, {95, 7523}, {275, 321}, {314, 39277}, {319, 35519}, {668, 46138}, {3998, 37872}, {7066, 34388}, {27801, 34385}, {34384, 42711}, {39287, 42703}

X(56189) = isotomic conjugate of X(18180)
X(56189) = trilinear pole of line {15412, 42701}
X(56189) = X(i)-isoconjugate-of-X(j) for these {i, j}: {5, 2206}, {25, 44709}, {27, 217}, {31, 18180}, {32, 17167}, {51, 58}, {81, 2179}, {86, 40981}, {216, 1474}, {418, 8747}, {649, 1625}, {667, 2617}, {849, 21807}, {1333, 1953}, {1393, 2194}, {1408, 7069}, {1437, 2181}, {1459, 52604}, {1576, 21102}, {1790, 3199}, {1919, 14570}, {1973, 16697}, {2203, 44706}, {2204, 44708}, {2299, 30493}, {4556, 55219}, {27374, 52394}, {42293, 52919}
X(56189) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 18180}, {10, 51}, {37, 1953}, {226, 30493}, {1214, 1393}, {4075, 21807}, {4858, 21102}, {5375, 1625}, {6337, 16697}, {6376, 17167}, {6505, 44709}, {6631, 2617}, {9296, 14570}, {40586, 2179}, {40600, 40981}, {40603, 5}, {51574, 216}
X(56189) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(7523)}}, {{A, B, C, X(37), X(42711)}}, {{A, B, C, X(72), X(3990)}}, {{A, B, C, X(95), X(275)}}, {{A, B, C, X(226), X(286)}}, {{A, B, C, X(290), X(40412)}}, {{A, B, C, X(313), X(314)}}, {{A, B, C, X(319), X(668)}}, {{A, B, C, X(321), X(20336)}}, {{A, B, C, X(1441), X(18816)}}, {{A, B, C, X(2997), X(4080)}}
X(56189) = barycentric product X(i)*X(j) for these (i, j): {276, 72}, {306, 40440}, {321, 95}, {349, 44687}, {1978, 2616}, {2167, 313}, {2190, 40071}, {2623, 6386}, {3954, 41488}, {3998, 8795}, {4601, 8901}, {4705, 55218}, {15412, 668}, {20336, 275}, {27801, 54}, {34384, 37}, {34385, 42700}, {34386, 41013}, {42300, 42711}, {42701, 46138}
X(56189) = barycentric quotient X(i)/X(j) for these (i, j): {2, 18180}, {10, 1953}, {37, 51}, {42, 2179}, {54, 1333}, {63, 44709}, {69, 16697}, {72, 216}, {75, 17167}, {95, 81}, {97, 1437}, {100, 1625}, {190, 2617}, {213, 40981}, {226, 1393}, {228, 217}, {275, 28}, {276, 286}, {306, 44706}, {307, 44708}, {313, 14213}, {321, 5}, {594, 21807}, {668, 14570}, {1089, 21011}, {1214, 30493}, {1332, 23181}, {1577, 21102}, {1783, 52604}, {1824, 3199}, {1826, 2181}, {2148, 2206}, {2167, 58}, {2190, 1474}, {2321, 7069}, {2616, 649}, {2623, 667}, {3694, 44707}, {3969, 35194}, {3990, 418}, {3998, 5562}, {4036, 12077}, {4553, 35319}, {4705, 55219}, {5360, 52967}, {6335, 35360}, {8882, 2203}, {8884, 5317}, {8901, 3125}, {15412, 513}, {15414, 4131}, {16813, 52920}, {19166, 18603}, {20336, 343}, {21814, 27374}, {23286, 22383}, {27801, 311}, {34384, 274}, {34386, 1444}, {35196, 2150}, {39182, 18108}, {39287, 52376}, {40071, 18695}, {40440, 27}, {41013, 53}, {42700, 52}, {42701, 1154}, {42704, 5891}, {42713, 41586}, {43768, 51420}, {44687, 284}, {52345, 42459}, {52623, 2618}, {53576, 18210}, {55218, 4623}, {55232, 15451}, {56186, 17500}

X(56190) = KP2(X(37)) OF X(1) AND X(10)

Barycentrics    a*(b+c)*(a^2+a*(-2*b+c)+b*(b+c))*(a^2+a*(b-2*c)+c*(b+c)) : :

X(56190) lies on these lines: {1, 341}, {2, 40451}, {9, 15621}, {10, 1042}, {31, 200}, {42, 3950}, {55, 40528}, {210, 1402}, {213, 4515}, {612, 40148}, {741, 8706}, {936, 1476}, {1245, 3293}, {1376, 53389}, {1973, 5574}, {2258, 52549}, {4418, 50346}, {5268, 30801}, {5400, 29673}, {6555, 41276}, {8580, 40420}, {53008, 53663}

X(56190) = trilinear pole of line {798, 4171}
X(56190) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 18600}, {21, 1122}, {56, 17183}, {57, 18163}, {58, 3663}, {81, 3752}, {86, 1201}, {99, 6363}, {274, 20228}, {284, 52563}, {286, 22344}, {593, 4415}, {662, 48334}, {757, 4642}, {1014, 3057}, {1019, 21362}, {1333, 26563}, {1408, 20895}, {1412, 3452}, {1414, 6615}, {1434, 2347}, {1444, 1828}, {1509, 21796}, {1817, 42549}, {3733, 21272}, {4565, 21120}, {7192, 23845}, {7254, 17906}, {7257, 42336}, {7341, 21031}, {17925, 23113}, {27499, 27644}, {46367, 52352}
X(56190) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 17183}, {9, 18600}, {10, 3663}, {37, 26563}, {1084, 48334}, {5452, 18163}, {38986, 6363}, {40586, 3752}, {40590, 52563}, {40599, 3452}, {40600, 1201}, {40607, 4642}, {40608, 6615}, {40611, 1122}, {55064, 21120}
X(56190) = X(i)-cross conjugate of X(j) for these {i, j}: {3709, 1018}, {44729, 4069}
X(56190) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(31)}}, {{A, B, C, X(9), X(14624)}}, {{A, B, C, X(10), X(200)}}, {{A, B, C, X(25), X(13741)}}, {{A, B, C, X(37), X(1743)}}, {{A, B, C, X(55), X(996)}}, {{A, B, C, X(57), X(18098)}}, {{A, B, C, X(282), X(2321)}}, {{A, B, C, X(321), X(34525)}}, {{A, B, C, X(612), X(3293)}}, {{A, B, C, X(756), X(3992)}}, {{A, B, C, X(936), X(4061)}}, {{A, B, C, X(1050), X(52521)}}, {{A, B, C, X(1215), X(20683)}}, {{A, B, C, X(1222), X(51476)}}, {{A, B, C, X(1824), X(4674)}}, {{A, B, C, X(3062), X(42027)}}, {{A, B, C, X(3294), X(21384)}}, {{A, B, C, X(3747), X(18192)}}, {{A, B, C, X(3991), X(32560)}}, {{A, B, C, X(4512), X(8666)}}, {{A, B, C, X(7050), X(56145)}}, {{A, B, C, X(8056), X(16606)}}, {{A, B, C, X(8605), X(39697)}}, {{A, B, C, X(13462), X(21870)}}, {{A, B, C, X(13576), X(39959)}}, {{A, B, C, X(15621), X(52139)}}, {{A, B, C, X(18082), X(56179)}}, {{A, B, C, X(18698), X(21039)}}, {{A, B, C, X(23617), X(32017)}}, {{A, B, C, X(39980), X(40747)}}
X(56190) = barycentric product X(i)*X(j) for these (i, j): {10, 23617}, {210, 40420}, {321, 51476}, {661, 8706}, {1222, 37}, {1261, 226}, {1476, 2321}, {3451, 3701}, {3694, 40446}, {4171, 6613}, {32017, 42}, {52549, 65}, {56173, 9}
X(56190) = barycentric quotient X(i)/X(j) for these (i, j): {1, 18600}, {9, 17183}, {10, 26563}, {37, 3663}, {42, 3752}, {55, 18163}, {65, 52563}, {210, 3452}, {213, 1201}, {512, 48334}, {756, 4415}, {798, 6363}, {872, 21796}, {1018, 21272}, {1222, 274}, {1261, 333}, {1334, 3057}, {1400, 1122}, {1476, 1434}, {1500, 4642}, {1918, 20228}, {2200, 22344}, {2321, 20895}, {2333, 1828}, {2357, 42549}, {3451, 1014}, {3709, 6615}, {3952, 21580}, {4041, 21120}, {4069, 25268}, {4171, 42337}, {4515, 6736}, {4557, 21362}, {4849, 45204}, {6613, 4635}, {7064, 21809}, {8706, 799}, {21805, 51415}, {23493, 27499}, {23617, 86}, {32017, 310}, {40451, 16727}, {40528, 17197}, {51476, 81}, {52370, 22072}, {52549, 314}, {56173, 85}
X(56190) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1261, 23617, 51476}

X(56191) = KP2(X(37)) OF X(1) AND X(45)

Barycentrics    a*(b+c)*(a^2+3*b*c+a*(b+c)) : :

X(56191) lies on these lines: {1, 2}, {9, 49500}, {12, 1464}, {35, 859}, {36, 16374}, {37, 1018}, {38, 5883}, {40, 54287}, {55, 4245}, {56, 19261}, {58, 5260}, {65, 51504}, {71, 2093}, {80, 47515}, {86, 668}, {100, 4653}, {101, 37675}, {165, 19262}, {171, 5251}, {209, 7322}, {213, 46196}, {244, 3833}, {313, 3761}, {321, 46895}, {392, 22325}, {405, 3052}, {484, 846}, {500, 18357}, {517, 21363}, {581, 5818}, {595, 5047}, {740, 4714}, {750, 993}, {756, 758}, {940, 9708}, {956, 19534}, {958, 16357}, {968, 54286}, {970, 11521}, {984, 5902}, {986, 19258}, {999, 16499}, {1001, 19239}, {1042, 3947}, {1064, 5400}, {1089, 49598}, {1191, 16842}, {1215, 3992}, {1220, 25526}, {1329, 37693}, {1458, 51782}, {1573, 24512}, {1706, 19257}, {1724, 5711}, {1736, 50195}, {1739, 3666}, {1785, 30686}, {1909, 17175}, {1918, 15485}, {1962, 3968}, {2140, 26100}, {2223, 19263}, {2292, 3754}, {2295, 3294}, {2533, 4040}, {2650, 3678}, {2667, 4732}, {3159, 17164}, {3247, 9331}, {3295, 19250}, {3303, 19253}, {3315, 31514}, {3421, 4648}, {3468, 21686}, {3550, 19260}, {3576, 19550}, {3579, 52524}, {3583, 33109}, {3670, 3812}, {3698, 3931}, {3742, 4694}, {3743, 3918}, {3746, 19241}, {3749, 19267}, {3750, 48696}, {3751, 9038}, {3814, 33105}, {3820, 5718}, {3841, 21935}, {3877, 22294}, {3892, 17450}, {3894, 49448}, {3921, 4849}, {3925, 37715}, {3953, 5439}, {3956, 21805}, {3997, 52708}, {4002, 4646}, {4026, 39688}, {4036, 21173}, {4038, 16474}, {4134, 53114}, {4216, 5010}, {4300, 19925}, {4306, 5261}, {4450, 14020}, {4472, 50160}, {4649, 52897}, {4692, 24325}, {4705, 14421}, {4731, 37593}, {4738, 25106}, {4792, 40434}, {5204, 19252}, {5217, 19251}, {5219, 24806}, {5247, 37559}, {5255, 5259}, {5258, 37607}, {5275, 16788}, {5283, 16549}, {5284, 40091}, {5285, 19264}, {5291, 40750}, {5315, 17123}, {5396, 38042}, {5443, 51870}, {5492, 13145}, {5563, 19249}, {5692, 22275}, {5697, 22300}, {5710, 11108}, {5774, 19732}, {5790, 50317}, {5793, 16458}, {5836, 6051}, {5903, 22299}, {5919, 22313}, {7951, 33111}, {8167, 16483}, {8715, 17782}, {9548, 12435}, {9578, 37523}, {9709, 19765}, {9956, 37732}, {10013, 49680}, {10448, 25440}, {10571, 10588}, {10827, 15232}, {11230, 32486}, {11552, 33099}, {12433, 56132}, {13745, 44419}, {14839, 56131}, {16418, 37540}, {16484, 19265}, {16496, 22277}, {16552, 17750}, {16600, 21921}, {16611, 21840}, {16705, 24170}, {16777, 21858}, {17056, 17757}, {17245, 24222}, {17594, 19266}, {17719, 26725}, {17790, 24342}, {18480, 48897}, {19244, 37588}, {20150, 30473}, {20255, 25499}, {21025, 52538}, {21080, 49532}, {21290, 27295}, {21373, 36404}, {21714, 53314}, {21808, 28594}, {22271, 49490}, {22276, 25415}, {22289, 45223}, {22307, 53115}, {22316, 49469}, {22320, 48337}, {22392, 31399}, {24473, 49515}, {24487, 50302}, {25089, 39244}, {25349, 50179}, {27785, 37598}, {28653, 54308}, {33082, 38302}, {33857, 52371}, {39748, 43531}, {49462, 50083}

X(56191) = reflection of X(i) in X(j) for these {i,j}: {1, 3720}, {4651, 10}
X(56191) = X(i)-isoconjugate-of-X(j) for these {i, j}: {58, 42285}, {81, 39974}, {7252, 46480}
X(56191) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 42285}, {40586, 39974}
X(56191) = X(i)-Ceva conjugate of X(j) for these {i, j}: {32013, 3294}, {40434, 37}
X(56191) = intersection, other than A, B, C, of these circumconics: {{A, B, C, X(2), X(4674)}}, {{A, B, C, X(10), X(32487)}}, {{A, B, C, X(37), X(519)}}, {{A, B, C, X(65), X(1125)}}, {{A, B, C, X(80), X(4651)}}, {{A, B, C, X(86), X(49997)}}, {{A, B, C, X(87), X(5313)}}, {{A, B, C, X(105), X(29823)}}, {{A, B, C, X(239), X(48320)}}, {{A, B, C, X(291), X(29822)}}, {{A, B, C, X(386), X(5035)}}, {{A, B, C, X(551), X(53114)}}, {{A, B, C, X(899), X(40718)}}, {{A, B, C, X(957), X(3622)}}, {{A, B, C, X(979), X(5312)}}, {{A, B, C, X(1018), X(17780)}}, {{A, B, C, X(1193), X(39949)}}, {{A, B, C, X(1220), X(3293)}}, {{A, B, C, X(1224), X(26115)}}, {{A, B, C, X(1390), X(20045)}}, {{A, B, C, X(1647), X(3125)}}, {{A, B, C, X(3216), X(43531)}}, {{A, B, C, X(3240), X(18793)}}, {{A, B, C, X(3634), X(56174)}}, {{A, B, C, X(3636), X(31503)}}, {{A, B, C, X(4424), X(30588)}}, {{A, B, C, X(4828), X(30109)}}, {{A, B, C, X(8028), X(21821)}}, {{A, B, C, X(17135), X(38955)}}, {{A, B, C, X(17946), X(29586)}}, {{A, B, C, X(18082), X(31855)}}, {{A, B, C, X(18785), X(36480)}}, {{A, B, C, X(29655), X(34895)}}, {{A, B, C, X(29824), X(30571)}}, {{A, B, C, X(31339), X(39708)}}
X(56191) = barycentric product X(i)*X(j) for these (i, j): {1, 31025}, {10, 37633}, {313, 5035}, {1018, 47780}, {3952, 48320}, {4557, 4828}
X(56191) = barycentric quotient X(i)/X(j) for these (i, j): {37, 42285}, {42, 39974}, {4551, 46480}, {4828, 52619}, {5035, 58}, {31025, 75}, {37633, 86}, {47780, 7199}, {48320, 7192}
X(56191) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 10, 3293}, {1, 16569, 5313}, {1, 1698, 3216}, {1, 19875, 43}, {1, 2, 49997}, {1, 25502, 25055}, {1, 31855, 42}, {1, 34595, 21214}, {1, 6048, 5312}, {1, 9623, 49494}, {10, 1125, 26115}, {10, 16828, 1698}, {10, 42, 31855}, {10, 519, 4651}, {37, 3753, 4424}, {171, 5251, 52680}, {1064, 10175, 5400}, {1125, 10459, 1}, {1125, 19847, 3624}, {1125, 49993, 2}, {1125, 50749, 29689}, {1573, 24512, 45751}, {1698, 5313, 16569}, {1962, 4695, 4868}, {2295, 16589, 3294}, {3698, 3931, 3987}, {3743, 3918, 4642}, {3753, 4424, 4674}, {3968, 4868, 4695}, {16819, 41240, 29433}, {17751, 19874, 10}, {17752, 31996, 29383}, {50604, 51073, 27627}

X(56192) = KP2(X(37)) OF X(1) AND X(90)

Barycentrics    a*(b+c)*(a*(b-2*c)+b*(b+c))*(a*(2*b-c)-c*(b+c)) : :

X(56192) lies on these lines: {10, 982}, {42, 1449}, {57, 3214}, {171, 1126}, {181, 4849}, {291, 4685}, {756, 3778}, {1254, 4695}, {1500, 16584}, {2333, 5338}, {3122, 4082}, {4052, 21963}, {5285, 6187}, {6057, 22214}, {8690, 28482}, {22276, 22323}, {43223, 56131}

X(56192) = trilinear pole of line {4079, 4822}
X(56192) = X(i)-isoconjugate-of-X(j) for these {i, j}: {58, 3875}, {81, 4383}, {86, 3915}, {110, 4106}, {274, 16946}, {593, 3175}, {662, 4498}, {757, 3214}, {765, 17214}, {1014, 3913}, {1333, 18135}, {1412, 30568}, {1414, 42312}, {1434, 3217}, {1444, 4186}, {2185, 28387}, {4139, 52935}, {4565, 20317}, {4600, 17477}, {21963, 24041}, {27813, 33628}
X(56192) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 3875}, {37, 18135}, {244, 4106}, {513, 17214}, {1084, 4498}, {3005, 21963}, {40586, 4383}, {40599, 30568}, {40600, 3915}, {40607, 3214}, {40608, 42312}, {50497, 17477}, {55064, 20317}
X(56192) = X(i)-Ceva conjugate of X(j) for these {i, j}: {34860, 56123}, {56155, 37}
X(56192) = X(i)-cross conjugate of X(j) for these {i, j}: {20684, 226}
X(56192) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(5105)}}, {{A, B, C, X(10), X(42)}}, {{A, B, C, X(25), X(33833)}}, {{A, B, C, X(31), X(596)}}, {{A, B, C, X(37), X(57)}}, {{A, B, C, X(55), X(7241)}}, {{A, B, C, X(65), X(5269)}}, {{A, B, C, X(75), X(2258)}}, {{A, B, C, X(171), X(21803)}}, {{A, B, C, X(209), X(52139)}}, {{A, B, C, X(210), X(3158)}}, {{A, B, C, X(226), X(16606)}}, {{A, B, C, X(321), X(17756)}}, {{A, B, C, X(656), X(2318)}}, {{A, B, C, X(661), X(4052)}}, {{A, B, C, X(871), X(982)}}, {{A, B, C, X(1096), X(56136)}}, {{A, B, C, X(1395), X(24046)}}, {{A, B, C, X(1416), X(24171)}}, {{A, B, C, X(1460), X(4424)}}, {{A, B, C, X(1824), X(4674)}}, {{A, B, C, X(2319), X(2321)}}, {{A, B, C, X(3214), X(4061)}}, {{A, B, C, X(4041), X(4082)}}, {{A, B, C, X(7093), X(18793)}}, {{A, B, C, X(8013), X(50587)}}, {{A, B, C, X(8817), X(13576)}}, {{A, B, C, X(9436), X(20683)}}, {{A, B, C, X(22174), X(23532)}}, {{A, B, C, X(39697), X(40148)}}, {{A, B, C, X(39956), X(40012)}}
X(56192) = barycentric product X(i)*X(j) for these (i, j): {1, 56123}, {10, 39956}, {210, 42304}, {2321, 56155}, {4024, 8690}, {34860, 37}, {40012, 42}
X(56192) = barycentric quotient X(i)/X(j) for these (i, j): {10, 18135}, {37, 3875}, {42, 4383}, {181, 28387}, {210, 30568}, {213, 3915}, {512, 4498}, {661, 4106}, {756, 3175}, {1015, 17214}, {1334, 3913}, {1500, 3214}, {1918, 16946}, {2333, 4186}, {3121, 17477}, {3124, 21963}, {3709, 42312}, {4041, 20317}, {4079, 4139}, {7148, 27432}, {8034, 23777}, {8690, 4610}, {31993, 18078}, {34860, 274}, {39956, 86}, {40012, 310}, {56123, 75}, {56155, 1434}, {56174, 27813}

X(56193) = KP2(X(37)) OF X(1) AND X(100)

Barycentrics    a*(a-b)*(a-c)*(b+c)*(a^2+a*b+b^2-c^2)*(a^2-b^2+a*c+c^2) : :

X(56193) lies on these lines: {10, 7100}, {42, 1989}, {79, 3293}, {100, 13486}, {692, 4705}, {2160, 7077}, {3214, 32259}, {3699, 6742}, {3939, 21891}, {4041, 21784}, {8606, 52139}, {8694, 26700}, {37138, 38340}

X(56193) = trilinear pole of line {1334, 21816}
X(56193) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 16755}, {35, 7192}, {58, 4467}, {81, 14838}, {86, 2605}, {249, 21141}, {286, 23226}, {319, 3733}, {514, 40214}, {593, 7265}, {649, 34016}, {662, 7202}, {693, 17104}, {1014, 35057}, {1015, 55235}, {1019, 3219}, {1333, 18160}, {1399, 18155}, {1414, 53524}, {1434, 9404}, {1442, 3737}, {1444, 54244}, {1509, 55210}, {2003, 4560}, {2174, 7199}, {2611, 52935}, {3676, 35193}, {4420, 7203}, {4556, 8287}, {4610, 20982}, {7186, 7255}, {7252, 17095}, {7254, 52412}, {7266, 13486}, {7282, 23189}, {17096, 52405}, {17190, 47947}, {24002, 35192}
X(56193) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 16755}, {10, 4467}, {37, 18160}, {1084, 7202}, {5375, 34016}, {38986, 53542}, {40586, 14838}, {40600, 2605}, {40608, 53524}, {55065, 17886}
X(56193) = intersection, other than A, B, C, of these circumconics: {{A, B, C, X(37), X(651)}}, {{A, B, C, X(42), X(692)}}, {{A, B, C, X(100), X(40521)}}, {{A, B, C, X(1783), X(21859)}}, {{A, B, C, X(1826), X(4605)}}, {{A, B, C, X(1989), X(15455)}}, {{A, B, C, X(2214), X(42362)}}, {{A, B, C, X(3699), X(3939)}}, {{A, B, C, X(4569), X(15320)}}, {{A, B, C, X(4705), X(21043)}}, {{A, B, C, X(6742), X(14560)}}
X(56193) = barycentric product X(i)*X(j) for these (i, j): {37, 6742}, {100, 8818}, {101, 6757}, {210, 38340}, {1018, 79}, {1783, 52388}, {2160, 3952}, {2321, 26700}, {3939, 43682}, {4033, 6186}, {4053, 476}, {4069, 52374}, {4103, 52375}, {4551, 7110}, {4552, 7073}, {4559, 52344}, {13486, 594}, {15455, 42}, {21859, 3615}, {30690, 4557}, {30730, 52372}, {34922, 8611}, {40521, 52393}, {52382, 644}, {55209, 872}, {55236, 765}
X(56193) = barycentric quotient X(i)/X(j) for these (i, j): {1, 16755}, {10, 18160}, {37, 4467}, {42, 14838}, {79, 7199}, {100, 34016}, {213, 2605}, {512, 7202}, {692, 40214}, {756, 7265}, {765, 55235}, {798, 53542}, {872, 55210}, {1018, 319}, {1334, 35057}, {2160, 7192}, {2200, 23226}, {2333, 54244}, {2643, 21141}, {3709, 53524}, {3952, 33939}, {4024, 17886}, {4053, 3268}, {4069, 42033}, {4079, 2611}, {4551, 17095}, {4552, 52421}, {4557, 3219}, {4559, 1442}, {4705, 8287}, {6186, 1019}, {6742, 274}, {6757, 3261}, {7073, 4560}, {7100, 15419}, {7110, 18155}, {8818, 693}, {13486, 1509}, {15455, 310}, {21859, 40999}, {26700, 1434}, {30690, 52619}, {32739, 17104}, {35327, 17190}, {39258, 53554}, {40521, 3969}, {43682, 52621}, {50487, 20982}, {52372, 17096}, {52382, 24002}, {52388, 15413}, {55210, 7266}, {55236, 1111}

X(56194) = KP2(X(37)) OF X(1) AND X(101)

Barycentrics    a*(a-b)*(a-c)*(-b^3+b*c^2+a*c*(-b+c)+a^2*(b+c))*(a*b*(b-c)+a^2*(b+c)+c*(b^2-c^2)) : :

X(56194) lies on these lines: {1, 26095}, {42, 46880}, {43, 1699}, {80, 3293}, {100, 2617}, {109, 21173}, {291, 53083}, {692, 36050}, {1018, 2427}, {1201, 40451}, {3216, 4674}, {3952, 25268}, {4040, 53279}, {4551, 21362}, {4566, 20520}, {5247, 52150}, {17860, 32931}, {17861, 40619}, {17906, 23706}, {24026, 42078}, {27810, 54329}

X(56194) = reflection of X(i) in X(j) for these {i,j}: {1, 40613}
X(56194) = isogonal conjugate of X(21173)
X(56194) = trilinear pole of line {37, 1953}
X(56194) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 21173}, {4, 23187}, {6, 17496}, {21, 51662}, {101, 24237}, {109, 34589}, {110, 53566}, {513, 2975}, {514, 572}, {649, 14829}, {650, 17074}, {651, 11998}, {653, 38344}, {693, 20986}, {1019, 21061}, {1415, 40624}, {1459, 11109}, {2162, 27346}, {3733, 17751}, {3737, 37558}, {7192, 52139}, {7252, 52358}, {17924, 22118}
X(56194) = X(i)-vertex conjugate of X(j) for these {i, j}: {163, 36098}, {643, 32665}, {1415, 36050}, {32641, 52928}
X(56194) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 21173}, {9, 17496}, {11, 34589}, {244, 53566}, {1015, 24237}, {1146, 40624}, {2051, 23799}, {5375, 14829}, {36033, 23187}, {38991, 11998}, {39026, 2975}, {40611, 51662}
X(56194) = X(i)-cross conjugate of X(j) for these {i, j}: {522, 1}, {650, 46880}
X(56194) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(109)}}, {{A, B, C, X(43), X(1026)}}, {{A, B, C, X(57), X(43190)}}, {{A, B, C, X(80), X(100)}}, {{A, B, C, X(84), X(32704)}}, {{A, B, C, X(101), X(3699)}}, {{A, B, C, X(110), X(51562)}}, {{A, B, C, X(162), X(1956)}}, {{A, B, C, X(513), X(40451)}}, {{A, B, C, X(522), X(21173)}}, {{A, B, C, X(645), X(43069)}}, {{A, B, C, X(646), X(651)}}, {{A, B, C, X(650), X(20520)}}, {{A, B, C, X(653), X(2656)}}, {{A, B, C, X(658), X(8056)}}, {{A, B, C, X(660), X(8706)}}, {{A, B, C, X(664), X(1293)}}, {{A, B, C, X(666), X(37137)}}, {{A, B, C, X(901), X(6742)}}, {{A, B, C, X(978), X(23705)}}, {{A, B, C, X(1020), X(6335)}}, {{A, B, C, X(1743), X(23343)}}, {{A, B, C, X(2258), X(32739)}}, {{A, B, C, X(3216), X(17780)}}, {{A, B, C, X(3737), X(46041)}}, {{A, B, C, X(4040), X(40619)}}, {{A, B, C, X(4242), X(37357)}}, {{A, B, C, X(4397), X(21189)}}, {{A, B, C, X(5903), X(23703)}}, {{A, B, C, X(6011), X(36086)}}, {{A, B, C, X(6577), X(53321)}}, {{A, B, C, X(8694), X(36049)}}, {{A, B, C, X(8701), X(32641)}}, {{A, B, C, X(9057), X(39954)}}, {{A, B, C, X(13486), X(26711)}}, {{A, B, C, X(17861), X(53279)}}, {{A, B, C, X(24026), X(46393)}}, {{A, B, C, X(28226), X(37138)}}, {{A, B, C, X(30250), X(36108)}}, {{A, B, C, X(32040), X(39980)}}
X(56194) = barycentric product X(i)*X(j) for these (i, j): {1, 56188}, {100, 2051}, {101, 54121}, {190, 34434}, {1018, 20028}, {3952, 53083}, {4033, 52150}, {4551, 46880}, {51870, 662}, {53702, 908}
X(56194) = barycentric quotient X(i)/X(j) for these (i, j): {1, 17496}, {6, 21173}, {43, 27346}, {48, 23187}, {100, 14829}, {101, 2975}, {109, 17074}, {513, 24237}, {522, 40624}, {650, 34589}, {661, 53566}, {663, 11998}, {692, 572}, {1018, 17751}, {1400, 51662}, {1783, 11109}, {1946, 38344}, {2051, 693}, {4040, 26847}, {4551, 52358}, {4557, 21061}, {4559, 37558}, {20028, 7199}, {21807, 52322}, {21859, 52357}, {32656, 22118}, {32739, 20986}, {34434, 514}, {46880, 18155}, {51870, 1577}, {52150, 1019}, {53083, 7192}, {53702, 34234}, {54121, 3261}, {56188, 75}

X(56195) = KP2(X(37)) OF X(10) AND X(9)

Barycentrics    a*(b+c)*(a^4+a^3*c-a*(b-c)^2*c+b*(b-c)*(b+c)^2-a^2*(2*b^2+b*c+c^2))*(a^4+a^3*b-a*b*(b-c)^2-(b-c)*c*(b+c)^2-a^2*(b^2+b*c+2*c^2)) : :

X(56195) lies on these lines: {9, 17916}, {40, 318}, {72, 37558}, {78, 947}, {200, 15623}, {210, 22341}, {307, 21075}, {3694, 4006}, {3710, 17751}, {3718, 33932}, {12514, 44040}, {17757, 52388}

X(56195) = X(i)-isoconjugate-of-X(j) for these {i, j}: {27, 22063}, {28, 17102}, {58, 946}, {81, 2262}, {1408, 23528}, {1412, 20262}, {1434, 40957}
X(56195) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 946}, {40586, 2262}, {40591, 17102}, {40599, 20262}
X(56195) = X(i)-cross conjugate of X(j) for these {i, j}: {520, 4551}
X(56195) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2975)}}, {{A, B, C, X(3), X(37420)}}, {{A, B, C, X(4), X(6986)}}, {{A, B, C, X(9), X(10)}}, {{A, B, C, X(37), X(7160)}}, {{A, B, C, X(40), X(71)}}, {{A, B, C, X(65), X(84)}}, {{A, B, C, X(90), X(4674)}}, {{A, B, C, X(158), X(56153)}}, {{A, B, C, X(210), X(21075)}}, {{A, B, C, X(758), X(6597)}}, {{A, B, C, X(947), X(40417)}}, {{A, B, C, X(956), X(56145)}}, {{A, B, C, X(3294), X(5223)}}, {{A, B, C, X(3577), X(15232)}}, {{A, B, C, X(3678), X(17757)}}, {{A, B, C, X(3681), X(4006)}}, {{A, B, C, X(3697), X(21060)}}, {{A, B, C, X(7091), X(53114)}}, {{A, B, C, X(13576), X(38271)}}, {{A, B, C, X(18097), X(39273)}}, {{A, B, C, X(21078), X(41229)}}, {{A, B, C, X(42471), X(56140)}}, {{A, B, C, X(43739), X(51223)}}
X(56195) = barycentric product X(i)*X(j) for these (i, j): {10, 55987}, {37, 40417}, {306, 40396}, {321, 947}
X(56195) = barycentric quotient X(i)/X(j) for these (i, j): {37, 946}, {42, 2262}, {71, 17102}, {210, 20262}, {228, 22063}, {947, 81}, {2321, 23528}, {40396, 27}, {40417, 274}, {52370, 40945}, {55987, 86}

X(56196) = KP2(X(37)) OF X(10) AND X(42)

Barycentrics    (a^2-a*b+b^2)*(b+c)*(a^2-a*c+c^2) : :

X(56196) lies on these lines: {8, 238}, {10, 1284}, {42, 27438}, {43, 350}, {86, 38810}, {256, 17261}, {281, 2201}, {513, 17351}, {740, 3214}, {1193, 49472}, {1215, 1441}, {1376, 23182}, {1874, 41013}, {2238, 2321}, {2295, 21759}, {3507, 17787}, {3741, 55076}, {4085, 26772}, {20691, 40729}, {21320, 25140}, {21803, 40718}, {37677, 40735}, {50576, 56080}

X(56196) = isotomic conjugate of X(33947)
X(56196) = polar conjugate of X(31917)
X(56196) = trilinear pole of line {3700, 21832}
X(56196) = X(i)-isoconjugate-of-X(j) for these {i, j}: {21, 7248}, {28, 3784}, {31, 33947}, {48, 31917}, {56, 3794}, {58, 982}, {81, 2275}, {86, 7032}, {99, 50514}, {110, 3777}, {163, 3776}, {284, 41777}, {552, 4531}, {593, 3721}, {757, 3778}, {849, 2887}, {873, 40935}, {1014, 3056}, {1178, 7184}, {1333, 3662}, {1408, 3705}, {1412, 3061}, {1434, 20665}, {1509, 16584}, {2150, 16888}, {2194, 7185}, {2206, 33930}, {3733, 3888}, {7186, 52375}, {7203, 40499}, {18268, 33891}
X(56196) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 3794}, {2, 33947}, {10, 982}, {37, 3662}, {115, 3776}, {244, 3777}, {1214, 7185}, {1249, 31917}, {3741, 23473}, {4075, 2887}, {6741, 3810}, {16587, 7187}, {35068, 33891}, {38986, 50514}, {40586, 2275}, {40590, 41777}, {40591, 3784}, {40599, 3061}, {40600, 7032}, {40603, 33930}, {40607, 3778}, {40611, 7248}, {55065, 3801}
X(56196) = X(i)-cross conjugate of X(j) for these {i, j}: {21051, 3952}
X(56196) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3214)}}, {{A, B, C, X(2), X(4685)}}, {{A, B, C, X(4), X(17697)}}, {{A, B, C, X(8), X(10)}}, {{A, B, C, X(19), X(56138)}}, {{A, B, C, X(37), X(86)}}, {{A, B, C, X(42), X(43)}}, {{A, B, C, X(65), X(1120)}}, {{A, B, C, X(75), X(32941)}}, {{A, B, C, X(190), X(17351)}}, {{A, B, C, X(210), X(1215)}}, {{A, B, C, X(226), X(26685)}}, {{A, B, C, X(239), X(25425)}}, {{A, B, C, X(313), X(33165)}}, {{A, B, C, X(321), X(17280)}}, {{A, B, C, X(523), X(17765)}}, {{A, B, C, X(594), X(3773)}}, {{A, B, C, X(894), X(17261)}}, {{A, B, C, X(983), X(7033)}}, {{A, B, C, X(1016), X(39745)}}, {{A, B, C, X(1193), X(3293)}}, {{A, B, C, X(1213), X(4527)}}, {{A, B, C, X(1222), X(56174)}}, {{A, B, C, X(1400), X(18793)}}, {{A, B, C, X(1826), X(43534)}}, {{A, B, C, X(2295), X(20691)}}, {{A, B, C, X(3697), X(49598)}}, {{A, B, C, X(3741), X(4651)}}, {{A, B, C, X(3755), X(3950)}}, {{A, B, C, X(3886), X(25590)}}, {{A, B, C, X(3943), X(4085)}}, {{A, B, C, X(4029), X(4780)}}, {{A, B, C, X(4052), X(39749)}}, {{A, B, C, X(4133), X(5257)}}, {{A, B, C, X(4360), X(49472)}}, {{A, B, C, X(4373), X(13576)}}, {{A, B, C, X(7035), X(39977)}}, {{A, B, C, X(15320), X(39707)}}, {{A, B, C, X(16704), X(26772)}}, {{A, B, C, X(17393), X(32921)}}, {{A, B, C, X(17743), X(40834)}}, {{A, B, C, X(21803), X(40790)}}, {{A, B, C, X(21865), X(40521)}}, {{A, B, C, X(29822), X(49988)}}, {{A, B, C, X(51561), X(55037)}}
X(56196) = barycentric product X(i)*X(j) for these (i, j): {10, 17743}, {37, 7033}, {213, 7034}, {226, 56180}, {321, 983}, {3407, 3773}, {3701, 7132}, {3774, 46281}, {4103, 7255}, {4621, 523}, {21803, 40835}, {28654, 38813}, {38810, 756}, {40415, 594}, {43265, 86}
X(56196) = barycentric quotient X(i)/X(j) for these (i, j): {2, 33947}, {4, 31917}, {9, 3794}, {10, 3662}, {12, 16888}, {37, 982}, {42, 2275}, {65, 41777}, {71, 3784}, {210, 3061}, {213, 7032}, {226, 7185}, {321, 33930}, {523, 3776}, {594, 2887}, {661, 3777}, {740, 33891}, {756, 3721}, {762, 7237}, {798, 50514}, {872, 16584}, {983, 81}, {1018, 3888}, {1089, 20234}, {1215, 7187}, {1334, 3056}, {1400, 7248}, {1500, 3778}, {2295, 7184}, {2321, 3705}, {3690, 20727}, {3700, 3810}, {3773, 3314}, {3774, 3116}, {3952, 33946}, {3971, 33890}, {4024, 3801}, {4090, 41771}, {4120, 53533}, {4515, 4073}, {4621, 99}, {6057, 4136}, {6535, 16886}, {7033, 274}, {7034, 6385}, {7064, 20684}, {7109, 40935}, {7132, 1014}, {7305, 763}, {8684, 4584}, {8685, 4565}, {17743, 86}, {20684, 12836}, {20691, 41886}, {21803, 18905}, {21832, 3808}, {21838, 23473}, {38810, 873}, {38813, 593}, {40415, 1509}, {40521, 7239}, {43265, 10}, {52370, 20753}, {52651, 3865}, {56180, 333}
X(56196) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {17743, 56180, 983}

X(56197) = KP2(X(37)) OF X(42) AND X(2)

Barycentrics    (b+c)*(a*b*(b-2*c)+b^2*c+a^2*(b+c))*(b*c^2+a*c*(-2*b+c)+a^2*(b+c)) : :

X(56197) lies on the Kiepert hyperbola and on these lines: {2, 16969}, {76, 1278}, {321, 21868}, {3210, 40013}, {4444, 48334}, {4642, 43534}, {4850, 39994}, {17758, 24190}, {18600, 40017}, {20691, 56185}, {27162, 40031}, {35353, 50487}

X(56197) = isotomic conjugate of X(17178)
X(56197) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 18192}, {28, 22066}, {31, 17178}, {58, 17448}, {81, 22343}, {593, 22167}, {849, 21025}, {1333, 3840}, {2206, 20892}, {7121, 16722}
X(56197) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 17178}, {9, 18192}, {10, 17448}, {37, 3840}, {4075, 21025}, {40586, 22343}, {40591, 22066}, {40598, 16722}, {40603, 20892}
X(56197) = X(i)-cross conjugate of X(j) for these {i, j}: {21834, 3952}, {26772, 2}
X(56197) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(26756)}}, {{A, B, C, X(37), X(1278)}}, {{A, B, C, X(42), X(20691)}}, {{A, B, C, X(65), X(27809)}}, {{A, B, C, X(330), X(4674)}}, {{A, B, C, X(1500), X(50487)}}, {{A, B, C, X(2998), X(40504)}}, {{A, B, C, X(3210), X(3995)}}, {{A, B, C, X(3948), X(4642)}}, {{A, B, C, X(8049), X(18832)}}, {{A, B, C, X(15320), X(53677)}}, {{A, B, C, X(17178), X(26772)}}, {{A, B, C, X(26115), X(29593)}}, {{A, B, C, X(27162), X(31060)}}, {{A, B, C, X(27321), X(27690)}}, {{A, B, C, X(39740), X(56174)}}
X(56197) = barycentric product X(i)*X(j) for these (i, j): {10, 32011}
X(56197) = barycentric quotient X(i)/X(j) for these (i, j): {1, 18192}, {2, 17178}, {10, 3840}, {37, 17448}, {42, 22343}, {71, 22066}, {192, 16722}, {321, 20892}, {594, 21025}, {756, 22167}, {18082, 18102}, {32011, 86}

X(56198) = KP2(X(37)) OF X(65) AND X(71)

Barycentrics    a*(a+b-c)*(a-b+c)*(b+c)*(a^3+2*b*c*(b+c)-a*(b+c)^2) : :

X(56198) lies on circumconic {{A, B, C, X(5687), X(38955)}} and on these lines: {1, 3090}, {8, 1457}, {10, 73}, {12, 42}, {31, 11501}, {33, 1103}, {34, 200}, {40, 2635}, {43, 388}, {56, 899}, {71, 3330}, {100, 1935}, {201, 210}, {212, 11500}, {222, 9709}, {225, 2318}, {226, 3293}, {255, 11499}, {341, 23691}, {355, 22350}, {386, 9578}, {515, 22072}, {518, 1393}, {581, 31434}, {603, 1376}, {664, 25280}, {748, 11510}, {902, 7299}, {978, 3476}, {995, 37709}, {1042, 40663}, {1064, 10039}, {1066, 1737}, {1106, 9350}, {1149, 37738}, {1167, 2342}, {1193, 5252}, {1201, 10944}, {1214, 3697}, {1254, 21805}, {1319, 27627}, {1329, 25941}, {1334, 21859}, {1388, 28352}, {1394, 46917}, {1420, 17749}, {1450, 3216}, {1454, 32912}, {1458, 24914}, {1465, 34790}, {1496, 11502}, {1574, 52635}, {1706, 54400}, {1745, 5657}, {1757, 7098}, {1788, 6048}, {1818, 5552}, {1880, 3949}, {2654, 5587}, {3057, 45885}, {3074, 11491}, {3085, 14547}, {3240, 5261}, {3485, 50581}, {3617, 24806}, {3679, 10571}, {3681, 37591}, {3682, 17757}, {3870, 19372}, {3947, 50587}, {3953, 43048}, {4303, 26446}, {4322, 5433}, {4413, 34046}, {4848, 31855}, {5293, 54292}, {5312, 5726}, {5399, 9956}, {5400, 12053}, {5687, 34048}, {5887, 24028}, {6684, 22053}, {6796, 22361}, {7004, 14872}, {7066, 51377}, {7074, 15811}, {7288, 16569}, {9627, 52371}, {9780, 37523}, {10590, 37529}, {10914, 53530}, {11392, 40976}, {17102, 18908}, {17814, 42019}, {18524, 52408}, {21031, 51421}, {21801, 53861}, {24390, 52659}, {24592, 28771}, {28270, 38472}, {31397, 37732}, {31479, 37698}, {31803, 45269}, {37710, 54427}, {37828, 51649}, {41687, 49984}, {43043, 47742}, {50031, 51424}

X(56198) = barycentric product X(i)*X(j) for these (i, j): {10, 34048}, {226, 5687}, {4552, 48303}, {17894, 4559}, {56082, 65}
X(56198) = barycentric quotient X(i)/X(j) for these (i, j): {5687, 333}, {34048, 86}, {38389, 17197}, {48303, 4560}, {56082, 314}
X(56198) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 37694, 1457}, {10, 4551, 73}, {210, 227, 201}, {1254, 21805, 41538}, {1376, 9370, 603}, {3085, 37699, 14547}, {3216, 10106, 1450}

X(56199) = KP3(X(9)) OF X(1) AND X(1)

Barycentrics    a*(a-b-c)*(a^2-2*a*b+5*b^2+2*a*c-2*b*c+c^2)*(a^2+b^2+2*a*(b-c)-2*b*c+5*c^2) : :

X(56199) lies on these lines: {2, 52528}, {9, 3752}, {57, 23617}, {63, 55989}, {200, 2136}, {281, 20106}, {282, 42549}, {346, 3452}, {2287, 18163}, {2297, 5437}, {3061, 19605}, {3928, 55993}, {3929, 55992}, {6167, 36636}, {9311, 30567}, {36916, 42049}

X(56199) = trilinear pole of line {6615, 3900}
X(56199) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 4308}, {109, 43061}, {1461, 8710}
X(56199) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 4308}, {11, 43061}, {35508, 8710}
X(56199) = X(i)-cross conjugate of X(j) for these {i, j}: {10866, 7}
X(56199) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(6557)}}, {{A, B, C, X(2), X(9)}}, {{A, B, C, X(7), X(34991)}}, {{A, B, C, X(8), X(2136)}}, {{A, B, C, X(21), X(38255)}}, {{A, B, C, X(57), X(312)}}, {{A, B, C, X(63), X(30827)}}, {{A, B, C, X(78), X(20106)}}, {{A, B, C, X(88), X(31509)}}, {{A, B, C, X(189), X(34918)}}, {{A, B, C, X(333), X(37679)}}, {{A, B, C, X(614), X(3687)}}, {{A, B, C, X(728), X(52528)}}, {{A, B, C, X(899), X(11679)}}, {{A, B, C, X(1320), X(39980)}}, {{A, B, C, X(1427), X(2321)}}, {{A, B, C, X(2051), X(5665)}}, {{A, B, C, X(2339), X(4997)}}, {{A, B, C, X(3596), X(7249)}}, {{A, B, C, X(3729), X(30567)}}, {{A, B, C, X(3928), X(5328)}}, {{A, B, C, X(4900), X(36603)}}, {{A, B, C, X(5273), X(51780)}}, {{A, B, C, X(5437), X(18228)}}, {{A, B, C, X(5745), X(7308)}}, {{A, B, C, X(6546), X(52140)}}, {{A, B, C, X(7131), X(42339)}}, {{A, B, C, X(10390), X(44733)}}, {{A, B, C, X(13478), X(33576)}}, {{A, B, C, X(28808), X(42049)}}, {{A, B, C, X(30711), X(39962)}}, {{A, B, C, X(42015), X(42318)}}
X(56199) = barycentric product X(i)*X(j) for these (i, j): {4397, 6571}
X(56199) = barycentric quotient X(i)/X(j) for these (i, j): {1, 4308}, {650, 43061}, {3900, 8710}, {6571, 934}

X(56200) = KP3(X(9)) OF X(1) AND X(2)

Barycentrics    (a-b-c)*(a^2-6*a*b+b^2-c^2)*(a^2-b^2-6*a*c+c^2) : :

X(56200) lies on these lines: {2, 39126}, {9, 145}, {144, 21446}, {200, 3161}, {220, 23617}, {346, 44720}, {2287, 52352}, {2297, 19861}, {3177, 42483}, {3452, 4373}, {3731, 10580}, {4461, 36796}, {6553, 15829}, {6555, 52549}, {7110, 27508}, {18228, 56199}, {35160, 45789}

X(56200) = isotomic conjugate of X(43983)
X(56200) = trilinear pole of line {4521, 3900}
X(56200) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 7271}, {31, 43983}, {56, 5437}, {57, 3304}, {604, 31995}, {1407, 4853}, {1412, 3698}
X(56200) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 5437}, {2, 43983}, {9, 7271}, {3161, 31995}, {5452, 3304}, {24771, 4853}, {40599, 3698}
X(56200) = X(i)-cross conjugate of X(j) for these {i, j}: {8710, 3699}
X(56200) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(37556)}}, {{A, B, C, X(2), X(9)}}, {{A, B, C, X(7), X(8236)}}, {{A, B, C, X(8), X(145)}}, {{A, B, C, X(63), X(30681)}}, {{A, B, C, X(81), X(51341)}}, {{A, B, C, X(97), X(55111)}}, {{A, B, C, X(279), X(41441)}}, {{A, B, C, X(280), X(32635)}}, {{A, B, C, X(391), X(2325)}}, {{A, B, C, X(941), X(7050)}}, {{A, B, C, X(1219), X(4866)}}, {{A, B, C, X(2161), X(52223)}}, {{A, B, C, X(2321), X(4029)}}, {{A, B, C, X(3177), X(30695)}}, {{A, B, C, X(3219), X(27508)}}, {{A, B, C, X(3452), X(6555)}}, {{A, B, C, X(3680), X(35577)}}, {{A, B, C, X(3692), X(30680)}}, {{A, B, C, X(3693), X(4461)}}, {{A, B, C, X(4076), X(30479)}}, {{A, B, C, X(6552), X(15829)}}, {{A, B, C, X(6556), X(46872)}}, {{A, B, C, X(6601), X(36606)}}, {{A, B, C, X(7003), X(8796)}}, {{A, B, C, X(7080), X(44687)}}, {{A, B, C, X(7220), X(9309)}}, {{A, B, C, X(14100), X(26818)}}, {{A, B, C, X(14942), X(30712)}}, {{A, B, C, X(30711), X(39721)}}, {{A, B, C, X(43533), X(44040)}}
X(56200) = barycentric product X(i)*X(j) for these (i, j): {346, 44794}, {7320, 8}
X(56200) = barycentric quotient X(i)/X(j) for these (i, j): {1, 7271}, {2, 43983}, {8, 31995}, {9, 5437}, {55, 3304}, {200, 4853}, {210, 3698}, {7320, 7}, {44794, 279}

X(56201) = KP3(X(9)) OF X(1) AND X(8)

Barycentrics    (a-b-c)*(3*a+3*b-c)*(3*a-b+3*c) : :

X(56201) lies on these lines: {2, 1743}, {8, 3158}, {9, 6557}, {63, 50442}, {85, 5435}, {92, 4359}, {145, 46872}, {257, 5222}, {312, 3161}, {345, 4102}, {1150, 40435}, {1220, 5737}, {1311, 28162}, {3452, 38255}, {3616, 31359}, {3687, 30711}, {4113, 5218}, {4384, 10405}, {4847, 56088}, {4997, 18228}, {5278, 34234}, {5296, 37646}, {5437, 56054}, {5739, 56062}, {6546, 43061}, {8055, 31722}, {8056, 23649}, {11679, 56086}, {14555, 30608}, {14829, 29627}, {16602, 39956}, {16713, 46880}, {17277, 40420}, {17743, 29611}, {18359, 20881}, {25057, 33133}, {26038, 56164}, {26047, 32918}, {32851, 42030}, {33116, 55954}, {41915, 51583}, {52653, 56102}

X(56201) = isotomic conjugate of X(5226)
X(56201) = complement of X(41913)
X(56201) = trilinear pole of line {4162, 522}
X(56201) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 3340}, {31, 5226}, {56, 3731}, {604, 3617}, {608, 3984}, {651, 48338}, {1397, 42034}, {1408, 4058}, {1415, 28161}
X(56201) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 3731}, {2, 5226}, {9, 3340}, {1146, 28161}, {3161, 3617}, {3756, 14350}, {38991, 48338}
X(56201) = X(i)-cross conjugate of X(j) for these {i, j}: {391, 8}, {3486, 7}, {53526, 4560}
X(56201) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(8)}}, {{A, B, C, X(7), X(261)}}, {{A, B, C, X(9), X(1261)}}, {{A, B, C, X(21), X(57)}}, {{A, B, C, X(55), X(2350)}}, {{A, B, C, X(60), X(967)}}, {{A, B, C, X(63), X(1809)}}, {{A, B, C, X(75), X(21296)}}, {{A, B, C, X(80), X(45098)}}, {{A, B, C, X(81), X(2320)}}, {{A, B, C, X(88), X(2339)}}, {{A, B, C, X(89), X(2185)}}, {{A, B, C, X(277), X(8051)}}, {{A, B, C, X(278), X(44559)}}, {{A, B, C, X(314), X(28626)}}, {{A, B, C, X(345), X(4001)}}, {{A, B, C, X(673), X(5281)}}, {{A, B, C, X(958), X(959)}}, {{A, B, C, X(1255), X(1392)}}, {{A, B, C, X(2051), X(7319)}}, {{A, B, C, X(2269), X(45988)}}, {{A, B, C, X(2319), X(40779)}}, {{A, B, C, X(3008), X(43061)}}, {{A, B, C, X(3616), X(11679)}}, {{A, B, C, X(3687), X(9780)}}, {{A, B, C, X(3705), X(29611)}}, {{A, B, C, X(3911), X(4723)}}, {{A, B, C, X(4373), X(32093)}}, {{A, B, C, X(4391), X(34258)}}, {{A, B, C, X(4416), X(34277)}}, {{A, B, C, X(4513), X(4875)}}, {{A, B, C, X(4847), X(29627)}}, {{A, B, C, X(5222), X(7081)}}, {{A, B, C, X(5235), X(14555)}}, {{A, B, C, X(5271), X(27383)}}, {{A, B, C, X(5324), X(40193)}}, {{A, B, C, X(5437), X(18230)}}, {{A, B, C, X(5556), X(18231)}}, {{A, B, C, X(5737), X(19608)}}, {{A, B, C, X(5936), X(17272)}}, {{A, B, C, X(7155), X(39716)}}, {{A, B, C, X(10453), X(28797)}}, {{A, B, C, X(10527), X(34255)}}, {{A, B, C, X(11604), X(43757)}}, {{A, B, C, X(14829), X(16713)}}, {{A, B, C, X(16610), X(48559)}}, {{A, B, C, X(17120), X(52652)}}, {{A, B, C, X(17298), X(39749)}}, {{A, B, C, X(17364), X(39721)}}, {{A, B, C, X(17776), X(28930)}}, {{A, B, C, X(21255), X(55076)}}, {{A, B, C, X(24627), X(26065)}}, {{A, B, C, X(27549), X(52653)}}, {{A, B, C, X(27818), X(37887)}}, {{A, B, C, X(28605), X(32851)}}, {{A, B, C, X(30827), X(31188)}}, {{A, B, C, X(32023), X(38254)}}, {{A, B, C, X(32635), X(39963)}}, {{A, B, C, X(33576), X(34991)}}, {{A, B, C, X(34404), X(52344)}}, {{A, B, C, X(36948), X(40422)}}, {{A, B, C, X(39800), X(41913)}}, {{A, B, C, X(41514), X(56099)}}, {{A, B, C, X(44189), X(52381)}}
X(56201) = barycentric product X(i)*X(j) for these (i, j): {312, 39980}, {314, 31503}, {28162, 35519}, {30712, 8}
X(56201) = barycentric quotient X(i)/X(j) for these (i, j): {1, 3340}, {2, 5226}, {8, 3617}, {9, 3731}, {78, 3984}, {312, 42034}, {522, 28161}, {663, 48338}, {2321, 4058}, {3680, 10563}, {4521, 14350}, {4853, 11530}, {28162, 109}, {30712, 7}, {31503, 65}, {39980, 57}
X(56201) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 18231, 39800}

X(56202) = KP3(X(9)) OF X(8) AND X(6)

Barycentrics    (a-b-c)*(a^3+a^2*c+a*b*c+b^2*(b+c))*(a^3+a^2*b+a*b*c+c^2*(b+c)) : :

X(56202) lies on these lines: {8, 31}, {25, 318}, {41, 346}, {55, 341}, {56, 75}, {78, 904}, {280, 2208}, {1036, 3685}, {1043, 2194}, {2204, 2322}, {6186, 52344}, {6187, 52409}, {11679, 37603}, {34858, 51565}, {37087, 40445}, {37573, 41839}

X(56202) = trilinear pole of line {3063, 3239}
X(56202) = X(i)-isoconjugate-of-X(j) for these {i, j}: {56, 986}, {57, 2277}, {604, 27184}
X(56202) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 986}, {3161, 27184}, {5452, 2277}
X(56202) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(5255)}}, {{A, B, C, X(2), X(26065)}}, {{A, B, C, X(7), X(4339)}}, {{A, B, C, X(8), X(75)}}, {{A, B, C, X(9), X(979)}}, {{A, B, C, X(21), X(25)}}, {{A, B, C, X(29), X(4195)}}, {{A, B, C, X(78), X(7081)}}, {{A, B, C, X(86), X(38251)}}, {{A, B, C, X(261), X(36602)}}, {{A, B, C, X(314), X(56146)}}, {{A, B, C, X(333), X(37652)}}, {{A, B, C, X(958), X(34820)}}, {{A, B, C, X(1220), X(52549)}}, {{A, B, C, X(1791), X(26264)}}, {{A, B, C, X(1821), X(17743)}}, {{A, B, C, X(4076), X(4866)}}, {{A, B, C, X(4183), X(37091)}}, {{A, B, C, X(4518), X(33163)}}, {{A, B, C, X(5710), X(37542)}}, {{A, B, C, X(19765), X(37540)}}, {{A, B, C, X(36798), X(43531)}}, {{A, B, C, X(37573), X(37603)}}
X(56202) = barycentric product X(i)*X(j) for these (i, j): {312, 987}, {56046, 8}
X(56202) = barycentric quotient X(i)/X(j) for these (i, j): {8, 27184}, {9, 986}, {55, 2277}, {987, 57}, {56046, 7}

X(56203) = KP3(X(9)) OF X(8) AND X(9)

Barycentrics    a*(a-b-c)*(2*a+2*b+c)*(2*a+b+2*c) : :

X(56203) lies on the Feuerbach hyperbola and on these lines: {1, 2308}, {2, 79}, {3, 10308}, {4, 2355}, {7, 5550}, {8, 3683}, {9, 4420}, {10, 5560}, {21, 56177}, {44, 941}, {45, 2298}, {55, 32635}, {80, 3617}, {84, 37106}, {100, 51572}, {104, 8652}, {145, 13606}, {191, 16859}, {376, 26202}, {405, 11684}, {452, 6598}, {497, 43741}, {518, 56028}, {631, 9809}, {958, 1320}, {960, 2320}, {1000, 20050}, {1155, 5556}, {1156, 5217}, {1172, 11107}, {1389, 7489}, {1392, 3877}, {1697, 31509}, {1708, 5665}, {1770, 3634}, {2346, 5220}, {2478, 11604}, {2481, 32042}, {2975, 15179}, {3062, 21153}, {3065, 4189}, {3254, 10527}, {3296, 3616}, {3305, 35242}, {3523, 16005}, {3524, 22936}, {3545, 22937}, {3551, 27627}, {3621, 5559}, {3626, 43731}, {3650, 50202}, {3680, 5250}, {3685, 56087}, {3871, 56115}, {3935, 7162}, {4512, 4866}, {4640, 19877}, {4652, 31507}, {4900, 5234}, {5047, 5221}, {5260, 12702}, {5273, 43740}, {5424, 5692}, {5506, 17572}, {5557, 20078}, {5902, 17544}, {6601, 52653}, {6910, 10266}, {7319, 37568}, {9782, 17552}, {10032, 50714}, {11279, 30144}, {12514, 17098}, {12532, 56036}, {12867, 13615}, {14450, 16845}, {16866, 34195}, {17418, 23838}, {18483, 54357}, {19862, 27186}, {23958, 25542}, {27065, 36599}, {27383, 34919}, {33576, 35445}, {33696, 46933}, {35355, 48074}, {37567, 55924}, {37572, 46931}, {37582, 43733}, {37605, 55921}

X(56203) = isogonal conjugate of X(5221)
X(56203) = anticomplement of X(41862)
X(56203) = trilinear pole of line {650, 35057}
X(56203) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 5221}, {6, 4654}, {34, 3927}, {56, 1698}, {57, 16777}, {65, 4658}, {73, 31902}, {109, 4802}, {269, 3715}, {514, 36074}, {604, 28605}, {651, 4813}, {664, 4834}, {1397, 30596}, {1400, 5333}, {1405, 30589}, {1407, 4007}, {1408, 4066}, {1411, 4880}, {1414, 48005}, {1415, 4823}, {1427, 4877}, {1461, 4820}, {2334, 5586}, {4551, 4840}, {4559, 4960}, {4565, 4838}, {4573, 4826}, {4756, 43924}, {4898, 40151}, {4938, 7316}, {4949, 38828}
X(56203) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 1698}, {3, 5221}, {9, 4654}, {11, 4802}, {442, 3824}, {1146, 4823}, {3161, 28605}, {5452, 16777}, {6600, 3715}, {11517, 3927}, {24771, 4007}, {35204, 4880}, {35508, 4820}, {38991, 4813}, {39025, 4834}, {40582, 5333}, {40602, 4658}, {40608, 48005}, {41862, 41862}, {51576, 5586}, {55064, 4838}, {55067, 4960}
X(56203) = X(i)-Ceva conjugate of X(j) for these {i, j}: {30598, 25417}
X(56203) = X(i)-cross conjugate of X(j) for these {i, j}: {3876, 8}
X(56203) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(2), X(2349)}}, {{A, B, C, X(3), X(3579)}}, {{A, B, C, X(6), X(5302)}}, {{A, B, C, X(10), X(4067)}}, {{A, B, C, X(28), X(31156)}}, {{A, B, C, X(29), X(16865)}}, {{A, B, C, X(35), X(3431)}}, {{A, B, C, X(44), X(958)}}, {{A, B, C, X(45), X(960)}}, {{A, B, C, X(55), X(60)}}, {{A, B, C, X(56), X(41432)}}, {{A, B, C, X(58), X(33635)}}, {{A, B, C, X(78), X(3951)}}, {{A, B, C, X(88), X(2339)}}, {{A, B, C, X(89), X(333)}}, {{A, B, C, X(105), X(10385)}}, {{A, B, C, X(200), X(5550)}}, {{A, B, C, X(220), X(15254)}}, {{A, B, C, X(271), X(9778)}}, {{A, B, C, X(280), X(44687)}}, {{A, B, C, X(285), X(6605)}}, {{A, B, C, X(341), X(17249)}}, {{A, B, C, X(346), X(1098)}}, {{A, B, C, X(452), X(13739)}}, {{A, B, C, X(521), X(28146)}}, {{A, B, C, X(765), X(1219)}}, {{A, B, C, X(959), X(2161)}}, {{A, B, C, X(1001), X(17201)}}, {{A, B, C, X(1036), X(34820)}}, {{A, B, C, X(1043), X(41847)}}, {{A, B, C, X(1155), X(5217)}}, {{A, B, C, X(1167), X(37741)}}, {{A, B, C, X(1212), X(5220)}}, {{A, B, C, X(1220), X(56107)}}, {{A, B, C, X(1247), X(39956)}}, {{A, B, C, X(1334), X(2053)}}, {{A, B, C, X(1385), X(8148)}}, {{A, B, C, X(1443), X(4294)}}, {{A, B, C, X(1708), X(5273)}}, {{A, B, C, X(1793), X(34259)}}, {{A, B, C, X(2115), X(6065)}}, {{A, B, C, X(2164), X(3450)}}, {{A, B, C, X(2185), X(30711)}}, {{A, B, C, X(2218), X(9309)}}, {{A, B, C, X(3160), X(43178)}}, {{A, B, C, X(3161), X(5250)}}, {{A, B, C, X(3478), X(32427)}}, {{A, B, C, X(3615), X(56146)}}, {{A, B, C, X(3617), X(4511)}}, {{A, B, C, X(3621), X(4861)}}, {{A, B, C, X(3647), X(35193)}}, {{A, B, C, X(3678), X(6701)}}, {{A, B, C, X(3872), X(20050)}}, {{A, B, C, X(3876), X(4877)}}, {{A, B, C, X(3895), X(31722)}}, {{A, B, C, X(3935), X(10527)}}, {{A, B, C, X(4102), X(27789)}}, {{A, B, C, X(4518), X(7226)}}, {{A, B, C, X(4560), X(39740)}}, {{A, B, C, X(4567), X(32022)}}, {{A, B, C, X(5204), X(37568)}}, {{A, B, C, X(5234), X(16670)}}, {{A, B, C, X(6557), X(40434)}}, {{A, B, C, X(6740), X(43531)}}, {{A, B, C, X(7288), X(52429)}}, {{A, B, C, X(9083), X(17127)}}, {{A, B, C, X(11375), X(52371)}}, {{A, B, C, X(12702), X(13624)}}, {{A, B, C, X(20078), X(27065)}}, {{A, B, C, X(24798), X(56151)}}, {{A, B, C, X(25417), X(42030)}}, {{A, B, C, X(27549), X(33950)}}, {{A, B, C, X(31359), X(52409)}}, {{A, B, C, X(36588), X(56137)}}, {{A, B, C, X(37567), X(37600)}}, {{A, B, C, X(37606), X(50193)}}, {{A, B, C, X(40436), X(43533)}}, {{A, B, C, X(41872), X(52405)}}, {{A, B, C, X(42318), X(44178)}}, {{A, B, C, X(44040), X(55091)}}
X(56203) = barycentric product X(i)*X(j) for these (i, j): {1, 42030}, {318, 56070}, {2320, 30590}, {3699, 48074}, {4391, 8652}, {25417, 8}, {28625, 314}, {30597, 4007}, {30598, 9}, {32042, 650}, {34819, 3596}, {37211, 522}
X(56203) = barycentric quotient X(i)/X(j) for these (i, j): {1, 4654}, {6, 5221}, {8, 28605}, {9, 1698}, {21, 5333}, {55, 16777}, {200, 4007}, {219, 3927}, {220, 3715}, {284, 4658}, {312, 30596}, {522, 4823}, {644, 4756}, {650, 4802}, {663, 4813}, {692, 36074}, {1172, 31902}, {1449, 5586}, {2320, 30589}, {2321, 4066}, {2323, 4880}, {2328, 4877}, {3063, 4834}, {3158, 4898}, {3684, 4716}, {3689, 4727}, {3709, 48005}, {3737, 4960}, {3900, 4820}, {3907, 4842}, {4041, 4838}, {4162, 4949}, {4435, 4810}, {4513, 4942}, {4895, 4958}, {7252, 4840}, {8652, 651}, {25417, 7}, {28625, 65}, {30598, 85}, {32042, 4554}, {32635, 43260}, {34819, 56}, {35057, 23883}, {37211, 664}, {40937, 3824}, {42030, 75}, {48074, 3676}, {56070, 77}
X(56203) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3647, 41872, 2}

X(56204) = KP3(X(9)) OF X(8) AND X(21)

Barycentrics    a*(a+b)*(a-b-c)*(a+c)*(a+3*b+c)*(a+b+3*c) : :

X(56204) lies on these lines: {2, 1434}, {9, 81}, {10, 51505}, {21, 200}, {27, 281}, {270, 4183}, {333, 346}, {958, 2334}, {1014, 7308}, {1817, 19605}, {2184, 24635}, {2185, 2287}, {2297, 3305}, {2363, 5297}, {3945, 44306}, {4606, 5325}, {4614, 27174}, {4627, 52663}, {4633, 36796}, {4921, 36916}, {5333, 18228}, {5745, 7110}, {7079, 14014}, {8694, 53707}, {14005, 18250}, {16704, 56200}, {23617, 27065}, {26637, 55989}, {30599, 30854}

X(56204) = trilinear pole of line {3737, 3900}
X(56204) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 3671}, {34, 4047}, {37, 3361}, {42, 21454}, {56, 5257}, {57, 37593}, {65, 1449}, {109, 4841}, {181, 42028}, {391, 1042}, {461, 52373}, {608, 4101}, {651, 4822}, {658, 8653}, {664, 4832}, {1106, 42712}, {1214, 5338}, {1400, 3616}, {1402, 19804}, {1407, 4061}, {1409, 5342}, {1415, 4815}, {1427, 4512}, {1458, 14625}, {1461, 4843}, {1880, 4652}, {2197, 31903}, {3668, 4258}, {4551, 4790}, {4557, 30723}, {4559, 4778}, {4765, 53321}, {5586, 28625}, {7250, 30728}
X(56204) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 5257}, {9, 3671}, {11, 4841}, {1146, 4815}, {5452, 37593}, {6552, 42712}, {11517, 4047}, {24771, 4061}, {35508, 4843}, {38991, 4822}, {39025, 4832}, {40582, 3616}, {40589, 3361}, {40592, 21454}, {40602, 1449}, {40605, 19804}, {40625, 4801}, {55067, 4778}, {55068, 4765}
X(56204) = X(i)-cross conjugate of X(j) for these {i, j}: {4877, 21}
X(56204) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(5234)}}, {{A, B, C, X(2), X(9)}}, {{A, B, C, X(8), X(1255)}}, {{A, B, C, X(21), X(27)}}, {{A, B, C, X(55), X(967)}}, {{A, B, C, X(63), X(1792)}}, {{A, B, C, X(88), X(2339)}}, {{A, B, C, X(226), X(12867)}}, {{A, B, C, X(284), X(1171)}}, {{A, B, C, X(285), X(46880)}}, {{A, B, C, X(312), X(32635)}}, {{A, B, C, X(314), X(39734)}}, {{A, B, C, X(345), X(19822)}}, {{A, B, C, X(943), X(13478)}}, {{A, B, C, X(960), X(5302)}}, {{A, B, C, X(1029), X(6598)}}, {{A, B, C, X(1156), X(44733)}}, {{A, B, C, X(1170), X(1751)}}, {{A, B, C, X(1320), X(42030)}}, {{A, B, C, X(1793), X(1812)}}, {{A, B, C, X(3218), X(5325)}}, {{A, B, C, X(3219), X(5745)}}, {{A, B, C, X(3305), X(18228)}}, {{A, B, C, X(3452), X(27065)}}, {{A, B, C, X(3680), X(27789)}}, {{A, B, C, X(3687), X(5297)}}, {{A, B, C, X(4866), X(25430)}}, {{A, B, C, X(7259), X(37216)}}, {{A, B, C, X(10308), X(55090)}}, {{A, B, C, X(11679), X(17018)}}, {{A, B, C, X(16948), X(17185)}}, {{A, B, C, X(18750), X(24635)}}, {{A, B, C, X(27174), X(52891)}}, {{A, B, C, X(30582), X(30713)}}, {{A, B, C, X(30608), X(39962)}}, {{A, B, C, X(38271), X(45100)}}, {{A, B, C, X(43757), X(45393)}}
X(56204) = barycentric product X(i)*X(j) for these (i, j): {21, 5936}, {274, 34820}, {284, 40023}, {1021, 4624}, {2334, 314}, {3737, 53658}, {4391, 4627}, {4397, 5545}, {4560, 4606}, {4614, 522}, {4633, 650}, {4866, 86}, {18155, 8694}, {25430, 333}, {47915, 645}, {56048, 8}, {56086, 81}
X(56204) = barycentric quotient X(i)/X(j) for these (i, j): {1, 3671}, {9, 5257}, {21, 3616}, {29, 5342}, {55, 37593}, {58, 3361}, {78, 4101}, {81, 21454}, {200, 4061}, {219, 4047}, {270, 31903}, {283, 4652}, {284, 1449}, {294, 14625}, {333, 19804}, {346, 42712}, {522, 4815}, {650, 4841}, {663, 4822}, {1019, 30723}, {1021, 4765}, {1043, 4673}, {2185, 42028}, {2287, 391}, {2299, 5338}, {2328, 4512}, {2334, 65}, {3063, 4832}, {3684, 4771}, {3689, 4819}, {3737, 4778}, {3900, 4843}, {4183, 461}, {4267, 4719}, {4433, 4829}, {4435, 4839}, {4560, 4801}, {4606, 4552}, {4614, 664}, {4627, 651}, {4633, 4554}, {4658, 5586}, {4866, 10}, {5545, 934}, {5936, 1441}, {7252, 4790}, {7253, 4811}, {7259, 30728}, {8641, 8653}, {8694, 4551}, {25430, 226}, {34074, 4559}, {34820, 37}, {40023, 349}, {47915, 7178}, {56048, 7}, {56086, 321}, {56181, 4734}

X(56205) = KP3(X(9)) OF X(8) AND X(33)

Barycentrics    (a-b-c)*(a^2+b^2+2*a*c+2*b*c-c^2)*(a^2+2*a*b-b^2+2*b*c+c^2) : :

X(56205) lies on these lines: {2, 4451}, {8, 193}, {75, 7196}, {318, 37384}, {341, 17787}, {346, 5281}, {1043, 27958}, {2322, 14006}, {5686, 6556}, {7172, 56180}, {8769, 39721}, {11683, 24280}, {11997, 56102}

X(56205) = trilinear pole of line {3239, 3907}
X(56205) = X(i)-isoconjugate-of-X(j) for these {i, j}: {56, 17594}, {109, 48136}, {604, 17257}, {1408, 4104}
X(56205) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 17594}, {11, 48136}, {3161, 17257}
X(56205) = X(i)-cross conjugate of X(j) for these {i, j}: {11679, 8}
X(56205) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(894)}}, {{A, B, C, X(7), X(3424)}}, {{A, B, C, X(8), X(75)}}, {{A, B, C, X(9), X(291)}}, {{A, B, C, X(19), X(21)}}, {{A, B, C, X(29), X(50408)}}, {{A, B, C, X(55), X(45966)}}, {{A, B, C, X(82), X(2320)}}, {{A, B, C, X(193), X(333)}}, {{A, B, C, X(256), X(2319)}}, {{A, B, C, X(261), X(34919)}}, {{A, B, C, X(281), X(314)}}, {{A, B, C, X(391), X(17731)}}, {{A, B, C, X(393), X(52550)}}, {{A, B, C, X(522), X(5847)}}, {{A, B, C, X(673), X(5281)}}, {{A, B, C, X(897), X(56203)}}, {{A, B, C, X(941), X(56154)}}, {{A, B, C, X(1261), X(24477)}}, {{A, B, C, X(1320), X(23051)}}, {{A, B, C, X(2053), X(9292)}}, {{A, B, C, X(2344), X(13610)}}, {{A, B, C, X(3161), X(5686)}}, {{A, B, C, X(3705), X(7172)}}, {{A, B, C, X(4373), X(43749)}}, {{A, B, C, X(4518), X(5936)}}, {{A, B, C, X(4876), X(17038)}}, {{A, B, C, X(6557), X(7229)}}, {{A, B, C, X(17363), X(30711)}}, {{A, B, C, X(49529), X(55076)}}
X(56205) = barycentric product X(i)*X(j) for these (i, j): {56044, 8}
X(56205) = barycentric quotient X(i)/X(j) for these (i, j): {8, 17257}, {9, 17594}, {650, 48136}, {2321, 4104}, {56044, 7}

X(56206) = KP3(X(9)) OF X(9) AND X(21)

Barycentrics    a*(a-b-c)*(3*a+4*b+3*c)*(3*a+3*b+4*c) : :

X(56206) lies on the Feuerbach hyperbola and on these lines: {1, 3988}, {2, 5551}, {4, 28216}, {7, 56061}, {104, 28214}, {1000, 20054}, {1698, 43732}, {2298, 15492}, {3296, 15325}, {3715, 56203}, {4745, 17501}, {5556, 10895}, {7317, 20052}, {10266, 18253}, {10308, 22937}, {10592, 43733}, {15171, 43734}, {15481, 17546}, {18490, 50398}

X(56206) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 4114}, {56, 19862}, {109, 28213}, {3649, 39670}
X(56206) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 19862}, {9, 4114}, {11, 28213}
X(56206) = X(i)-Ceva conjugate of X(j) for these {i, j}: {56061, 56037}
X(56206) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(10), X(3988)}}, {{A, B, C, X(29), X(16861)}}, {{A, B, C, X(517), X(31666)}}, {{A, B, C, X(521), X(28216)}}, {{A, B, C, X(960), X(15492)}}, {{A, B, C, X(3872), X(20054)}}, {{A, B, C, X(4518), X(42041)}}
X(56206) = barycentric product X(i)*X(j) for these (i, j): {28214, 4391}, {56037, 8}, {56061, 9}
X(56206) = barycentric quotient X(i)/X(j) for these (i, j): {1, 4114}, {9, 19862}, {650, 28213}, {28214, 651}, {56037, 7}, {56061, 85}

X(56207) = KP3(X(9)) OF X(9) AND X(33)

Barycentrics    a*(a-b-c)*(a^2+3*b^2+c^2)*(a^2+b^2+3*c^2) : :

X(56207) lies on these lines: {9, 5324}, {33, 33299}, {37, 614}, {210, 2082}, {226, 7195}, {479, 28739}, {497, 2321}, {1826, 1851}, {1903, 34817}, {7308, 16600}, {35144, 54971}

X(56207) = X(i)-isoconjugate-of-X(j) for these {i, j}: {7, 30435}, {56, 3618}, {109, 48060}, {222, 6995}, {278, 3796}, {604, 39731}, {608, 3785}, {651, 3803}, {1397, 40022}, {1401, 42037}, {1415, 48109}, {3793, 7316}, {3800, 4565}, {3804, 4573}
X(56207) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 3618}, {11, 48060}, {1146, 48109}, {3161, 39731}, {38991, 3803}, {40182, 57}, {55064, 3800}
X(56207) = X(i)-Ceva conjugate of X(j) for these {i, j}: {18840, 23051}
X(56207) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(17599)}}, {{A, B, C, X(8), X(34)}}, {{A, B, C, X(9), X(33)}}, {{A, B, C, X(78), X(15523)}}, {{A, B, C, X(200), X(17284)}}, {{A, B, C, X(1212), X(31435)}}, {{A, B, C, X(2285), X(3974)}}, {{A, B, C, X(2298), X(45100)}}, {{A, B, C, X(2339), X(4876)}}, {{A, B, C, X(3061), X(39248)}}, {{A, B, C, X(4423), X(4866)}}, {{A, B, C, X(4514), X(4863)}}, {{A, B, C, X(5750), X(7308)}}, {{A, B, C, X(7018), X(56179)}}, {{A, B, C, X(8801), X(23051)}}, {{A, B, C, X(28070), X(28739)}}, {{A, B, C, X(32635), X(56102)}}
X(56207) = barycentric product X(i)*X(j) for these (i, j): {78, 8801}, {312, 39951}, {318, 34817}, {4041, 54971}, {4086, 907}, {18840, 9}, {23051, 8}
X(56207) = barycentric quotient X(i)/X(j) for these (i, j): {8, 39731}, {9, 3618}, {33, 6995}, {41, 30435}, {78, 3785}, {212, 3796}, {312, 40022}, {522, 48109}, {650, 48060}, {663, 3803}, {907, 1414}, {4041, 3800}, {8801, 273}, {18840, 85}, {23051, 7}, {33299, 8362}, {34817, 77}, {39951, 57}, {54971, 4625}

X(56208) = KP3(X(9)) OF X(9) AND X(55)

Barycentrics    a*(a-b-c)*(2*b*c+a*(2*b+c))*(2*b*c+a*(b+2*c)) : :

X(56208) lies on these lines: {2, 42302}, {6, 748}, {9, 3706}, {19, 1889}, {55, 3691}, {57, 4059}, {284, 37658}, {333, 28809}, {405, 1174}, {673, 5278}, {2258, 5283}, {2291, 6013}, {2299, 28044}, {3715, 7077}, {5115, 5275}, {17110, 19730}

X(56208) = trilinear pole of line {663, 4501}
X(56208) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 16878}, {56, 4687}, {57, 17018}, {109, 47666}, {226, 39673}, {651, 6005}, {4554, 8655}, {4565, 48407}, {4573, 50483}
X(56208) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 4687}, {11, 47666}, {5452, 17018}, {32664, 16878}, {38991, 6005}, {55064, 48407}
X(56208) = X(i)-Ceva conjugate of X(j) for these {i, j}: {56051, 10013}
X(56208) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(210)}}, {{A, B, C, X(6), X(9)}}, {{A, B, C, X(8), X(3691)}}, {{A, B, C, X(21), X(1889)}}, {{A, B, C, X(200), X(16832)}}, {{A, B, C, X(220), X(16552)}}, {{A, B, C, X(354), X(5686)}}, {{A, B, C, X(391), X(940)}}, {{A, B, C, X(405), X(1212)}}, {{A, B, C, X(522), X(9038)}}, {{A, B, C, X(748), X(4387)}}, {{A, B, C, X(958), X(5283)}}, {{A, B, C, X(1334), X(2350)}}, {{A, B, C, X(2287), X(19732)}}, {{A, B, C, X(2321), X(39983)}}, {{A, B, C, X(3684), X(3715)}}, {{A, B, C, X(3700), X(34258)}}, {{A, B, C, X(4183), X(37075)}}, {{A, B, C, X(4254), X(5115)}}, {{A, B, C, X(4423), X(4866)}}, {{A, B, C, X(4512), X(39980)}}, {{A, B, C, X(4876), X(42030)}}, {{A, B, C, X(5275), X(14555)}}, {{A, B, C, X(7220), X(39748)}}, {{A, B, C, X(17330), X(28920)}}, {{A, B, C, X(30711), X(40779)}}, {{A, B, C, X(56154), X(56203)}}
X(56208) = barycentric product X(i)*X(j) for these (i, j): {1, 56087}, {21, 46772}, {522, 6013}, {10013, 8}, {56051, 9}
X(56208) = barycentric quotient X(i)/X(j) for these (i, j): {9, 4687}, {31, 16878}, {55, 17018}, {650, 47666}, {663, 6005}, {2194, 39673}, {4041, 48407}, {6013, 664}, {10013, 7}, {46772, 1441}, {56051, 85}, {56087, 75}

X(56209) = KP3(X(10)) OF X(2) AND X(10)

Barycentrics    (b+c)*(3*a+4*b+3*c)*(3*a+3*b+4*c) : :

X(56209) lies on the Kiepert hyperbola and on these lines: {2, 4399}, {4, 28216}, {98, 28214}, {3617, 19743}, {4049, 47678}, {6625, 43990}, {17758, 29593}, {19804, 39994}, {27797, 41809}, {30473, 40013}, {32014, 51353}

X(56209) = X(i)-isoconjugate-of-X(j) for these {i, j}: {163, 28213}, {1100, 39670}, {1333, 19862}, {2194, 4114}
X(56209) = X(i)-Dao conjugate of X(j) for these {i, j}: {37, 19862}, {115, 28213}, {1214, 4114}
X(56209) = X(i)-cross conjugate of X(j) for these {i, j}: {4838, 3952}
X(56209) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(30582)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(330), X(3995)}}, {{A, B, C, X(525), X(28216)}}, {{A, B, C, X(1268), X(32089)}}, {{A, B, C, X(1654), X(43990)}}, {{A, B, C, X(3992), X(31011)}}, {{A, B, C, X(4651), X(29593)}}, {{A, B, C, X(4674), X(25417)}}, {{A, B, C, X(4714), X(26860)}}, {{A, B, C, X(5224), X(19743)}}, {{A, B, C, X(8013), X(51353)}}, {{A, B, C, X(27809), X(46772)}}, {{A, B, C, X(28605), X(39738)}}, {{A, B, C, X(28650), X(30594)}}, {{A, B, C, X(30711), X(30713)}}, {{A, B, C, X(35058), X(39708)}}
X(56209) = barycentric product X(i)*X(j) for these (i, j): {10, 56061}, {321, 56037}, {1441, 56206}, {28214, 850}
X(56209) = barycentric quotient X(i)/X(j) for these (i, j): {10, 19862}, {226, 4114}, {523, 28213}, {1126, 39670}, {28214, 110}, {56037, 81}, {56061, 86}, {56206, 21}

X(56210) = KP3(X(10)) OF X(2) AND X(37)

Barycentrics    (a*(b+c)+b*(2*b+c))*(a*(b+c)+c*(b+2*c)) : :

X(56210) lies on the Kiepert hyperbola and on these lines: {2, 21024}, {4, 1654}, {8, 40718}, {10, 192}, {69, 6625}, {76, 17238}, {83, 17349}, {98, 43359}, {194, 10479}, {226, 3212}, {274, 40031}, {321, 6376}, {330, 3741}, {391, 5395}, {594, 53675}, {2996, 5232}, {3617, 13576}, {3831, 41836}, {3948, 34258}, {4444, 50457}, {4658, 10449}, {4772, 20255}, {7783, 37660}, {13478, 37416}, {14534, 37683}, {16996, 33954}, {17230, 30588}, {17232, 17758}, {17239, 20943}, {17499, 50074}, {17503, 50271}, {18135, 40024}, {20081, 30966}, {20913, 40012}, {21071, 27268}, {24688, 25625}, {25102, 48630}, {26043, 26801}, {27040, 56167}, {27318, 50605}, {27430, 41527}, {31330, 41838}, {31999, 50608}, {33297, 50133}, {34284, 40017}, {35353, 47666}, {40848, 43534}

X(56210) = isotomic conjugate of X(17379)
X(56210) = anticomplement of X(41849)
X(56210) = trilinear pole of line {3835, 4500}
X(56210) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 17379}, {32, 31997}, {692, 4932}, {1333, 43223}, {17689, 18757}
X(56210) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 17379}, {37, 43223}, {1086, 4932}, {6376, 31997}, {41849, 41849}
X(56210) = X(i)-Ceva conjugate of X(j) for these {i, j}: {56052, 17038}
X(56210) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {28621, 17137}
X(56210) = X(i)-cross conjugate of X(j) for these {i, j}: {5224, 2}, {33154, 7}, {47514, 264}
X(56210) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(27494)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(48875)}}, {{A, B, C, X(6), X(17238)}}, {{A, B, C, X(7), X(17248)}}, {{A, B, C, X(8), X(3661)}}, {{A, B, C, X(27), X(37164)}}, {{A, B, C, X(69), X(1654)}}, {{A, B, C, X(75), X(192)}}, {{A, B, C, X(85), X(27483)}}, {{A, B, C, X(141), X(17349)}}, {{A, B, C, X(193), X(5232)}}, {{A, B, C, X(274), X(31060)}}, {{A, B, C, X(310), X(18832)}}, {{A, B, C, X(334), X(5936)}}, {{A, B, C, X(335), X(31359)}}, {{A, B, C, X(391), X(3620)}}, {{A, B, C, X(514), X(28522)}}, {{A, B, C, X(594), X(1502)}}, {{A, B, C, X(596), X(9328)}}, {{A, B, C, X(673), X(39730)}}, {{A, B, C, X(966), X(17300)}}, {{A, B, C, X(1211), X(37683)}}, {{A, B, C, X(1218), X(46772)}}, {{A, B, C, X(1219), X(6630)}}, {{A, B, C, X(1246), X(5224)}}, {{A, B, C, X(1432), X(51844)}}, {{A, B, C, X(1509), X(39720)}}, {{A, B, C, X(2165), X(23927)}}, {{A, B, C, X(2292), X(51311)}}, {{A, B, C, X(3227), X(39711)}}, {{A, B, C, X(3314), X(4136)}}, {{A, B, C, X(3617), X(3912)}}, {{A, B, C, X(3679), X(17230)}}, {{A, B, C, X(3741), X(6382)}}, {{A, B, C, X(3948), X(7235)}}, {{A, B, C, X(4373), X(39712)}}, {{A, B, C, X(4431), X(10405)}}, {{A, B, C, X(4461), X(24547)}}, {{A, B, C, X(4492), X(40432)}}, {{A, B, C, X(4658), X(25417)}}, {{A, B, C, X(4678), X(29594)}}, {{A, B, C, X(4791), X(30590)}}, {{A, B, C, X(5361), X(31037)}}, {{A, B, C, X(5739), X(37653)}}, {{A, B, C, X(6381), X(47666)}}, {{A, B, C, X(7148), X(52651)}}, {{A, B, C, X(8024), X(21016)}}, {{A, B, C, X(9780), X(29576)}}, {{A, B, C, X(14996), X(27081)}}, {{A, B, C, X(15315), X(17946)}}, {{A, B, C, X(17232), X(17277)}}, {{A, B, C, X(17251), X(50133)}}, {{A, B, C, X(17271), X(50074)}}, {{A, B, C, X(17493), X(18891)}}, {{A, B, C, X(17555), X(37416)}}, {{A, B, C, X(17743), X(39729)}}, {{A, B, C, X(18135), X(20913)}}, {{A, B, C, X(20917), X(27430)}}, {{A, B, C, X(23493), X(30496)}}, {{A, B, C, X(24603), X(46933)}}, {{A, B, C, X(25446), X(27709)}}, {{A, B, C, X(27299), X(29679)}}, {{A, B, C, X(29591), X(29659)}}, {{A, B, C, X(32782), X(37652)}}, {{A, B, C, X(39721), X(39724)}}, {{A, B, C, X(39957), X(56174)}}, {{A, B, C, X(40776), X(51223)}}, {{A, B, C, X(49560), X(51353)}}
X(56210) = barycentric product X(i)*X(j) for these (i, j): {10, 56052}, {321, 56066}, {17038, 75}, {39967, 76}, {43359, 850}
X(56210) = barycentric quotient X(i)/X(j) for these (i, j): {2, 17379}, {10, 43223}, {75, 31997}, {514, 4932}, {1654, 17689}, {5224, 41849}, {17038, 1}, {28621, 56047}, {39967, 6}, {43359, 110}, {56052, 86}, {56066, 81}
X(56210) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {39967, 56052, 2}

X(56211) = KP3(X(10)) OF X(37) AND X(37)

Barycentrics    (b+c)*(2*a*b^2*c+b^2*c^2+a^2*(b^2+c^2))*(2*a*b*c^2+b^2*c^2+a^2*(b^2+c^2)) : :

X(56211) lies on the Kiepert hyperbola and on these lines: {2, 1740}, {4, 51913}, {10, 21838}, {75, 40162}, {76, 3741}, {226, 39780}, {321, 3728}, {2051, 45305}, {3223, 23652}, {3840, 17758}, {4651, 56197}, {22039, 34475}, {31330, 41838}, {50295, 56161}

X(56211) = trilinear pole of line {40627, 523}
X(56211) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(37), X(6384)}}, {{A, B, C, X(42), X(256)}}, {{A, B, C, X(75), X(1740)}}, {{A, B, C, X(291), X(1245)}}, {{A, B, C, X(594), X(21257)}}, {{A, B, C, X(2296), X(31330)}}, {{A, B, C, X(3840), X(4651)}}, {{A, B, C, X(4685), X(30942)}}, {{A, B, C, X(15320), X(40418)}}, {{A, B, C, X(16887), X(21814)}}, {{A, B, C, X(20888), X(21753)}}, {{A, B, C, X(27701), X(33138)}}, {{A, B, C, X(32010), X(40747)}}

X(56212) = KP3(X(10)) OF X(37) AND X(75)

Barycentrics    b*c*(b*c+a*(3*b+c))*(b*c+a*(b+3*c)) : :

X(56212) lies on these lines: {2, 17144}, {7, 26038}, {10, 6384}, {43, 86}, {75, 3971}, {310, 6376}, {312, 27483}, {335, 19804}, {350, 5936}, {675, 29199}, {899, 2296}, {1268, 30963}, {1698, 56052}, {3741, 40027}, {4359, 27494}, {4383, 14621}, {4479, 55955}, {4688, 25116}, {16569, 40418}, {16606, 41836}, {19875, 34020}, {27439, 27447}, {30598, 43223}, {31002, 31330}

X(56212) = isotomic conjugate of X(26102)
X(56212) = complement of X(41912)
X(56212) = trilinear pole of line {4502, 21834}
X(56212) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 26102}, {32, 4699}, {692, 29198}, {32739, 48399}
X(56212) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 26102}, {1086, 29198}, {6376, 4699}, {40619, 48399}
X(56212) = X(i)-cross conjugate of X(j) for these {i, j}: {27147, 85}, {48005, 4033}
X(56212) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(7)}}, {{A, B, C, X(8), X(26038)}}, {{A, B, C, X(10), X(43)}}, {{A, B, C, X(42), X(749)}}, {{A, B, C, X(57), X(39717)}}, {{A, B, C, X(85), X(40024)}}, {{A, B, C, X(256), X(39966)}}, {{A, B, C, X(274), X(7033)}}, {{A, B, C, X(291), X(2334)}}, {{A, B, C, X(312), X(51865)}}, {{A, B, C, X(330), X(32095)}}, {{A, B, C, X(334), X(34258)}}, {{A, B, C, X(350), X(19804)}}, {{A, B, C, X(751), X(2350)}}, {{A, B, C, X(899), X(31330)}}, {{A, B, C, X(1220), X(56161)}}, {{A, B, C, X(1698), X(43223)}}, {{A, B, C, X(1909), X(27439)}}, {{A, B, C, X(3223), X(39798)}}, {{A, B, C, X(3741), X(16569)}}, {{A, B, C, X(4359), X(30963)}}, {{A, B, C, X(4383), X(30966)}}, {{A, B, C, X(4479), X(24589)}}, {{A, B, C, X(6686), X(29827)}}, {{A, B, C, X(8026), X(41836)}}, {{A, B, C, X(8056), X(32010)}}, {{A, B, C, X(18827), X(25430)}}, {{A, B, C, X(27807), X(39706)}}, {{A, B, C, X(30571), X(34860)}}, {{A, B, C, X(32018), X(40031)}}, {{A, B, C, X(39395), X(40145)}}, {{A, B, C, X(40017), X(40023)}}
X(56212) = barycentric product X(i)*X(j) for these (i, j): {29199, 3261}, {39738, 75}, {39972, 76}
X(56212) = barycentric quotient X(i)/X(j) for these (i, j): {2, 26102}, {75, 4699}, {514, 29198}, {693, 48399}, {29199, 101}, {39738, 1}, {39972, 6}

X(56213) = KP3(X(37)) OF X(1) AND X(1)

Barycentrics    a*(b+c)*(a^2+2*b^2+2*b*c+c^2+2*a*(b+c))*(a^2+b^2+2*b*c+2*c^2+2*a*(b+c)) : :

X(56213) lies on these lines: {2, 40085}, {37, 17011}, {321, 18140}, {335, 5333}, {594, 3995}, {756, 3293}, {1255, 3954}, {1824, 4222}, {2298, 33761}, {6156, 40592}, {18098, 21816}

X(56213) = trilinear pole of line {4705, 4132}
X(56213) = X(i)-isoconjugate-of-X(j) for these {i, j}: {58, 17398}, {110, 50522}, {284, 52783}
X(56213) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 17398}, {244, 50522}, {40590, 52783}
X(56213) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(6539)}}, {{A, B, C, X(2), X(3293)}}, {{A, B, C, X(10), X(81)}}, {{A, B, C, X(21), X(30713)}}, {{A, B, C, X(37), X(321)}}, {{A, B, C, X(42), X(29610)}}, {{A, B, C, X(226), X(4015)}}, {{A, B, C, X(2238), X(4813)}}, {{A, B, C, X(3954), X(21816)}}, {{A, B, C, X(4043), X(27475)}}, {{A, B, C, X(4080), X(25430)}}, {{A, B, C, X(4674), X(25417)}}, {{A, B, C, X(5276), X(32782)}}, {{A, B, C, X(17038), X(27809)}}, {{A, B, C, X(27789), X(27797)}}, {{A, B, C, X(28606), X(31359)}}
X(56213) = barycentric quotient X(i)/X(j) for these (i, j): {37, 17398}, {65, 52783}, {661, 50522}

X(56214) = KP3(X(37)) OF X(1) AND X(8)

Barycentrics    (b+c)*(a^3*(b+c)+2*a^2*b*(b+c)+b*c*(b^2-c^2)+a*(b^3+2*b^2*c+2*b*c^2-c^3))*(-(b^3*c)+b*c^3+a^3*(b+c)+2*a^2*c*(b+c)+a*(-b^3+2*b^2*c+2*b*c^2+c^3)) : :

X(56214) lies on the Kiepert hyperbola and on these lines: {2, 10468}, {4, 30116}, {10, 14973}, {37, 2051}, {76, 18045}, {226, 40491}, {958, 43531}, {1751, 19731}, {3159, 43677}, {3588, 53083}, {4415, 40515}, {5249, 40013}, {13478, 34261}, {27802, 54972}

X(56214) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(12), X(22020)}}, {{A, B, C, X(37), X(14973)}}, {{A, B, C, X(65), X(53083)}}, {{A, B, C, X(181), X(40147)}}, {{A, B, C, X(306), X(30116)}}, {{A, B, C, X(4674), X(44733)}}, {{A, B, C, X(10408), X(31993)}}, {{A, B, C, X(18097), X(37887)}}, {{A, B, C, X(18134), X(19731)}}, {{A, B, C, X(21688), X(30106)}}, {{A, B, C, X(29653), X(41232)}}, {{A, B, C, X(30710), X(42471)}}, {{A, B, C, X(30713), X(45095)}}

X(56215) = KP3(X(37)) OF X(1) AND X(37)

Barycentrics    a*(b+c)*(3*a+4*b+3*c)*(3*a+3*b+4*c) : :

X(56215) lies on these lines: {1, 3988}, {10, 56209}, {75, 56061}, {596, 3624}, {759, 28214}, {1757, 46971}, {2214, 3731}, {3616, 39697}, {3632, 42285}, {3743, 56134}, {3994, 39711}, {4668, 31359}, {40438, 51294}

X(56215) = X(i)-isoconjugate-of-X(j) for these {i, j}: {58, 19862}, {110, 28213}, {284, 4114}, {1125, 39670}
X(56215) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 19862}, {244, 28213}, {40590, 4114}
X(56215) = X(i)-Ceva conjugate of X(j) for these {i, j}: {56061, 56209}
X(56215) = X(i)-cross conjugate of X(j) for these {i, j}: {48005, 1018}
X(56215) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}}, {{A, B, C, X(4), X(16861)}}, {{A, B, C, X(12), X(3988)}}, {{A, B, C, X(87), X(3293)}}, {{A, B, C, X(756), X(32487)}}, {{A, B, C, X(1255), X(27797)}}, {{A, B, C, X(1698), X(39972)}}, {{A, B, C, X(3616), X(15315)}}, {{A, B, C, X(3649), X(3956)}}, {{A, B, C, X(4080), X(25430)}}, {{A, B, C, X(13576), X(43732)}}, {{A, B, C, X(21816), X(51294)}}, {{A, B, C, X(27789), X(30582)}}, {{A, B, C, X(39748), X(39983)}}, {{A, B, C, X(42041), X(43534)}}
X(56215) = barycentric product X(i)*X(j) for these (i, j): {1, 56209}, {10, 56037}, {37, 56061}, {226, 56206}, {1577, 28214}
X(56215) = barycentric quotient X(i)/X(j) for these (i, j): {37, 19862}, {65, 4114}, {661, 28213}, {28214, 662}, {28615, 39670}, {56037, 86}, {56061, 274}, {56206, 333}, {56209, 75}

X(56216) = KP3(X(37)) OF X(10) AND X(3)

Barycentrics    (a^6+a^5*(b+c)+(b-c)^2*c*(b+c)^3-a^4*(2*b^2+b*c+c^2)-2*a^3*(b^3+c^3)+a^2*(b^4-c^4)+a*(b^5-b^4*c-b*c^4+c^5))*(a^6+a^5*(b+c)+b*(b-c)^2*(b+c)^3-a^4*(b^2+b*c+2*c^2)-2*a^3*(b^3+c^3)+a^2*(-b^4+c^4)+a*(b^5-b^4*c-b*c^4+c^5)) : :

X(56216) lies on the Kiepert hyperbola and on these lines: {4, 2360}, {10, 7078}, {222, 8808}, {223, 40149}, {226, 7011}, {281, 40407}, {459, 5712}, {1751, 23292}, {2051, 11347}, {2052, 41083}, {17532, 54661}, {18641, 54972}

X(56216) = polar conjugate of X(52248)
X(56216) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 52248}
X(56216) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(222)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(29), X(2184)}}, {{A, B, C, X(57), X(36123)}}, {{A, B, C, X(63), X(10570)}}, {{A, B, C, X(86), X(8809)}}, {{A, B, C, X(92), X(17073)}}, {{A, B, C, X(281), X(329)}}, {{A, B, C, X(581), X(3682)}}, {{A, B, C, X(948), X(40960)}}, {{A, B, C, X(996), X(40399)}}, {{A, B, C, X(2297), X(2316)}}, {{A, B, C, X(2339), X(8777)}}, {{A, B, C, X(3346), X(46014)}}, {{A, B, C, X(5712), X(5930)}}, {{A, B, C, X(5739), X(24553)}}, {{A, B, C, X(7532), X(37279)}}, {{A, B, C, X(11109), X(11347)}}, {{A, B, C, X(18134), X(23292)}}, {{A, B, C, X(18641), X(26942)}}, {{A, B, C, X(19684), X(37659)}}, {{A, B, C, X(27398), X(44692)}}
X(56216) = barycentric quotient X(i)/X(j) for these (i, j): {4, 52248}

X(56217) = KP3(X(37)) OF X(10) AND X(7)

Barycentrics    (a^2+(b-c)^2-2*a*(2*b+c))*(a^2+(b-c)^2-2*a*(b+2*c)) : :

X(56217) lies on these lines: {1, 4878}, {2, 3991}, {37, 277}, {57, 3730}, {81, 218}, {105, 3295}, {274, 344}, {278, 17916}, {279, 8232}, {948, 52374}, {1002, 5045}, {1125, 39959}, {1170, 5543}, {1255, 5222}, {1280, 3616}, {1390, 16020}, {2345, 56051}, {3008, 25430}, {4000, 42326}, {4698, 19855}, {5325, 39980}, {8056, 24181}, {16572, 25072}, {16578, 34578}, {17014, 27789}, {17263, 30701}, {17280, 39736}, {25417, 29624}, {27268, 39724}, {27304, 39738}, {30723, 37626}, {34018, 52422}, {43065, 56043}

X(56217) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 4666}
X(56217) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 4666}
X(56217) = X(i)-cross conjugate of X(j) for these {i, j}: {49296, 190}
X(56217) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(4), X(16053)}}, {{A, B, C, X(7), X(6666)}}, {{A, B, C, X(8), X(17758)}}, {{A, B, C, X(9), X(8232)}}, {{A, B, C, X(10), X(5308)}}, {{A, B, C, X(27), X(17552)}}, {{A, B, C, X(37), X(218)}}, {{A, B, C, X(76), X(32013)}}, {{A, B, C, X(85), X(1000)}}, {{A, B, C, X(86), X(18841)}}, {{A, B, C, X(220), X(16601)}}, {{A, B, C, X(241), X(3295)}}, {{A, B, C, X(281), X(2338)}}, {{A, B, C, X(333), X(15998)}}, {{A, B, C, X(335), X(32022)}}, {{A, B, C, X(345), X(44307)}}, {{A, B, C, X(348), X(1807)}}, {{A, B, C, X(514), X(7320)}}, {{A, B, C, X(673), X(3296)}}, {{A, B, C, X(943), X(7131)}}, {{A, B, C, X(948), X(6198)}}, {{A, B, C, X(949), X(2335)}}, {{A, B, C, X(1121), X(7317)}}, {{A, B, C, X(1125), X(4989)}}, {{A, B, C, X(1126), X(42290)}}, {{A, B, C, X(1434), X(18490)}}, {{A, B, C, X(1698), X(29624)}}, {{A, B, C, X(1783), X(42303)}}, {{A, B, C, X(2051), X(10429)}}, {{A, B, C, X(2345), X(4687)}}, {{A, B, C, X(2346), X(44178)}}, {{A, B, C, X(3008), X(3616)}}, {{A, B, C, X(3085), X(25930)}}, {{A, B, C, X(3622), X(31183)}}, {{A, B, C, X(3624), X(17014)}}, {{A, B, C, X(4000), X(17263)}}, {{A, B, C, X(5045), X(5228)}}, {{A, B, C, X(5226), X(5325)}}, {{A, B, C, X(5287), X(19855)}}, {{A, B, C, X(5395), X(32012)}}, {{A, B, C, X(5543), X(10481)}}, {{A, B, C, X(5550), X(50114)}}, {{A, B, C, X(5558), X(14377)}}, {{A, B, C, X(5559), X(10405)}}, {{A, B, C, X(6185), X(43527)}}, {{A, B, C, X(7160), X(21446)}}, {{A, B, C, X(7162), X(36101)}}, {{A, B, C, X(9311), X(32015)}}, {{A, B, C, X(9328), X(44559)}}, {{A, B, C, X(9442), X(17038)}}, {{A, B, C, X(16020), X(17023)}}, {{A, B, C, X(17279), X(17321)}}, {{A, B, C, X(17280), X(27268)}}, {{A, B, C, X(17284), X(39587)}}, {{A, B, C, X(17353), X(28015)}}, {{A, B, C, X(18810), X(38261)}}, {{A, B, C, X(18840), X(31359)}}, {{A, B, C, X(21450), X(41785)}}, {{A, B, C, X(26102), X(27304)}}, {{A, B, C, X(28742), X(41276)}}, {{A, B, C, X(29578), X(50282)}}, {{A, B, C, X(29579), X(50291)}}, {{A, B, C, X(29596), X(48856)}}, {{A, B, C, X(30705), X(39977)}}, {{A, B, C, X(31721), X(43186)}}, {{A, B, C, X(36954), X(43531)}}, {{A, B, C, X(45085), X(45098)}}
X(56217) = barycentric quotient X(i)/X(j) for these (i, j): {1, 4666}

X(56218) = KP3(X(37)) OF X(10) AND X(8)

Barycentrics    (a^3+a^2*(b-c)+(b-c)^2*(b+c)+a*(b^2+4*b*c-c^2))*(a^3+a^2*(-b+c)+(b-c)^2*(b+c)+a*(-b^2+4*b*c+c^2)) : :

X(56218) lies on these lines: {1, 2551}, {2, 20270}, {28, 7952}, {57, 1766}, {81, 329}, {88, 19785}, {89, 9965}, {105, 5020}, {226, 1422}, {277, 3772}, {278, 17720}, {499, 1224}, {517, 959}, {527, 39980}, {938, 1257}, {940, 34051}, {961, 999}, {1002, 12915}, {1219, 4385}, {1255, 37651}, {1280, 10580}, {1997, 3596}, {2401, 23880}, {2990, 5422}, {3086, 44417}, {3672, 44794}, {4000, 6692}, {5226, 34056}, {5292, 51499}, {7271, 7365}, {8102, 41799}, {8257, 39947}, {11019, 39959}, {12652, 24210}, {15474, 33133}, {17019, 56041}, {18743, 30701}, {20196, 25430}, {24440, 33135}, {26745, 33155}, {28161, 35348}, {28808, 30710}, {31142, 39948}, {37594, 37822}, {40836, 41013}

X(56218) = trilinear pole of line {21120, 47136}
X(56218) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 19861}, {284, 12709}
X(56218) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 19861}, {40590, 12709}
X(56218) = X(i)-cross conjugate of X(j) for these {i, j}: {2285, 4}, {3304, 7}
X(56218) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(4), X(312)}}, {{A, B, C, X(7), X(2051)}}, {{A, B, C, X(8), X(5795)}}, {{A, B, C, X(27), X(5084)}}, {{A, B, C, X(37), X(40160)}}, {{A, B, C, X(79), X(45100)}}, {{A, B, C, X(83), X(34523)}}, {{A, B, C, X(92), X(3421)}}, {{A, B, C, X(104), X(2339)}}, {{A, B, C, X(226), X(329)}}, {{A, B, C, X(281), X(1766)}}, {{A, B, C, X(333), X(1000)}}, {{A, B, C, X(344), X(3772)}}, {{A, B, C, X(345), X(1807)}}, {{A, B, C, X(498), X(17019)}}, {{A, B, C, X(499), X(17011)}}, {{A, B, C, X(517), X(940)}}, {{A, B, C, X(527), X(5226)}}, {{A, B, C, X(650), X(7050)}}, {{A, B, C, X(673), X(26105)}}, {{A, B, C, X(938), X(40940)}}, {{A, B, C, X(939), X(1427)}}, {{A, B, C, X(941), X(2316)}}, {{A, B, C, X(948), X(31627)}}, {{A, B, C, X(967), X(42019)}}, {{A, B, C, X(987), X(7281)}}, {{A, B, C, X(999), X(3666)}}, {{A, B, C, X(1068), X(5712)}}, {{A, B, C, X(1171), X(52186)}}, {{A, B, C, X(1217), X(31623)}}, {{A, B, C, X(1434), X(42339)}}, {{A, B, C, X(1476), X(42467)}}, {{A, B, C, X(1997), X(3752)}}, {{A, B, C, X(2297), X(31325)}}, {{A, B, C, X(2338), X(51476)}}, {{A, B, C, X(2341), X(36916)}}, {{A, B, C, X(2985), X(42360)}}, {{A, B, C, X(2999), X(14986)}}, {{A, B, C, X(3008), X(10580)}}, {{A, B, C, X(3085), X(5287)}}, {{A, B, C, X(3086), X(5256)}}, {{A, B, C, X(3296), X(4997)}}, {{A, B, C, X(3582), X(17013)}}, {{A, B, C, X(3664), X(36640)}}, {{A, B, C, X(3672), X(7271)}}, {{A, B, C, X(4000), X(18743)}}, {{A, B, C, X(4102), X(43734)}}, {{A, B, C, X(4358), X(19785)}}, {{A, B, C, X(4385), X(7365)}}, {{A, B, C, X(5020), X(15149)}}, {{A, B, C, X(5219), X(9965)}}, {{A, B, C, X(5222), X(11019)}}, {{A, B, C, X(5228), X(12915)}}, {{A, B, C, X(5308), X(13405)}}, {{A, B, C, X(5435), X(6692)}}, {{A, B, C, X(5558), X(38255)}}, {{A, B, C, X(5559), X(30711)}}, {{A, B, C, X(6591), X(39951)}}, {{A, B, C, X(7317), X(42030)}}, {{A, B, C, X(7961), X(34919)}}, {{A, B, C, X(8025), X(37651)}}, {{A, B, C, X(8051), X(44559)}}, {{A, B, C, X(8814), X(40424)}}, {{A, B, C, X(9311), X(40420)}}, {{A, B, C, X(10056), X(17021)}}, {{A, B, C, X(10072), X(17012)}}, {{A, B, C, X(10428), X(34260)}}, {{A, B, C, X(10520), X(36620)}}, {{A, B, C, X(10578), X(29571)}}, {{A, B, C, X(12848), X(25525)}}, {{A, B, C, X(17321), X(44417)}}, {{A, B, C, X(17595), X(51788)}}, {{A, B, C, X(17776), X(33133)}}, {{A, B, C, X(17917), X(37800)}}, {{A, B, C, X(17924), X(37874)}}, {{A, B, C, X(20196), X(21454)}}, {{A, B, C, X(23618), X(25568)}}, {{A, B, C, X(24239), X(26626)}}, {{A, B, C, X(33150), X(46938)}}, {{A, B, C, X(36279), X(37595)}}, {{A, B, C, X(37759), X(41839)}}
X(56218) = barycentric quotient X(i)/X(j) for these (i, j): {1, 19861}, {65, 12709}, {3304, 22754}

X(56219) = KP3(X(37)) OF X(10) AND X(10)

Barycentrics    a*(b+c)*(a^2+2*a*b+b^2+c^2)*(a^2+b^2+2*a*c+c^2) : :

X(56219) lies on cubic K689 and on these lines: {1, 25}, {2, 304}, {6, 63}, {37, 306}, {42, 72}, {65, 18202}, {81, 1169}, {92, 393}, {111, 1310}, {169, 19725}, {226, 1880}, {251, 17011}, {257, 1999}, {293, 1976}, {321, 14624}, {940, 46010}, {941, 5739}, {942, 19714}, {967, 980}, {1214, 1400}, {1427, 5244}, {1468, 1472}, {2092, 3998}, {2165, 17720}, {2167, 8882}, {2184, 41489}, {2248, 37596}, {2286, 45126}, {2298, 3101}, {2349, 8749}, {2350, 37597}, {2582, 8105}, {2583, 8106}, {2999, 39951}, {3108, 17012}, {3228, 54982}, {3444, 37595}, {3672, 52223}, {3743, 4028}, {3752, 39798}, {3870, 37548}, {4352, 18663}, {4841, 55261}, {4850, 39956}, {5271, 41015}, {5287, 8770}, {5814, 33088}, {6051, 33171}, {6508, 42485}, {6546, 47965}, {7085, 17594}, {16081, 46273}, {16968, 37323}, {17013, 39955}, {17020, 39389}, {17022, 21448}, {17054, 19718}, {17267, 39983}, {17788, 19786}, {19684, 20227}, {19701, 40941}, {19715, 20271}, {23988, 39979}, {25060, 40571}, {26702, 32691}, {26893, 45966}, {34288, 50068}, {34818, 56033}, {37128, 37215}, {37539, 54371}

X(56219) = isogonal conjugate of X(2303)
X(56219) = trilinear pole of line {656, 50330}
X(56219) = perspector of circumconic {{A, B, C, X(1310), X(36099)}}
X(56219) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 2303}, {2, 44119}, {6, 1010}, {9, 5323}, {21, 2285}, {27, 7085}, {28, 5227}, {29, 2286}, {32, 44154}, {58, 2345}, {63, 4206}, {81, 612}, {86, 54416}, {99, 2484}, {101, 47844}, {110, 6590}, {112, 23874}, {162, 2522}, {163, 2517}, {284, 388}, {333, 1460}, {662, 8678}, {799, 8646}, {1038, 1172}, {1098, 8898}, {1333, 4385}, {1412, 3974}, {1474, 54433}, {1790, 7102}, {2203, 19799}, {2287, 4320}, {2327, 7103}, {2328, 7365}, {4556, 48395}, {4610, 50494}, {5331, 34261}, {7252, 14594}, {19459, 40411}
X(56219) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 2303}, {9, 1010}, {10, 2345}, {37, 4385}, {115, 2517}, {125, 2522}, {244, 6590}, {478, 5323}, {1015, 47844}, {1084, 8678}, {3162, 4206}, {6376, 44154}, {15267, 8898}, {18589, 5286}, {32664, 44119}, {34591, 23874}, {36908, 7365}, {38986, 2484}, {38996, 8646}, {40586, 612}, {40590, 388}, {40591, 5227}, {40599, 3974}, {40600, 54416}, {40611, 2285}, {51574, 54433}
X(56219) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(63)}}, {{A, B, C, X(2), X(6)}}, {{A, B, C, X(4), X(16368)}}, {{A, B, C, X(10), X(57)}}, {{A, B, C, X(27), X(256)}}, {{A, B, C, X(65), X(81)}}, {{A, B, C, X(73), X(3998)}}, {{A, B, C, X(89), X(6539)}}, {{A, B, C, X(209), X(2280)}}, {{A, B, C, X(210), X(294)}}, {{A, B, C, X(241), X(3930)}}, {{A, B, C, X(284), X(3694)}}, {{A, B, C, X(333), X(18097)}}, {{A, B, C, X(469), X(13723)}}, {{A, B, C, X(513), X(56047)}}, {{A, B, C, X(523), X(34377)}}, {{A, B, C, X(525), X(44662)}}, {{A, B, C, X(893), X(2203)}}, {{A, B, C, X(894), X(1999)}}, {{A, B, C, X(940), X(1867)}}, {{A, B, C, X(949), X(2318)}}, {{A, B, C, X(1039), X(2339)}}, {{A, B, C, X(1100), X(1230)}}, {{A, B, C, X(1245), X(2221)}}, {{A, B, C, X(1255), X(4641)}}, {{A, B, C, X(1412), X(34914)}}, {{A, B, C, X(1439), X(1763)}}, {{A, B, C, X(1468), X(28606)}}, {{A, B, C, X(1500), X(16583)}}, {{A, B, C, X(1824), X(40747)}}, {{A, B, C, X(1903), X(2298)}}, {{A, B, C, X(1905), X(36121)}}, {{A, B, C, X(2276), X(19791)}}, {{A, B, C, X(2294), X(18607)}}, {{A, B, C, X(2994), X(15232)}}, {{A, B, C, X(3175), X(4850)}}, {{A, B, C, X(3752), X(3995)}}, {{A, B, C, X(3936), X(48300)}}, {{A, B, C, X(3991), X(16600)}}, {{A, B, C, X(4028), X(5287)}}, {{A, B, C, X(4052), X(39948)}}, {{A, B, C, X(4062), X(17019)}}, {{A, B, C, X(4080), X(11396)}}, {{A, B, C, X(4674), X(39980)}}, {{A, B, C, X(6354), X(43675)}}, {{A, B, C, X(13476), X(39700)}}, {{A, B, C, X(15523), X(16696)}}, {{A, B, C, X(16609), X(34252)}}, {{A, B, C, X(17056), X(40571)}}, {{A, B, C, X(17441), X(37755)}}, {{A, B, C, X(17720), X(42700)}}, {{A, B, C, X(18593), X(47965)}}, {{A, B, C, X(21216), X(21775)}}, {{A, B, C, X(26377), X(40160)}}, {{A, B, C, X(26942), X(28787)}}, {{A, B, C, X(36124), X(40718)}}, {{A, B, C, X(40394), X(46187)}}, {{A, B, C, X(40407), X(52389)}}, {{A, B, C, X(40435), X(43073)}}, {{A, B, C, X(40515), X(55090)}}, {{A, B, C, X(42704), X(50068)}}
X(56219) = barycentric product X(i)*X(j) for these (i, j): {226, 2339}, {512, 54982}, {1036, 1441}, {1039, 307}, {1245, 75}, {1310, 523}, {1472, 313}, {2221, 321}, {2281, 76}, {14208, 32691}, {20336, 51686}, {21750, 40831}, {30479, 65}, {31993, 34260}, {36099, 525}, {37215, 661}
X(56219) = barycentric quotient X(i)/X(j) for these (i, j): {1, 1010}, {6, 2303}, {10, 4385}, {25, 4206}, {31, 44119}, {37, 2345}, {42, 612}, {56, 5323}, {65, 388}, {71, 5227}, {72, 54433}, {73, 1038}, {75, 44154}, {210, 3974}, {213, 54416}, {228, 7085}, {306, 19799}, {512, 8678}, {513, 47844}, {523, 2517}, {647, 2522}, {656, 23874}, {661, 6590}, {669, 8646}, {798, 2484}, {1036, 21}, {1039, 29}, {1042, 4320}, {1245, 1}, {1310, 99}, {1400, 2285}, {1402, 1460}, {1409, 2286}, {1426, 7103}, {1427, 7365}, {1472, 58}, {1824, 7102}, {2221, 81}, {2281, 6}, {2339, 333}, {3949, 3610}, {4551, 14594}, {4705, 48395}, {7143, 10376}, {16583, 5286}, {17441, 7386}, {18210, 26933}, {21750, 1184}, {22363, 19459}, {30479, 314}, {32691, 162}, {34260, 37870}, {36099, 648}, {37215, 799}, {50487, 50494}, {51686, 28}, {54982, 670}

X(56220) = KP3(X(37)) OF X(10) AND X(19)

Barycentrics    a*(a^3+b^3+a^2*(b-c)+b^2*c+b*c^2+c^3+a*(b^2-c^2))*(a^3+b^3+b^2*c+b*c^2+c^3+a^2*(-b+c)+a*(-b^2+c^2)) : :

X(56220) lies on these lines: {1, 3710}, {6, 3694}, {8, 998}, {9, 1474}, {10, 34}, {33, 44040}, {56, 72}, {58, 78}, {86, 975}, {87, 5293}, {106, 19861}, {200, 937}, {269, 307}, {318, 8747}, {612, 43531}, {978, 7194}, {979, 3961}, {1062, 44416}, {1125, 2191}, {1126, 3870}, {1211, 52372}, {1220, 4737}, {1413, 52389}, {1431, 10974}, {1438, 5248}, {1612, 26690}, {1763, 25440}, {1829, 54286}, {2215, 4253}, {3678, 54377}, {3938, 56140}, {6198, 54389}, {7085, 8193}, {7129, 17355}, {9432, 50594}, {26890, 36507}, {32931, 54401}, {40746, 54406}

X(56220) = trilinear pole of line {649, 8611}
X(56220) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 19785}, {28, 41340}, {56, 2478}
X(56220) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 2478}, {9, 19785}, {40591, 41340}
X(56220) = X(i)-cross conjugate of X(j) for these {i, j}: {976, 1}
X(56220) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(6)}}, {{A, B, C, X(2), X(943)}}, {{A, B, C, X(3), X(1801)}}, {{A, B, C, X(4), X(1257)}}, {{A, B, C, X(7), X(56137)}}, {{A, B, C, X(8), X(997)}}, {{A, B, C, X(9), X(10)}}, {{A, B, C, X(21), X(475)}}, {{A, B, C, X(28), X(17526)}}, {{A, B, C, X(29), X(37249)}}, {{A, B, C, X(40), X(17355)}}, {{A, B, C, X(42), X(975)}}, {{A, B, C, X(43), X(5293)}}, {{A, B, C, X(57), X(5266)}}, {{A, B, C, X(63), X(14376)}}, {{A, B, C, X(65), X(40401)}}, {{A, B, C, X(75), X(90)}}, {{A, B, C, X(77), X(4347)}}, {{A, B, C, X(80), X(20029)}}, {{A, B, C, X(84), X(596)}}, {{A, B, C, X(104), X(1219)}}, {{A, B, C, X(200), X(936)}}, {{A, B, C, X(212), X(3682)}}, {{A, B, C, X(282), X(56146)}}, {{A, B, C, X(285), X(6601)}}, {{A, B, C, X(291), X(987)}}, {{A, B, C, X(326), X(1794)}}, {{A, B, C, X(386), X(612)}}, {{A, B, C, X(519), X(19861)}}, {{A, B, C, X(749), X(2363)}}, {{A, B, C, X(765), X(7162)}}, {{A, B, C, X(951), X(1041)}}, {{A, B, C, X(978), X(3961)}}, {{A, B, C, X(989), X(994)}}, {{A, B, C, X(993), X(10461)}}, {{A, B, C, X(1038), X(8193)}}, {{A, B, C, X(1039), X(2316)}}, {{A, B, C, X(1125), X(3870)}}, {{A, B, C, X(1170), X(18841)}}, {{A, B, C, X(1211), X(3678)}}, {{A, B, C, X(1215), X(10974)}}, {{A, B, C, X(1224), X(15175)}}, {{A, B, C, X(1247), X(33164)}}, {{A, B, C, X(1280), X(3296)}}, {{A, B, C, X(1476), X(11546)}}, {{A, B, C, X(1829), X(4737)}}, {{A, B, C, X(2203), X(15376)}}, {{A, B, C, X(2218), X(39798)}}, {{A, B, C, X(2298), X(51223)}}, {{A, B, C, X(2345), X(12514)}}, {{A, B, C, X(3065), X(39711)}}, {{A, B, C, X(3467), X(39708)}}, {{A, B, C, X(3501), X(3923)}}, {{A, B, C, X(3680), X(17614)}}, {{A, B, C, X(3730), X(50314)}}, {{A, B, C, X(3872), X(30144)}}, {{A, B, C, X(4373), X(10308)}}, {{A, B, C, X(4866), X(17272)}}, {{A, B, C, X(5248), X(18206)}}, {{A, B, C, X(5256), X(30142)}}, {{A, B, C, X(5936), X(56203)}}, {{A, B, C, X(6513), X(17206)}}, {{A, B, C, X(6553), X(15179)}}, {{A, B, C, X(6765), X(8583)}}, {{A, B, C, X(7091), X(39697)}}, {{A, B, C, X(7160), X(42285)}}, {{A, B, C, X(7284), X(34860)}}, {{A, B, C, X(10393), X(27396)}}, {{A, B, C, X(10570), X(56101)}}, {{A, B, C, X(15315), X(23051)}}, {{A, B, C, X(16468), X(16519)}}, {{A, B, C, X(18840), X(36101)}}, {{A, B, C, X(19860), X(22836)}}, {{A, B, C, X(24036), X(36819)}}, {{A, B, C, X(25430), X(56219)}}, {{A, B, C, X(26890), X(26893)}}, {{A, B, C, X(30614), X(56155)}}, {{A, B, C, X(40396), X(51497)}}, {{A, B, C, X(56100), X(56143)}}
X(56220) = barycentric product X(i)*X(j) for these (i, j): {10, 56045}
X(56220) = barycentric quotient X(i)/X(j) for these (i, j): {1, 19785}, {9, 2478}, {71, 41340}, {56045, 86}

X(56221) = KP3(X(37)) OF X(10) AND X(37)

Barycentrics    a*(b+c)*(2*a+2*b+c)*(2*a+b+2*c) : :

X(56221) lies on these lines: {1, 2308}, {2, 39708}, {8, 30590}, {10, 1962}, {19, 3247}, {35, 1255}, {37, 3678}, {58, 40438}, {65, 3743}, {75, 1125}, {91, 13411}, {100, 25431}, {158, 13405}, {225, 3947}, {226, 52382}, {267, 4354}, {386, 17038}, {519, 31359}, {551, 596}, {740, 46772}, {758, 31503}, {759, 8652}, {876, 6005}, {897, 37211}, {975, 8769}, {984, 39737}, {994, 5697}, {1247, 30115}, {2153, 46073}, {2154, 46077}, {2166, 18359}, {2214, 5248}, {2292, 53114}, {2363, 4653}, {2901, 10180}, {3159, 42027}, {3244, 42285}, {3293, 56134}, {3295, 53855}, {3361, 7190}, {3612, 56070}, {3616, 39711}, {3624, 4365}, {3634, 17592}, {3636, 34860}, {3647, 37595}, {3697, 37593}, {3811, 16673}, {3868, 31320}, {3918, 3931}, {3971, 42471}, {4002, 4868}, {4066, 43223}, {4674, 14752}, {5045, 13476}, {5266, 35007}, {6051, 50604}, {6155, 52708}, {8672, 55244}, {9957, 34434}, {16828, 27804}, {18398, 28606}, {18827, 32042}, {23051, 30148}, {23604, 36250}, {27274, 31308}, {28619, 32936}, {30143, 56136}, {31318, 49992}, {31445, 46971}, {37594, 55925}, {39702, 51103}, {39717, 49477}, {46904, 51073}, {56135, 56191}

X(56221) = isogonal conjugate of X(4658)
X(56221) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 4658}, {3, 31902}, {6, 5333}, {21, 5221}, {28, 3927}, {57, 4877}, {58, 1698}, {81, 16777}, {99, 4834}, {100, 4840}, {101, 4960}, {110, 4802}, {163, 4823}, {284, 4654}, {662, 4813}, {691, 30595}, {741, 4716}, {759, 4880}, {849, 4066}, {1014, 3715}, {1175, 3824}, {1333, 28605}, {1412, 4007}, {2206, 30596}, {3733, 4756}, {4273, 30589}, {4556, 4838}, {4560, 36074}, {4565, 4820}, {4591, 4958}, {4610, 4826}, {48005, 52935}
X(56221) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 4658}, {9, 5333}, {10, 1698}, {37, 28605}, {115, 4823}, {244, 4802}, {1015, 4960}, {1084, 4813}, {4075, 4066}, {5452, 4877}, {8054, 4840}, {8299, 4716}, {34586, 4880}, {36103, 31902}, {38986, 4834}, {40586, 16777}, {40590, 4654}, {40591, 3927}, {40599, 4007}, {40603, 30596}, {40611, 5221}, {55064, 4820}
X(56221) = X(i)-Ceva conjugate of X(j) for these {i, j}: {25417, 28625}, {32042, 48074}
X(56221) = X(i)-cross conjugate of X(j) for these {i, j}: {4822, 1018}
X(56221) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}}, {{A, B, C, X(2), X(17562)}}, {{A, B, C, X(3), X(4262)}}, {{A, B, C, X(4), X(16865)}}, {{A, B, C, X(12), X(4067)}}, {{A, B, C, X(21), X(2321)}}, {{A, B, C, X(42), X(58)}}, {{A, B, C, X(56), X(52555)}}, {{A, B, C, X(72), X(3247)}}, {{A, B, C, X(79), X(41506)}}, {{A, B, C, X(106), X(1245)}}, {{A, B, C, X(226), X(502)}}, {{A, B, C, X(256), X(43972)}}, {{A, B, C, X(306), X(30142)}}, {{A, B, C, X(321), X(27789)}}, {{A, B, C, X(386), X(28622)}}, {{A, B, C, X(512), X(28522)}}, {{A, B, C, X(519), X(8672)}}, {{A, B, C, X(551), X(3293)}}, {{A, B, C, X(740), X(6005)}}, {{A, B, C, X(756), X(42031)}}, {{A, B, C, X(758), X(28161)}}, {{A, B, C, X(893), X(15376)}}, {{A, B, C, X(932), X(4103)}}, {{A, B, C, X(941), X(43531)}}, {{A, B, C, X(975), X(4028)}}, {{A, B, C, X(987), X(11599)}}, {{A, B, C, X(1042), X(4021)}}, {{A, B, C, X(1126), X(1400)}}, {{A, B, C, X(1224), X(40433)}}, {{A, B, C, X(1334), X(4845)}}, {{A, B, C, X(1388), X(4424)}}, {{A, B, C, X(1420), X(3931)}}, {{A, B, C, X(1442), X(33670)}}, {{A, B, C, X(1500), X(3993)}}, {{A, B, C, X(1826), X(15175)}}, {{A, B, C, X(2171), X(6538)}}, {{A, B, C, X(2292), X(4125)}}, {{A, B, C, X(2320), X(3701)}}, {{A, B, C, X(2335), X(56146)}}, {{A, B, C, X(2346), X(39130)}}, {{A, B, C, X(3159), X(3971)}}, {{A, B, C, X(3178), X(30115)}}, {{A, B, C, X(3214), X(3636)}}, {{A, B, C, X(3294), X(15569)}}, {{A, B, C, X(3296), X(13576)}}, {{A, B, C, X(3361), X(37593)}}, {{A, B, C, X(3616), X(50587)}}, {{A, B, C, X(3671), X(3697)}}, {{A, B, C, X(3682), X(13405)}}, {{A, B, C, X(3896), X(17127)}}, {{A, B, C, X(3918), X(4848)}}, {{A, B, C, X(3932), X(47713)}}, {{A, B, C, X(3989), X(34475)}}, {{A, B, C, X(3991), X(4350)}}, {{A, B, C, X(4029), X(4868)}}, {{A, B, C, X(4066), X(16777)}}, {{A, B, C, X(4078), X(16600)}}, {{A, B, C, X(4256), X(35007)}}, {{A, B, C, X(5248), X(28606)}}, {{A, B, C, X(5424), X(45095)}}, {{A, B, C, X(5557), X(15320)}}, {{A, B, C, X(5559), X(15232)}}, {{A, B, C, X(7226), X(43534)}}, {{A, B, C, X(7320), X(38955)}}, {{A, B, C, X(9277), X(52375)}}, {{A, B, C, X(9957), X(37558)}}, {{A, B, C, X(10013), X(15315)}}, {{A, B, C, X(16484), X(21802)}}, {{A, B, C, X(25430), X(56219)}}, {{A, B, C, X(26102), X(50590)}}, {{A, B, C, X(26115), X(50604)}}, {{A, B, C, X(27809), X(39738)}}, {{A, B, C, X(28594), X(50290)}}, {{A, B, C, X(28625), X(30598)}}, {{A, B, C, X(32014), X(40776)}}, {{A, B, C, X(32912), X(33942)}}, {{A, B, C, X(34585), X(39949)}}, {{A, B, C, X(37865), X(55090)}}, {{A, B, C, X(39748), X(39974)}}, {{A, B, C, X(39945), X(45129)}}, {{A, B, C, X(40412), X(43680)}}, {{A, B, C, X(40432), X(44572)}}
X(56221) = barycentric product X(i)*X(j) for these (i, j): {10, 25417}, {226, 56203}, {313, 34819}, {1577, 8652}, {3952, 48074}, {28625, 75}, {30590, 53114}, {30598, 37}, {32042, 661}, {37211, 523}, {41013, 56070}, {42030, 65}
X(56221) = barycentric quotient X(i)/X(j) for these (i, j): {1, 5333}, {6, 4658}, {10, 28605}, {19, 31902}, {37, 1698}, {42, 16777}, {55, 4877}, {65, 4654}, {71, 3927}, {210, 4007}, {321, 30596}, {512, 4813}, {513, 4960}, {523, 4823}, {594, 4066}, {649, 4840}, {661, 4802}, {798, 4834}, {1018, 4756}, {1334, 3715}, {1400, 5221}, {2238, 4716}, {2245, 4880}, {2294, 3824}, {2533, 4842}, {2642, 30595}, {4041, 4820}, {4079, 48005}, {4705, 4838}, {4729, 4949}, {4730, 4958}, {4849, 4898}, {8652, 662}, {21805, 4727}, {21832, 4810}, {21839, 4938}, {25417, 86}, {28625, 1}, {30598, 274}, {32042, 799}, {34819, 58}, {37211, 99}, {42030, 314}, {48005, 53585}, {48074, 7192}, {50487, 4826}, {53114, 30589}, {56070, 1444}, {56203, 333}
X(56221) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1125, 3993, 42031}

X(56222) = KP3(X(37)) OF X(10) AND X(42)

Barycentrics    (a^2+3*a*b+b^2)*(b+c)*(a^2+3*a*c+c^2) : :

X(56222) lies on these lines: {86, 7240}, {238, 1468}, {256, 16826}, {350, 10436}, {513, 28639}, {894, 30571}, {1284, 3671}, {1400, 10180}, {2238, 4104}, {3778, 56131}, {4670, 34585}

X(56222) = trilinear pole of line {4841, 21832}
X(56222) = X(i)-isoconjugate-of-X(j) for these {i, j}: {99, 4507}, {110, 4490}, {163, 4500}, {284, 7201}, {662, 4502}, {741, 4489}, {849, 48644}, {1333, 48628}, {7275, 38832}
X(56222) = X(i)-Dao conjugate of X(j) for these {i, j}: {37, 48628}, {115, 4500}, {244, 4490}, {1084, 4502}, {4075, 48644}, {8299, 4489}, {38986, 4507}, {40590, 7201}
X(56222) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1400)}}, {{A, B, C, X(2), X(17379)}}, {{A, B, C, X(7), X(10)}}, {{A, B, C, X(21), X(12567)}}, {{A, B, C, X(37), X(86)}}, {{A, B, C, X(42), X(87)}}, {{A, B, C, X(190), X(28639)}}, {{A, B, C, X(213), X(9403)}}, {{A, B, C, X(226), X(4104)}}, {{A, B, C, X(333), X(10180)}}, {{A, B, C, X(523), X(17771)}}, {{A, B, C, X(527), X(4151)}}, {{A, B, C, X(873), X(9277)}}, {{A, B, C, X(894), X(4039)}}, {{A, B, C, X(903), X(46772)}}, {{A, B, C, X(941), X(43531)}}, {{A, B, C, X(957), X(53114)}}, {{A, B, C, X(1125), X(26115)}}, {{A, B, C, X(1178), X(1402)}}, {{A, B, C, X(2296), X(17038)}}, {{A, B, C, X(3720), X(40147)}}, {{A, B, C, X(4871), X(29822)}}, {{A, B, C, X(7240), X(21803)}}, {{A, B, C, X(7271), X(42289)}}, {{A, B, C, X(13576), X(30712)}}, {{A, B, C, X(13610), X(40439)}}, {{A, B, C, X(14624), X(28626)}}, {{A, B, C, X(15320), X(39704)}}, {{A, B, C, X(20072), X(30588)}}, {{A, B, C, X(23493), X(40729)}}, {{A, B, C, X(28625), X(37129)}}, {{A, B, C, X(28658), X(40433)}}, {{A, B, C, X(29653), X(29838)}}, {{A, B, C, X(30598), X(41683)}}, {{A, B, C, X(32014), X(54117)}}, {{A, B, C, X(42285), X(55035)}}
X(56222) = barycentric product X(i)*X(j) for these (i, j): {10, 56042}
X(56222) = barycentric quotient X(i)/X(j) for these (i, j): {10, 48628}, {65, 7201}, {512, 4502}, {523, 4500}, {594, 48644}, {661, 4490}, {798, 4507}, {2238, 4489}, {16606, 7275}, {56042, 86}

X(56223) = KP3(X(37)) OF X(10) AND X(44)

Barycentrics    a*(2*a^3-2*a^2*b+3*b^3-b^2*c-2*b*c^2+2*c^3-a*b*(b+c))*(2*a^3+2*b^3-2*a^2*c-2*b^2*c-b*c^2+3*c^3-a*c*(b+c)) : :

X(56223) lies on these lines: {44, 758}, {226, 14584}, {519, 3936}, {1168, 30575}, {1319, 18593}, {2718, 3315}, {3218, 18173}, {9325, 17960}, {20924, 30939}, {36872, 48866}

X(56223) = trilinear pole of line {1635, 53527}
X(56223) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(44)}}, {{A, B, C, X(10), X(7649)}}, {{A, B, C, X(79), X(36935)}}, {{A, B, C, X(81), X(226)}}, {{A, B, C, X(89), X(54974)}}, {{A, B, C, X(256), X(4653)}}, {{A, B, C, X(896), X(48544)}}, {{A, B, C, X(977), X(15173)}}, {{A, B, C, X(994), X(18173)}}, {{A, B, C, X(1016), X(27789)}}, {{A, B, C, X(1411), X(24222)}}, {{A, B, C, X(2802), X(3315)}}, {{A, B, C, X(4567), X(48587)}}, {{A, B, C, X(5665), X(7012)}}, {{A, B, C, X(6549), X(15635)}}, {{A, B, C, X(8056), X(40509)}}, {{A, B, C, X(9269), X(17960)}}, {{A, B, C, X(25417), X(35168)}}, {{A, B, C, X(25430), X(36954)}}, {{A, B, C, X(30116), X(50023)}}, {{A, B, C, X(33136), X(42285)}}, {{A, B, C, X(36125), X(40400)}}, {{A, B, C, X(48303), X(52640)}}, {{A, B, C, X(48855), X(50018)}}

X(56224) = KP3(X(37)) OF X(10) AND X(58)

Barycentrics    (a^3+c*(b+c)^2+a^2*(2*b+c)+a*(b^2+c^2))*(a^3+b*(b+c)^2+a^2*(b+2*c)+a*(b^2+c^2)) : :

X(56224) lies on these lines: {8, 13740}, {29, 49542}, {189, 5749}, {257, 27064}, {312, 4360}, {333, 5294}, {1412, 5750}, {2221, 2345}, {3305, 31359}, {4102, 50306}, {17353, 40435}, {17368, 56046}, {19742, 30711}, {20043, 56086}, {37445, 41791}

X(56224) = trilinear pole of line {4063, 47711}
X(56224) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 37592}, {31, 54311}
X(56224) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 54311}, {9, 37592}
X(56224) = X(i)-cross conjugate of X(j) for these {i, j}: {14349, 190}
X(56224) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1412)}}, {{A, B, C, X(2), X(8)}}, {{A, B, C, X(27), X(83)}}, {{A, B, C, X(57), X(996)}}, {{A, B, C, X(81), X(1222)}}, {{A, B, C, X(86), X(1255)}}, {{A, B, C, X(226), X(5294)}}, {{A, B, C, X(278), X(18841)}}, {{A, B, C, X(321), X(17289)}}, {{A, B, C, X(329), X(5749)}}, {{A, B, C, X(469), X(1010)}}, {{A, B, C, X(561), X(1268)}}, {{A, B, C, X(673), X(24552)}}, {{A, B, C, X(894), X(27064)}}, {{A, B, C, X(967), X(979)}}, {{A, B, C, X(1016), X(37870)}}, {{A, B, C, X(1065), X(2051)}}, {{A, B, C, X(1120), X(25417)}}, {{A, B, C, X(1125), X(50306)}}, {{A, B, C, X(1215), X(41534)}}, {{A, B, C, X(1434), X(35058)}}, {{A, B, C, X(2297), X(2316)}}, {{A, B, C, X(2321), X(5750)}}, {{A, B, C, X(2339), X(51565)}}, {{A, B, C, X(3305), X(10436)}}, {{A, B, C, X(3616), X(20043)}}, {{A, B, C, X(5249), X(17353)}}, {{A, B, C, X(6336), X(43527)}}, {{A, B, C, X(14534), X(32017)}}, {{A, B, C, X(14621), X(39694)}}, {{A, B, C, X(17368), X(27184)}}, {{A, B, C, X(19742), X(25507)}}, {{A, B, C, X(25430), X(36124)}}, {{A, B, C, X(26627), X(26688)}}, {{A, B, C, X(30513), X(34404)}}, {{A, B, C, X(37874), X(52781)}}, {{A, B, C, X(39698), X(56047)}}, {{A, B, C, X(39948), X(56145)}}
X(56224) = barycentric quotient X(i)/X(j) for these (i, j): {1, 37592}, {2, 54311}

X(56225) = KP3(X(37)) OF X(10) AND X(63)

Barycentrics    a*(a-b-c)*(a^3+a^2*(b+c)+(b-c)*(b+c)^2+a*(b^2+2*b*c-c^2))*(a^3+a^2*(b+c)-(b-c)*(b+c)^2+a*(-b^2+2*b*c+c^2)) : :

X(56225) lies on these lines: {1, 1826}, {3, 37}, {6, 1069}, {9, 283}, {19, 3422}, {33, 284}, {48, 52185}, {71, 54401}, {77, 226}, {78, 2321}, {210, 219}, {312, 332}, {469, 45126}, {1060, 1901}, {1100, 38248}, {1433, 1903}, {1442, 31042}, {1794, 25063}, {1795, 2250}, {3247, 40442}, {5795, 20263}, {6505, 27052}, {7015, 52651}, {7100, 8818}, {7163, 54385}, {8736, 21147}, {35996, 54420}, {37445, 53996}

X(56225) = isogonal conjugate of X(45126)
X(56225) = trilinear pole of line {652, 4041}
X(56225) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 45126}, {7, 36744}, {56, 5739}, {57, 12514}, {63, 1452}, {65, 27174}, {222, 406}, {348, 44086}, {1408, 42707}, {1460, 14258}
X(56225) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 5739}, {3, 45126}, {3162, 1452}, {5452, 12514}, {40602, 27174}
X(56225) = X(i)-cross conjugate of X(j) for these {i, j}: {2268, 9}
X(56225) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3)}}, {{A, B, C, X(2), X(1172)}}, {{A, B, C, X(6), X(913)}}, {{A, B, C, X(7), X(990)}}, {{A, B, C, X(8), X(975)}}, {{A, B, C, X(9), X(33)}}, {{A, B, C, X(19), X(2006)}}, {{A, B, C, X(57), X(7129)}}, {{A, B, C, X(63), X(5747)}}, {{A, B, C, X(81), X(27395)}}, {{A, B, C, X(92), X(7097)}}, {{A, B, C, X(200), X(5287)}}, {{A, B, C, X(256), X(46475)}}, {{A, B, C, X(281), X(1766)}}, {{A, B, C, X(485), X(7133)}}, {{A, B, C, X(486), X(42013)}}, {{A, B, C, X(612), X(11679)}}, {{A, B, C, X(650), X(2214)}}, {{A, B, C, X(941), X(52663)}}, {{A, B, C, X(998), X(1169)}}, {{A, B, C, X(1039), X(27802)}}, {{A, B, C, X(1041), X(56144)}}, {{A, B, C, X(1061), X(5397)}}, {{A, B, C, X(1217), X(42464)}}, {{A, B, C, X(1255), X(2287)}}, {{A, B, C, X(1390), X(6601)}}, {{A, B, C, X(1449), X(6603)}}, {{A, B, C, X(2189), X(3615)}}, {{A, B, C, X(2193), X(6513)}}, {{A, B, C, X(2289), X(41087)}}, {{A, B, C, X(2297), X(2316)}}, {{A, B, C, X(2326), X(18651)}}, {{A, B, C, X(2337), X(2342)}}, {{A, B, C, X(2648), X(17038)}}, {{A, B, C, X(3254), X(23051)}}, {{A, B, C, X(4183), X(37185)}}, {{A, B, C, X(4328), X(8544)}}, {{A, B, C, X(8748), X(40169)}}, {{A, B, C, X(16831), X(28043)}}, {{A, B, C, X(34820), X(52371)}}, {{A, B, C, X(39393), X(46952)}}, {{A, B, C, X(40141), X(45129)}}
X(56225) = barycentric product X(i)*X(j) for these (i, j): {312, 46010}
X(56225) = barycentric quotient X(i)/X(j) for these (i, j): {6, 45126}, {9, 5739}, {25, 1452}, {33, 406}, {41, 36744}, {55, 12514}, {284, 27174}, {2212, 44086}, {2321, 42707}, {2339, 14258}, {46010, 57}

X(56226) = KP3(X(37)) OF X(10) AND X(65)

Barycentrics    (3*a+3*b-c)*(b+c)*(3*a-b+3*c) : :

X(56226) lies on the Kiepert hyperbola and on these lines: {1, 43533}, {2, 1743}, {4, 1125}, {10, 4035}, {37, 4052}, {76, 18743}, {98, 28162}, {142, 2051}, {226, 3986}, {306, 6539}, {321, 3950}, {519, 54786}, {551, 3772}, {598, 19812}, {1427, 25081}, {1751, 19701}, {2996, 16831}, {3008, 32022}, {3452, 17758}, {3812, 10440}, {3821, 54883}, {3912, 56210}, {4058, 31993}, {4080, 4656}, {4138, 40718}, {4657, 54586}, {4896, 38000}, {5333, 18645}, {5395, 29603}, {5437, 45098}, {6682, 38054}, {6685, 38204}, {10444, 45100}, {13478, 15668}, {13576, 43223}, {14534, 25507}, {16844, 19862}, {17206, 32014}, {19786, 54686}, {19804, 34258}, {29600, 44417}, {48649, 50290}, {50302, 56144}, {50808, 54657}

X(56226) = trilinear pole of line {4729, 23755}
X(56226) = X(i)-isoconjugate-of-X(j) for these {i, j}: {58, 3731}, {163, 28161}, {284, 3340}, {662, 48338}, {849, 4058}, {1333, 3617}, {1474, 3984}, {2194, 5226}, {2206, 42034}, {10563, 33628}
X(56226) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 3731}, {37, 3617}, {115, 28161}, {1084, 48338}, {1214, 5226}, {4075, 4058}, {40590, 3340}, {40603, 42034}, {51574, 3984}
X(56226) = X(i)-Ceva conjugate of X(j) for these {i, j}: {30712, 31503}
X(56226) = X(i)-cross conjugate of X(j) for these {i, j}: {5257, 10}
X(56226) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1427)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(27), X(43972)}}, {{A, B, C, X(37), X(1743)}}, {{A, B, C, X(42), X(29571)}}, {{A, B, C, X(57), X(53114)}}, {{A, B, C, X(65), X(8056)}}, {{A, B, C, X(72), X(5436)}}, {{A, B, C, X(86), X(3664)}}, {{A, B, C, X(92), X(42285)}}, {{A, B, C, X(142), X(52358)}}, {{A, B, C, X(274), X(55090)}}, {{A, B, C, X(306), X(1125)}}, {{A, B, C, X(307), X(25525)}}, {{A, B, C, X(469), X(16844)}}, {{A, B, C, X(514), X(37870)}}, {{A, B, C, X(525), X(28164)}}, {{A, B, C, X(1211), X(3947)}}, {{A, B, C, X(1214), X(3576)}}, {{A, B, C, X(1441), X(4035)}}, {{A, B, C, X(2287), X(25081)}}, {{A, B, C, X(2321), X(3986)}}, {{A, B, C, X(3671), X(19804)}}, {{A, B, C, X(3701), X(38255)}}, {{A, B, C, X(3912), X(43223)}}, {{A, B, C, X(3936), X(4823)}}, {{A, B, C, X(3992), X(4656)}}, {{A, B, C, X(4028), X(16831)}}, {{A, B, C, X(4058), X(5226)}}, {{A, B, C, X(4078), X(4356)}}, {{A, B, C, X(4125), X(5219)}}, {{A, B, C, X(4138), X(16603)}}, {{A, B, C, X(4416), X(42335)}}, {{A, B, C, X(4417), X(15668)}}, {{A, B, C, X(4642), X(45204)}}, {{A, B, C, X(5745), X(19607)}}, {{A, B, C, X(6703), X(41878)}}, {{A, B, C, X(10436), X(44735)}}, {{A, B, C, X(17023), X(29653)}}, {{A, B, C, X(17120), X(32017)}}, {{A, B, C, X(17272), X(30598)}}, {{A, B, C, X(18134), X(19701)}}, {{A, B, C, X(21060), X(31627)}}, {{A, B, C, X(25430), X(56219)}}, {{A, B, C, X(27475), X(42027)}}, {{A, B, C, X(29600), X(29822)}}, {{A, B, C, X(31247), X(41818)}}, {{A, B, C, X(31312), X(46772)}}, {{A, B, C, X(31503), X(39980)}}, {{A, B, C, X(39741), X(53112)}}, {{A, B, C, X(48633), X(48651)}}
X(56226) = barycentric product X(i)*X(j) for these (i, j): {10, 30712}, {226, 56201}, {321, 39980}, {28162, 850}, {31503, 75}
X(56226) = barycentric quotient X(i)/X(j) for these (i, j): {10, 3617}, {37, 3731}, {65, 3340}, {72, 3984}, {226, 5226}, {321, 42034}, {512, 48338}, {523, 28161}, {594, 4058}, {3698, 11530}, {14321, 14350}, {28162, 110}, {30712, 86}, {31503, 1}, {39980, 81}, {56174, 10563}, {56201, 333}
X(56226) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 30712, 56201}, {30712, 56201, 39980}

X(56227) = KP3(X(37)) OF X(10) AND X(71)

Barycentrics    (b+c)*(a^6+a^5*c+a*c*(b^2-c^2)^2-2*a^3*c*(b^2+c^2)-a^4*(2*b^2+c^2)+(-(b^2*c)+c^3)^2+a^2*(b^4-c^4))*(a^6+a^5*b+a*b*(b^2-c^2)^2-2*a^3*b*(b^2+c^2)-a^4*(b^2+2*c^2)+(b^3-b*c^2)^2+a^2*(-b^4+c^4)) : :

X(56227) lies on the Kiepert hyperbola and on these lines: {1, 2052}, {2, 255}, {4, 48}, {10, 3990}, {73, 40149}, {76, 326}, {226, 22341}, {275, 2169}, {321, 3682}, {459, 19614}, {681, 26701}, {1751, 19755}, {2051, 51759}, {2584, 2592}, {2585, 2593}, {16080, 35200}, {32591, 32593}

X(56227) = trilinear pole of line {822, 523}
X(56227) = X(i)-isoconjugate-of-X(j) for these {i, j}: {21, 19366}, {107, 680}, {1172, 53819}, {2194, 53821}, {2204, 53818}, {32713, 35521}
X(56227) = X(i)-Dao conjugate of X(j) for these {i, j}: {1214, 53821}, {38985, 680}, {40611, 19366}
X(56227) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(48)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(12), X(1881)}}, {{A, B, C, X(29), X(72)}}, {{A, B, C, X(37), X(3074)}}, {{A, B, C, X(65), X(3075)}}, {{A, B, C, X(71), X(3362)}}, {{A, B, C, X(1427), X(8747)}}, {{A, B, C, X(1441), X(3615)}}, {{A, B, C, X(1745), X(53012)}}, {{A, B, C, X(2184), X(39585)}}, {{A, B, C, X(2311), X(56225)}}, {{A, B, C, X(5906), X(6757)}}, {{A, B, C, X(32590), X(32593)}}, {{A, B, C, X(32591), X(32592)}}, {{A, B, C, X(40836), X(52560)}}, {{A, B, C, X(40942), X(52673)}}, {{A, B, C, X(51496), X(53114)}}
X(56227) = barycentric product X(i)*X(j) for these (i, j): {307, 53817}, {24018, 681}
X(56227) = barycentric quotient X(i)/X(j) for these (i, j): {73, 53819}, {226, 53821}, {307, 53818}, {681, 823}, {822, 680}, {1400, 19366}, {24018, 35521}, {53817, 29}

X(56228) = KP3(X(37)) OF X(10) AND X(79)

Barycentrics    (a^3+(b-c)^2*(b+c)-a^2*(2*b+c)-a*(2*b^2+5*b*c+c^2))*(a^3+(b-c)^2*(b+c)-a^2*(b+2*c)-a*(b^2+5*b*c+2*c^2)) : :

X(56228) lies on these lines: {1, 50205}, {57, 17245}, {89, 5273}, {1125, 56137}, {1255, 26723}, {3666, 42326}, {16578, 21907}, {17263, 30710}, {32777, 56051}, {37887, 44307}

X(56228) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(27), X(50205)}}, {{A, B, C, X(37), X(1174)}}, {{A, B, C, X(55), X(7110)}}, {{A, B, C, X(226), X(32008)}}, {{A, B, C, X(333), X(17245)}}, {{A, B, C, X(354), X(34585)}}, {{A, B, C, X(1125), X(26723)}}, {{A, B, C, X(1167), X(2003)}}, {{A, B, C, X(1214), X(47487)}}, {{A, B, C, X(1223), X(40573)}}, {{A, B, C, X(1751), X(27475)}}, {{A, B, C, X(1807), X(52381)}}, {{A, B, C, X(3666), X(17263)}}, {{A, B, C, X(4654), X(5556)}}, {{A, B, C, X(4687), X(32777)}}, {{A, B, C, X(4698), X(19808)}}, {{A, B, C, X(4720), X(5219)}}, {{A, B, C, X(5559), X(30690)}}, {{A, B, C, X(17758), X(40435)}}, {{A, B, C, X(25006), X(29571)}}, {{A, B, C, X(28626), X(40154)}}, {{A, B, C, X(33116), X(44307)}}

X(56229) = KP3(X(37)) OF X(10) AND X(83)

Barycentrics    a*(a^3*c+a^2*b*(b+c)+b^2*c*(b+c)+a*(b^3+2*b^2*c+b*c^2+c^3))*(a^3*b+a^2*c*(b+c)+b*c^2*(b+c)+a*(b^3+b^2*c+2*b*c^2+c^3)) : :

X(56229) lies on these lines: {6, 37090}, {37, 3757}, {42, 41239}, {239, 56219}, {333, 39957}, {1400, 5276}, {1427, 41245}, {2350, 37261}, {5275, 45988}, {16353, 39951}

X(56229) = trilinear pole of line {21389, 512}
X(56229) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3757)}}, {{A, B, C, X(2), X(6)}}, {{A, B, C, X(4), X(37090)}}, {{A, B, C, X(27), X(2298)}}, {{A, B, C, X(31), X(40432)}}, {{A, B, C, X(105), X(5331)}}, {{A, B, C, X(239), X(612)}}, {{A, B, C, X(256), X(9285)}}, {{A, B, C, X(294), X(333)}}, {{A, B, C, X(981), X(1751)}}, {{A, B, C, X(1013), X(26052)}}, {{A, B, C, X(1220), X(1390)}}, {{A, B, C, X(1244), X(40718)}}, {{A, B, C, X(1438), X(37870)}}, {{A, B, C, X(1937), X(7249)}}, {{A, B, C, X(2296), X(52030)}}, {{A, B, C, X(3920), X(32914)}}, {{A, B, C, X(4426), X(16519)}}, {{A, B, C, X(5275), X(37652)}}, {{A, B, C, X(6995), X(16353)}}, {{A, B, C, X(7378), X(16403)}}, {{A, B, C, X(14004), X(37261)}}, {{A, B, C, X(16587), X(21355)}}, {{A, B, C, X(30646), X(40738)}}

X(56230) = KP3(X(37)) OF X(10) AND X(84)

Barycentrics    a*(a^4+8*a*b^2*c+(b^2-c^2)^2-2*a^2*(b^2+c^2))*(a^4+8*a*b*c^2+(b^2-c^2)^2-2*a^2*(b^2+c^2)) : :

X(56230) lies on these lines: {1, 17658}, {9, 1422}, {28, 1753}, {57, 2324}, {81, 26669}, {105, 10388}, {277, 23681}, {278, 3452}, {279, 329}, {936, 7046}, {1219, 19861}, {2006, 20196}, {2982, 8257}, {2999, 56218}, {3305, 34056}, {8056, 25939}, {12555, 53083}, {16578, 34051}, {31142, 52374}, {32017, 52406}, {53996, 54414}

X(56230) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 14986}
X(56230) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 14986}
X(56230) = X(i)-cross conjugate of X(j) for these {i, j}: {40137, 100}
X(56230) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(3), X(936)}}, {{A, B, C, X(8), X(34546)}}, {{A, B, C, X(9), X(329)}}, {{A, B, C, X(10), X(1753)}}, {{A, B, C, X(63), X(3452)}}, {{A, B, C, X(75), X(43744)}}, {{A, B, C, X(78), X(1073)}}, {{A, B, C, X(86), X(17825)}}, {{A, B, C, X(92), X(17658)}}, {{A, B, C, X(189), X(3680)}}, {{A, B, C, X(200), X(2338)}}, {{A, B, C, X(223), X(1167)}}, {{A, B, C, X(241), X(10388)}}, {{A, B, C, X(282), X(2983)}}, {{A, B, C, X(306), X(47344)}}, {{A, B, C, X(312), X(2184)}}, {{A, B, C, X(321), X(26669)}}, {{A, B, C, X(333), X(25934)}}, {{A, B, C, X(335), X(37874)}}, {{A, B, C, X(459), X(1041)}}, {{A, B, C, X(527), X(3305)}}, {{A, B, C, X(673), X(25893)}}, {{A, B, C, X(801), X(17743)}}, {{A, B, C, X(1063), X(38253)}}, {{A, B, C, X(1214), X(6282)}}, {{A, B, C, X(1807), X(41081)}}, {{A, B, C, X(2051), X(30500)}}, {{A, B, C, X(2094), X(51780)}}, {{A, B, C, X(2221), X(2999)}}, {{A, B, C, X(2297), X(2316)}}, {{A, B, C, X(2339), X(4564)}}, {{A, B, C, X(2994), X(4900)}}, {{A, B, C, X(3218), X(20196)}}, {{A, B, C, X(3219), X(31142)}}, {{A, B, C, X(3306), X(6692)}}, {{A, B, C, X(3445), X(6612)}}, {{A, B, C, X(5044), X(31424)}}, {{A, B, C, X(5249), X(8257)}}, {{A, B, C, X(5256), X(8583)}}, {{A, B, C, X(5560), X(6504)}}, {{A, B, C, X(5785), X(31658)}}, {{A, B, C, X(6557), X(56101)}}, {{A, B, C, X(7308), X(9965)}}, {{A, B, C, X(12555), X(37558)}}, {{A, B, C, X(17022), X(19860)}}, {{A, B, C, X(18743), X(25939)}}, {{A, B, C, X(23617), X(51341)}}, {{A, B, C, X(23681), X(27819)}}, {{A, B, C, X(38255), X(56100)}}
X(56230) = barycentric product X(i)*X(j) for these (i, j): {8, 8829}, {312, 8828}
X(56230) = barycentric quotient X(i)/X(j) for these (i, j): {1, 14986}, {8828, 57}, {8829, 7}

X(56231) = KP3(X(37)) OF X(10) AND X(90)

Barycentrics    a*(a+b-c)*(a-b+c)*(a^3+a^2*(b-c)-(b-c)*(b+c)^2-a*(b^2+4*b*c+c^2))*(a^3+a^2*(-b+c)+(b-c)*(b+c)^2-a*(b^2+4*b*c+c^2)) : :

X(56231) lies on these lines: {1, 6883}, {2, 7269}, {57, 2178}, {81, 1708}, {223, 52374}, {226, 15474}, {274, 31631}, {278, 52033}, {985, 8270}, {1219, 4511}, {1422, 2003}, {2006, 2999}, {2910, 6826}, {2990, 16578}, {4654, 34578}, {5219, 37887}, {5422, 56041}, {6198, 40836}, {7073, 37696}, {7146, 40188}, {8056, 26742}, {8257, 40399}, {11518, 51498}, {25417, 37787}, {34489, 51223}, {37543, 39947}, {45126, 56050}

X(56231) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 10527}, {7, 32561}, {9, 3338}, {57, 42012}, {100, 13401}, {284, 12609}, {664, 17412}, {2337, 10044}
X(56231) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 10527}, {478, 3338}, {5452, 42012}, {8054, 13401}, {39025, 17412}, {40590, 12609}
X(56231) = X(i)-cross conjugate of X(j) for these {i, j}: {52424, 57}
X(56231) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(6), X(913)}}, {{A, B, C, X(9), X(1857)}}, {{A, B, C, X(27), X(6883)}}, {{A, B, C, X(33), X(1174)}}, {{A, B, C, X(58), X(7130)}}, {{A, B, C, X(63), X(2051)}}, {{A, B, C, X(78), X(45127)}}, {{A, B, C, X(92), X(44178)}}, {{A, B, C, X(189), X(1389)}}, {{A, B, C, X(222), X(1807)}}, {{A, B, C, X(223), X(2003)}}, {{A, B, C, X(226), X(1708)}}, {{A, B, C, X(269), X(7269)}}, {{A, B, C, X(329), X(44861)}}, {{A, B, C, X(937), X(5397)}}, {{A, B, C, X(967), X(998)}}, {{A, B, C, X(997), X(5256)}}, {{A, B, C, X(1041), X(40149)}}, {{A, B, C, X(1061), X(40397)}}, {{A, B, C, X(1096), X(2279)}}, {{A, B, C, X(1945), X(39967)}}, {{A, B, C, X(2149), X(2258)}}, {{A, B, C, X(2167), X(42467)}}, {{A, B, C, X(2334), X(8777)}}, {{A, B, C, X(2339), X(14554)}}, {{A, B, C, X(2994), X(56152)}}, {{A, B, C, X(2999), X(4511)}}, {{A, B, C, X(4564), X(44733)}}, {{A, B, C, X(4654), X(37787)}}, {{A, B, C, X(5227), X(34276)}}, {{A, B, C, X(7146), X(8270)}}, {{A, B, C, X(32008), X(40573)}}, {{A, B, C, X(34489), X(37543)}}, {{A, B, C, X(36100), X(45098)}}, {{A, B, C, X(36599), X(55027)}}
X(56231) = barycentric product X(i)*X(j) for these (i, j): {7, 7162}
X(56231) = barycentric quotient X(i)/X(j) for these (i, j): {1, 10527}, {41, 32561}, {55, 42012}, {56, 3338}, {65, 12609}, {649, 13401}, {1454, 10044}, {3063, 17412}, {7162, 8}

X(56232) = KP3(X(37)) OF X(10) AND X(92)

Barycentrics    a*(a-b-c)*(-b^3+b*c^2+a^2*(b+c)+a*c*(2*b+c))*(a^2*(b+c)+a*b*(b+2*c)+c*(b^2-c^2)) : :

X(56232) lies on these lines: {1, 40572}, {9, 54356}, {33, 46884}, {37, 579}, {210, 3190}, {270, 35192}, {273, 16577}, {1826, 1838}, {1903, 16601}, {2250, 3731}, {2268, 2341}, {2321, 6734}, {4687, 16578}, {7064, 37993}, {8818, 18591}, {29343, 45926}, {54287, 54407}

X(56232) = trilinear pole of line {4041, 8676}
X(56232) = X(i)-isoconjugate-of-X(j) for these {i, j}: {7, 584}, {56, 5278}, {57, 5248}, {651, 48297}, {37543, 45128}
X(56232) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 5278}, {5452, 5248}, {38991, 48297}
X(56232) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(270)}}, {{A, B, C, X(2), X(284)}}, {{A, B, C, X(6), X(2006)}}, {{A, B, C, X(9), X(33)}}, {{A, B, C, X(21), X(3596)}}, {{A, B, C, X(29), X(16290)}}, {{A, B, C, X(55), X(7110)}}, {{A, B, C, X(212), X(16577)}}, {{A, B, C, X(264), X(56153)}}, {{A, B, C, X(281), X(2338)}}, {{A, B, C, X(349), X(22021)}}, {{A, B, C, X(393), X(1174)}}, {{A, B, C, X(522), X(17038)}}, {{A, B, C, X(581), X(1068)}}, {{A, B, C, X(847), X(943)}}, {{A, B, C, X(941), X(2316)}}, {{A, B, C, X(947), X(1217)}}, {{A, B, C, X(1172), X(1255)}}, {{A, B, C, X(1212), X(3247)}}, {{A, B, C, X(1807), X(7951)}}, {{A, B, C, X(1880), X(2279)}}, {{A, B, C, X(2066), X(3302)}}, {{A, B, C, X(2165), X(2259)}}, {{A, B, C, X(2167), X(7094)}}, {{A, B, C, X(2287), X(40434)}}, {{A, B, C, X(2294), X(43682)}}, {{A, B, C, X(2324), X(16601)}}, {{A, B, C, X(2346), X(36122)}}, {{A, B, C, X(2364), X(39798)}}, {{A, B, C, X(3254), X(10013)}}, {{A, B, C, X(3255), X(4492)}}, {{A, B, C, X(3300), X(5414)}}, {{A, B, C, X(3451), X(46952)}}, {{A, B, C, X(3693), X(4687)}}, {{A, B, C, X(3737), X(30598)}}, {{A, B, C, X(3738), X(29343)}}, {{A, B, C, X(3876), X(4877)}}, {{A, B, C, X(4876), X(17750)}}, {{A, B, C, X(5750), X(27659)}}, {{A, B, C, X(7318), X(13404)}}, {{A, B, C, X(8748), X(32008)}}, {{A, B, C, X(34585), X(40505)}}, {{A, B, C, X(34820), X(36910)}}, {{A, B, C, X(43220), X(56221)}}
X(56232) = barycentric quotient X(i)/X(j) for these (i, j): {9, 5278}, {41, 584}, {55, 5248}, {663, 48297}

X(56233) = KP3(X(37)) OF X(10) AND X(103)

Barycentrics    (a^5+a^4*c+c*(b^2-c^2)^2+2*a^2*c*(b^2+2*b*c-c^2)+a*(b-c)^2*(b^2+c^2)-2*a^3*(b^2+b*c+c^2))*(a^5+a^4*b+b*(b^2-c^2)^2+a*(b-c)^2*(b^2+c^2)-2*a^3*(b^2+b*c+c^2)+2*a^2*b*(-b^2+2*b*c+c^2)) : :

X(56233) lies on these lines: {75, 25930}, {86, 25019}, {273, 27384}, {310, 55241}, {651, 1440}, {673, 26006}, {1815, 6559}, {3912, 52781}, {4209, 55937}, {7318, 26668}, {26658, 39721}

X(56233) = trilinear pole of line {40, 514}
X(56233) = isotomic conjugate of X(26001)
X(56233) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(25930)}}, {{A, B, C, X(2), X(7)}}, {{A, B, C, X(29), X(7131)}}, {{A, B, C, X(63), X(27384)}}, {{A, B, C, X(92), X(30705)}}, {{A, B, C, X(226), X(25019)}}, {{A, B, C, X(318), X(34401)}}, {{A, B, C, X(329), X(27508)}}, {{A, B, C, X(651), X(1897)}}, {{A, B, C, X(801), X(40435)}}, {{A, B, C, X(908), X(40880)}}, {{A, B, C, X(1067), X(44178)}}, {{A, B, C, X(1275), X(36796)}}, {{A, B, C, X(2297), X(2316)}}, {{A, B, C, X(3618), X(24556)}}, {{A, B, C, X(3912), X(26006)}}, {{A, B, C, X(4564), X(8777)}}, {{A, B, C, X(14942), X(36101)}}, {{A, B, C, X(17316), X(26658)}}, {{A, B, C, X(26575), X(26660)}}, {{A, B, C, X(26639), X(26672)}}, {{A, B, C, X(26668), X(31631)}}, {{A, B, C, X(40450), X(43760)}}, {{A, B, C, X(40802), X(56179)}}, {{A, B, C, X(43762), X(54235)}}
X(56233) = barycentric quotient X(i)/X(j) for these (i, j): {2, 26001}

X(56234) = KP3(X(37)) OF X(10) AND X(104)

Barycentrics    a*(a^4+a^3*b-a*b*(b^2-6*b*c+c^2)+(b-c)^2*(2*b^2+3*b*c+c^2)-a^2*(3*b^2+b*c+2*c^2))*(a^4+a^3*c-a*c*(b^2-6*b*c+c^2)+(b-c)^2*(b^2+3*b*c+2*c^2)-a^2*(2*b^2+b*c+3*c^2)) : :

X(56234) lies on these lines: {1, 14740}, {28, 1872}, {57, 16578}, {274, 26591}, {278, 5748}, {279, 26611}, {651, 1422}, {957, 1482}, {1219, 24558}, {1897, 27383}, {4358, 16082}, {5422, 25417}, {25243, 39706}

X(56234) = trilinear pole of line {40, 513}
X(56234) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 44675}, {909, 1537}, {2183, 52178}
X(56234) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 44675}, {23980, 1537}
X(56234) = X(i)-cross conjugate of X(j) for these {i, j}: {46393, 100}
X(56234) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(37), X(26591)}}, {{A, B, C, X(63), X(5748)}}, {{A, B, C, X(104), X(14554)}}, {{A, B, C, X(226), X(44861)}}, {{A, B, C, X(321), X(1872)}}, {{A, B, C, X(335), X(9372)}}, {{A, B, C, X(651), X(1897)}}, {{A, B, C, X(908), X(45393)}}, {{A, B, C, X(1016), X(2988)}}, {{A, B, C, X(1252), X(2338)}}, {{A, B, C, X(1320), X(34234)}}, {{A, B, C, X(1807), X(4358)}}, {{A, B, C, X(2185), X(42339)}}, {{A, B, C, X(2994), X(56089)}}, {{A, B, C, X(2999), X(24558)}}, {{A, B, C, X(4511), X(16586)}}, {{A, B, C, X(4564), X(4997)}}, {{A, B, C, X(5121), X(26639)}}, {{A, B, C, X(5333), X(5422)}}, {{A, B, C, X(6336), X(43760)}}, {{A, B, C, X(7131), X(50442)}}, {{A, B, C, X(8582), X(17019)}}, {{A, B, C, X(14740), X(16578)}}, {{A, B, C, X(23617), X(56225)}}, {{A, B, C, X(25243), X(31035)}}, {{A, B, C, X(26637), X(37651)}}, {{A, B, C, X(36807), X(52780)}}, {{A, B, C, X(43736), X(51567)}}
X(56234) = barycentric quotient X(i)/X(j) for these (i, j): {1, 44675}, {104, 52178}, {517, 1537}, {13528, 52116}

X(56235) = TRILINEAR POLE OF LINE {40, 64}

Barycentrics    a*(a-b)*(a-c)*(a^4+b^4+2*b^2*c^2-3*c^4-2*a^2*(b^2-c^2))*(a^4-3*b^4+2*b^2*c^2+c^4+2*a^2*(b^2-c^2)) : :

X(56235) lies on these lines: {100, 1301}, {253, 6559}, {1073, 17776}, {1332, 7259}, {2405, 4552}, {6558, 52609}, {6574, 36079}, {7258, 44326}, {19611, 27396}, {27382, 46351}, {32849, 52514}, {46065, 51367}, {53639, 54970}

X(56235) = KP3(X(37)) of X(10) and X(108)
X(56235) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 21172}, {20, 649}, {27, 42658}, {56, 14331}, {58, 6587}, {154, 514}, {204, 905}, {513, 610}, {521, 3213}, {647, 44698}, {650, 1394}, {652, 44696}, {663, 18623}, {667, 18750}, {1019, 3198}, {1021, 40933}, {1249, 1459}, {1333, 17898}, {1412, 14308}, {1474, 8057}, {1790, 44705}, {1895, 22383}, {1919, 14615}, {1946, 44697}, {3063, 33673}, {3122, 36841}, {3172, 4025}, {3669, 7070}, {3733, 8804}, {3737, 30456}, {4091, 6525}, {5930, 7252}, {7254, 53011}, {7649, 15905}, {11125, 15291}, {16892, 51508}, {21102, 33629}, {21789, 36908}, {27382, 43924}
X(56235) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 14331}, {9, 21172}, {10, 6587}, {37, 17898}, {3343, 905}, {5375, 20}, {6631, 18750}, {7358, 40616}, {9296, 14615}, {10001, 33673}, {14092, 513}, {14390, 23224}, {39026, 610}, {39052, 44698}, {39053, 44697}, {40599, 14308}, {40839, 17924}, {51574, 8057}, {55063, 55058}
X(56235) = X(i)-cross conjugate of X(j) for these {i, j}: {1020, 190}, {1783, 100}
X(56235) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(32714)}}, {{A, B, C, X(2), X(2405)}}, {{A, B, C, X(100), X(1332)}}, {{A, B, C, X(190), X(644)}}, {{A, B, C, X(651), X(1897)}}, {{A, B, C, X(653), X(13138)}}, {{A, B, C, X(934), X(36099)}}, {{A, B, C, X(1020), X(1783)}}, {{A, B, C, X(1025), X(27508)}}, {{A, B, C, X(1301), X(44326)}}, {{A, B, C, X(2397), X(17776)}}, {{A, B, C, X(5382), X(46119)}}, {{A, B, C, X(13136), X(27834)}}, {{A, B, C, X(27396), X(42719)}}, {{A, B, C, X(32038), X(42303)}}, {{A, B, C, X(42700), X(42716)}}
X(56235) = barycentric product X(i)*X(j) for these (i, j): {37, 44326}, {64, 668}, {100, 253}, {190, 2184}, {321, 46639}, {341, 36079}, {1073, 6335}, {1301, 20336}, {1332, 459}, {1783, 34403}, {1897, 19611}, {1978, 2155}, {3699, 8809}, {4551, 5931}, {30457, 4554}, {33581, 6386}, {41530, 692}, {44692, 664}, {52345, 53886}, {52581, 906}, {53012, 811}, {53639, 72}
X(56235) = barycentric quotient X(i)/X(j) for these (i, j): {1, 21172}, {9, 14331}, {10, 17898}, {37, 6587}, {64, 513}, {72, 8057}, {100, 20}, {101, 610}, {108, 44696}, {109, 1394}, {162, 44698}, {190, 18750}, {210, 14308}, {228, 42658}, {253, 693}, {459, 17924}, {644, 27382}, {651, 18623}, {653, 44697}, {664, 33673}, {668, 14615}, {692, 154}, {906, 15905}, {1018, 8804}, {1020, 36908}, {1073, 905}, {1301, 28}, {1332, 37669}, {1783, 1249}, {1824, 44705}, {1897, 1895}, {2155, 649}, {2184, 514}, {3699, 52346}, {3939, 7070}, {3952, 52345}, {3998, 20580}, {4551, 5930}, {4557, 3198}, {4559, 30456}, {4567, 36841}, {4601, 55224}, {5379, 52913}, {5931, 18155}, {6335, 15466}, {8750, 204}, {8809, 3676}, {13138, 41084}, {14379, 23224}, {14642, 22383}, {15384, 52920}, {15394, 4131}, {19611, 4025}, {19614, 1459}, {30457, 650}, {32674, 3213}, {33581, 667}, {34403, 15413}, {36079, 269}, {41088, 6129}, {41489, 6591}, {41530, 40495}, {44326, 274}, {44692, 522}, {46639, 81}, {52158, 3737}, {52609, 42699}, {53012, 656}, {53321, 40933}, {53639, 286}, {55232, 1562}, {56183, 44695}

X(56236) = KP3(X(37)) OF X(37) AND X(42)

Barycentrics    a*(b+c)*(2*b*c+a*(2*b+c))*(2*b*c+a*(b+2*c)) : :

X(56236) lies on these lines: {1, 39961}, {2, 3760}, {6, 748}, {25, 40975}, {37, 4365}, {42, 16589}, {111, 6013}, {226, 42290}, {251, 5259}, {899, 39967}, {941, 5257}, {967, 17110}, {1218, 4687}, {1334, 40147}, {1400, 39793}, {2238, 28625}, {2276, 39983}, {2350, 30950}, {2998, 27268}, {3572, 4813}, {4651, 52708}, {5333, 37128}, {21071, 26037}, {21838, 56158}, {24592, 39971}, {26102, 39965}, {30821, 39957}, {31027, 40776}, {31136, 39974}

X(56236) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 39673}, {58, 4687}, {81, 17018}, {110, 47666}, {333, 16878}, {662, 6005}, {799, 8655}, {4556, 48407}, {4610, 50483}
X(56236) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 4687}, {244, 47666}, {1084, 6005}, {32664, 39673}, {38996, 8655}, {40586, 17018}
X(56236) = X(i)-Ceva conjugate of X(j) for these {i, j}: {56051, 46772}
X(56236) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(32092)}}, {{A, B, C, X(2), X(6)}}, {{A, B, C, X(10), X(310)}}, {{A, B, C, X(210), X(6557)}}, {{A, B, C, X(226), X(756)}}, {{A, B, C, X(291), X(56221)}}, {{A, B, C, X(523), X(9038)}}, {{A, B, C, X(649), X(37870)}}, {{A, B, C, X(748), X(3760)}}, {{A, B, C, X(899), X(43223)}}, {{A, B, C, X(1088), X(42289)}}, {{A, B, C, X(1255), X(40747)}}, {{A, B, C, X(1334), X(40586)}}, {{A, B, C, X(2238), X(4813)}}, {{A, B, C, X(2296), X(17038)}}, {{A, B, C, X(3954), X(5259)}}, {{A, B, C, X(4423), X(5556)}}, {{A, B, C, X(4651), X(30950)}}, {{A, B, C, X(7196), X(21803)}}, {{A, B, C, X(10013), X(46772)}}, {{A, B, C, X(15320), X(34585)}}, {{A, B, C, X(18098), X(40434)}}, {{A, B, C, X(18785), X(25430)}}, {{A, B, C, X(21805), X(36915)}}, {{A, B, C, X(21877), X(27268)}}, {{A, B, C, X(23493), X(25264)}}, {{A, B, C, X(30588), X(52651)}}, {{A, B, C, X(31330), X(31356)}}, {{A, B, C, X(40439), X(40775)}}
X(56236) = barycentric product X(i)*X(j) for these (i, j): {1, 46772}, {10, 10013}, {37, 56051}, {226, 56208}, {523, 6013}, {56087, 65}
X(56236) = barycentric quotient X(i)/X(j) for these (i, j): {31, 39673}, {37, 4687}, {42, 17018}, {512, 6005}, {661, 47666}, {669, 8655}, {1402, 16878}, {4705, 48407}, {6013, 99}, {10013, 86}, {46772, 75}, {50487, 50483}, {56051, 274}, {56087, 314}, {56208, 333}

X(56237) = KP3(X(37)) OF X(37) AND X(65)

Barycentrics    a*(b+c)*(a+3*b+c)*(a+b+3*c) : :
X(56237) = -5*X[1698]+X[39711]

X(56237) lies on these lines: {1, 210}, {10, 3175}, {12, 3668}, {19, 45}, {37, 3214}, {44, 2214}, {65, 756}, {72, 53114}, {75, 3701}, {82, 15254}, {225, 7140}, {267, 2941}, {518, 39739}, {596, 3634}, {759, 8694}, {876, 29198}, {897, 4606}, {960, 9330}, {969, 5220}, {984, 39742}, {1247, 4689}, {1698, 39711}, {1910, 34074}, {2217, 37600}, {2292, 4731}, {2363, 5297}, {3246, 56034}, {3617, 3714}, {3626, 42285}, {3663, 34501}, {3689, 54287}, {3694, 16676}, {3697, 37593}, {3698, 4674}, {3743, 3921}, {3842, 27432}, {3962, 56191}, {3967, 19874}, {4005, 31503}, {4009, 19853}, {4015, 21870}, {4059, 24797}, {4420, 40430}, {4424, 56135}, {4518, 18827}, {4642, 56159}, {4663, 32635}, {4906, 17534}, {5550, 39702}, {6051, 50575}, {13476, 14626}, {17536, 49465}, {19862, 24003}, {21674, 52382}, {26115, 41683}, {31855, 56215}, {46897, 46934}, {47842, 55244}, {49462, 56126}

X(56237) = trilinear pole of line {661, 4139}
X(56237) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 31903}, {6, 42028}, {21, 3361}, {28, 4652}, {58, 3616}, {60, 3671}, {81, 1449}, {101, 48580}, {110, 4778}, {163, 4801}, {284, 21454}, {391, 1412}, {593, 5257}, {662, 4790}, {757, 37593}, {1014, 4512}, {1333, 19804}, {1408, 4673}, {1434, 4258}, {1437, 5342}, {1444, 5338}, {2163, 17553}, {2363, 4719}, {4061, 7341}, {4556, 4841}, {4565, 4765}, {4591, 4773}, {4610, 4832}, {4627, 53586}, {4637, 4827}, {4822, 52935}, {5546, 30723}
X(56237) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 42028}, {10, 3616}, {37, 19804}, {115, 4801}, {244, 4778}, {960, 4719}, {1015, 48580}, {1084, 4790}, {6741, 4811}, {36103, 31903}, {40586, 1449}, {40587, 17553}, {40590, 21454}, {40591, 4652}, {40599, 391}, {40607, 37593}, {40611, 3361}, {52872, 4742}, {52875, 4706}, {55064, 4765}, {55065, 4815}
X(56237) = X(i)-Ceva conjugate of X(j) for these {i, j}: {53658, 47915}
X(56237) = X(i)-cross conjugate of X(j) for these {i, j}: {4646, 65}, {8672, 3952}
X(56237) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}}, {{A, B, C, X(2), X(3175)}}, {{A, B, C, X(4), X(11108)}}, {{A, B, C, X(12), X(210)}}, {{A, B, C, X(42), X(9780)}}, {{A, B, C, X(44), X(3992)}}, {{A, B, C, X(45), X(72)}}, {{A, B, C, X(79), X(34585)}}, {{A, B, C, X(86), X(55093)}}, {{A, B, C, X(88), X(56219)}}, {{A, B, C, X(201), X(3694)}}, {{A, B, C, X(226), X(3983)}}, {{A, B, C, X(321), X(1900)}}, {{A, B, C, X(512), X(28555)}}, {{A, B, C, X(740), X(29198)}}, {{A, B, C, X(758), X(28205)}}, {{A, B, C, X(899), X(26115)}}, {{A, B, C, X(979), X(28650)}}, {{A, B, C, X(1001), X(24797)}}, {{A, B, C, X(1156), X(25917)}}, {{A, B, C, X(1213), X(3931)}}, {{A, B, C, X(1214), X(37568)}}, {{A, B, C, X(1224), X(46187)}}, {{A, B, C, X(1268), X(43073)}}, {{A, B, C, X(1427), X(39963)}}, {{A, B, C, X(1698), X(50587)}}, {{A, B, C, X(1903), X(5044)}}, {{A, B, C, X(1989), X(51501)}}, {{A, B, C, X(2238), X(48027)}}, {{A, B, C, X(2292), X(4918)}}, {{A, B, C, X(2297), X(8951)}}, {{A, B, C, X(2334), X(5936)}}, {{A, B, C, X(3293), X(3634)}}, {{A, B, C, X(3294), X(49515)}}, {{A, B, C, X(3696), X(4059)}}, {{A, B, C, X(3697), X(51572)}}, {{A, B, C, X(3698), X(40663)}}, {{A, B, C, X(3842), X(20691)}}, {{A, B, C, X(3932), X(48395)}}, {{A, B, C, X(3954), X(15254)}}, {{A, B, C, X(3986), X(21896)}}, {{A, B, C, X(3993), X(25614)}}, {{A, B, C, X(4026), X(16583)}}, {{A, B, C, X(4420), X(21674)}}, {{A, B, C, X(4423), X(5556)}}, {{A, B, C, X(4492), X(20615)}}, {{A, B, C, X(4646), X(5257)}}, {{A, B, C, X(4663), X(21816)}}, {{A, B, C, X(4731), X(4848)}}, {{A, B, C, X(4854), X(52372)}}, {{A, B, C, X(4868), X(52706)}}, {{A, B, C, X(5221), X(37593)}}, {{A, B, C, X(5297), X(20653)}}, {{A, B, C, X(5302), X(21810)}}, {{A, B, C, X(7317), X(38955)}}, {{A, B, C, X(7319), X(41506)}}, {{A, B, C, X(9708), X(15232)}}, {{A, B, C, X(10693), X(56203)}}, {{A, B, C, X(15320), X(43733)}}, {{A, B, C, X(16605), X(50290)}}, {{A, B, C, X(19862), X(31855)}}, {{A, B, C, X(19870), X(50575)}}, {{A, B, C, X(21859), X(37138)}}, {{A, B, C, X(25430), X(40023)}}, {{A, B, C, X(27809), X(39740)}}, {{A, B, C, X(31993), X(41839)}}, {{A, B, C, X(34790), X(41013)}}, {{A, B, C, X(41711), X(56151)}}, {{A, B, C, X(43534), X(48644)}}, {{A, B, C, X(49468), X(52708)}}, {{A, B, C, X(52429), X(53013)}}
X(56237) = barycentric product X(i)*X(j) for these (i, j): {10, 25430}, {12, 56204}, {37, 5936}, {226, 4866}, {594, 56048}, {1441, 34820}, {1577, 8694}, {2334, 321}, {3952, 47915}, {4024, 4614}, {4036, 4627}, {4041, 4624}, {4606, 523}, {4633, 4705}, {31010, 35339}, {34074, 850}, {40023, 42}, {53658, 661}, {56086, 65}
X(56237) = barycentric quotient X(i)/X(j) for these (i, j): {1, 42028}, {10, 19804}, {19, 31903}, {37, 3616}, {42, 1449}, {45, 17553}, {65, 21454}, {71, 4652}, {210, 391}, {512, 4790}, {513, 48580}, {523, 4801}, {661, 4778}, {756, 5257}, {1334, 4512}, {1400, 3361}, {1500, 37593}, {1826, 5342}, {2092, 4719}, {2171, 3671}, {2321, 4673}, {2333, 5338}, {2334, 81}, {3690, 4047}, {3700, 4811}, {3930, 4684}, {3943, 4742}, {3949, 4101}, {4017, 30723}, {4024, 4815}, {4041, 4765}, {4069, 30728}, {4079, 4822}, {4155, 4839}, {4524, 4827}, {4606, 99}, {4614, 4610}, {4624, 4625}, {4627, 52935}, {4633, 4623}, {4705, 4841}, {4730, 4773}, {4822, 53586}, {4866, 333}, {5936, 274}, {6057, 42712}, {8694, 662}, {14626, 18206}, {20691, 4734}, {21801, 51423}, {21805, 4700}, {21832, 4830}, {21839, 4831}, {24290, 50357}, {25430, 86}, {34074, 110}, {34820, 21}, {40023, 310}, {47915, 7192}, {50487, 4832}, {52651, 4835}, {52959, 4706}, {53658, 799}, {56048, 1509}, {56086, 314}, {56204, 261}
X(56237) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4866, 25430, 2334}

X(56238) = KP3(X(37)) OF X(42) AND X(4)

Barycentrics    (a^3*(b-c)-a^2*b*c-b^3*c+b*c^3-a*(b^3+b^2*c+b*c^2+c^3))*(a^3*(b-c)+a^2*b*c-b^3*c+b*c^3+a*(b^3+b^2*c+b*c^2+c^3)) : :

X(56238) lies on the Feuerbach hyperbola and on these lines: {1, 20753}, {4, 3056}, {7, 3784}, {9, 3971}, {21, 192}, {212, 983}, {242, 1039}, {314, 6382}, {321, 7155}, {350, 30479}, {2276, 2335}, {2345, 4876}, {3254, 38484}, {10453, 43749}, {17863, 41527}

X(56238) = trilinear pole of line {650, 21051}
X(56238) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(2), X(4362)}}, {{A, B, C, X(19), X(40422)}}, {{A, B, C, X(69), X(12588)}}, {{A, B, C, X(87), X(54128)}}, {{A, B, C, X(192), X(321)}}, {{A, B, C, X(212), X(3056)}}, {{A, B, C, X(242), X(350)}}, {{A, B, C, X(257), X(19222)}}, {{A, B, C, X(608), X(1244)}}, {{A, B, C, X(976), X(10449)}}, {{A, B, C, X(1246), X(2214)}}, {{A, B, C, X(1390), X(2995)}}, {{A, B, C, X(2276), X(44140)}}, {{A, B, C, X(2991), X(17040)}}, {{A, B, C, X(3757), X(33137)}}, {{A, B, C, X(3961), X(10453)}}, {{A, B, C, X(4581), X(5936)}}, {{A, B, C, X(4812), X(33889)}}, {{A, B, C, X(7009), X(17787)}}, {{A, B, C, X(9309), X(30651)}}, {{A, B, C, X(13610), X(39741)}}, {{A, B, C, X(18816), X(23051)}}, {{A, B, C, X(20056), X(29652)}}, {{A, B, C, X(21334), X(23853)}}, {{A, B, C, X(23289), X(34820)}}, {{A, B, C, X(30710), X(34208)}}

X(56239) = KP3(X(37)) OF X(42) AND X(7)

Barycentrics    a^4*(b-c)^2+b^2*(b-c)^2*c^2-a^2*(b^4+8*b^3*c+7*b^2*c^2+8*b*c^3+c^4) : :

X(56239) lies on these lines: {239, 3305}, {350, 3974}, {612, 1447}, {756, 41527}, {870, 32937}, {873, 24349}, {984, 54128}, {3112, 27538}, {7192, 7226}, {9330, 27807}

X(56239) = trilinear pole of line {47965, 812}
X(56239) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(39741)}}, {{A, B, C, X(2), X(239)}}, {{A, B, C, X(7), X(1255)}}, {{A, B, C, X(8), X(33)}}, {{A, B, C, X(38), X(27538)}}, {{A, B, C, X(75), X(39694)}}, {{A, B, C, X(310), X(39703)}}, {{A, B, C, X(756), X(7235)}}, {{A, B, C, X(984), X(32937)}}, {{A, B, C, X(1000), X(8817)}}, {{A, B, C, X(1280), X(7320)}}, {{A, B, C, X(2296), X(39738)}}, {{A, B, C, X(2481), X(25430)}}, {{A, B, C, X(3952), X(7226)}}, {{A, B, C, X(5559), X(34409)}}, {{A, B, C, X(5936), X(54235)}}, {{A, B, C, X(8049), X(27789)}}, {{A, B, C, X(9330), X(17140)}}, {{A, B, C, X(21453), X(43750)}}, {{A, B, C, X(34258), X(39714)}}

X(56240) = KP3(X(37)) OF X(42) AND X(42)

Barycentrics    a*(b+c)*(2*a*b^2*c+b^2*c^2+a^2*(b^2+c^2))*(2*a*b*c^2+b^2*c^2+a^2*(b^2+c^2)) : :

X(56240) lies on these lines: {1, 1197}, {2, 18832}, {10, 21838}, {19, 11325}, {75, 194}, {82, 38834}, {893, 16827}, {1581, 47642}, {5283, 17038}, {13476, 17448}, {16819, 18833}, {16975, 39742}, {18298, 37596}, {30038, 39712}

X(56240) = trilinear pole of line {661, 3221}
X(56240) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}}, {{A, B, C, X(2), X(194)}}, {{A, B, C, X(42), X(330)}}, {{A, B, C, X(213), X(274)}}, {{A, B, C, X(756), X(21345)}}, {{A, B, C, X(894), X(16827)}}, {{A, B, C, X(3294), X(17448)}}, {{A, B, C, X(16696), X(16819)}}, {{A, B, C, X(20691), X(40844)}}, {{A, B, C, X(21387), X(21608)}}, {{A, B, C, X(21830), X(40881)}}, {{A, B, C, X(31996), X(52894)}}
X(56240) = barycentric product X(i)*X(j) for these (i, j): {1, 56211}
X(56240) = barycentric quotient X(i)/X(j) for these (i, j): {56211, 75}

X(56241) = KP3(X(37)) OF X(42) AND X(99)

Barycentrics    (a-b)*b*(a-c)*c*(b^2+a*c)*(a*b+c^2) : :

X(56241) lies on these lines: {75, 1581}, {192, 40729}, {256, 40844}, {523, 670}, {646, 3807}, {694, 9055}, {874, 3903}, {1178, 4360}, {3263, 52135}, {4367, 56053}, {4451, 20895}, {4552, 37137}, {4561, 29055}, {11611, 33941}, {18830, 33946}, {40017, 53559}, {40873, 40875}

X(56241) = isotomic conjugate of X(4367)
X(56241) = trilinear pole of line {257, 312}
X(56241) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 20981}, {25, 22093}, {31, 4367}, {32, 4369}, {58, 7234}, {110, 4128}, {162, 22373}, {163, 16592}, {171, 667}, {172, 649}, {184, 54229}, {213, 18200}, {513, 7122}, {560, 4374}, {604, 3287}, {662, 21755}, {669, 17103}, {692, 53541}, {741, 5027}, {875, 1580}, {876, 1933}, {894, 1919}, {1106, 4477}, {1397, 3907}, {1576, 53559}, {1691, 3572}, {1909, 1980}, {1911, 4164}, {1918, 17212}, {1922, 4107}, {1924, 8033}, {1977, 18047}, {2205, 16737}, {2206, 2533}, {2330, 43924}, {3051, 18111}, {3063, 7175}, {3248, 4579}, {3733, 20964}, {4140, 16947}, {4444, 14602}, {4529, 52410}, {4556, 21823}, {7119, 22383}, {7121, 24533}, {7200, 32739}, {14296, 14598}, {21752, 39179}, {22061, 43925}, {40745, 46386}, {40746, 45882}
X(56241) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 4367}, {9, 20981}, {10, 7234}, {115, 16592}, {125, 22373}, {244, 4128}, {1084, 21755}, {1086, 53541}, {3161, 3287}, {4858, 53559}, {5375, 172}, {6374, 4374}, {6376, 4369}, {6505, 22093}, {6552, 4477}, {6626, 18200}, {6631, 171}, {6651, 4164}, {6741, 40608}, {8299, 5027}, {9296, 894}, {9428, 8033}, {10001, 7175}, {16592, 7207}, {17755, 53553}, {18277, 14296}, {19584, 45882}, {27481, 3805}, {34021, 17212}, {39026, 7122}, {39028, 4107}, {39092, 875}, {40598, 24533}, {40603, 2533}, {40619, 7200}, {40624, 4459}, {52651, 45902}, {55065, 21725}
X(56241) = X(i)-Ceva conjugate of X(j) for these {i, j}: {7260, 27805}
X(56241) = X(i)-cross conjugate of X(j) for these {i, j}: {3700, 76}, {3703, 1016}, {21051, 2}, {21604, 799}, {27853, 4583}, {33938, 7035}
X(56241) = intersection, other than A, B, C, of these circumconics: {{A, B, C, X(75), X(670)}}, {{A, B, C, X(99), X(4552)}}, {{A, B, C, X(190), X(3807)}}, {{A, B, C, X(523), X(2643)}}, {{A, B, C, X(645), X(3596)}}, {{A, B, C, X(646), X(668)}}, {{A, B, C, X(662), X(35147)}}, {{A, B, C, X(693), X(42555)}}, {{A, B, C, X(789), X(6335)}}, {{A, B, C, X(883), X(20895)}}, {{A, B, C, X(1268), X(37205)}}, {{A, B, C, X(1581), X(3903)}}, {{A, B, C, X(1978), X(18830)}}, {{A, B, C, X(3573), X(51836)}}, {{A, B, C, X(3952), X(4609)}}, {{A, B, C, X(4367), X(21051)}}, {{A, B, C, X(4594), X(27805)}}, {{A, B, C, X(4602), X(53216)}}, {{A, B, C, X(4623), X(15455)}}, {{A, B, C, X(6742), X(17914)}}, {{A, B, C, X(8709), X(54458)}}, {{A, B, C, X(17930), X(38340)}}
X(56241) = barycentric product X(i)*X(j) for these (i, j): {10, 7260}, {100, 44187}, {190, 7018}, {257, 668}, {313, 4603}, {321, 4594}, {646, 7249}, {1581, 27853}, {1916, 874}, {1934, 3570}, {1978, 256}, {3596, 37137}, {3903, 76}, {4451, 4554}, {6335, 7019}, {6386, 893}, {17493, 4583}, {18829, 3948}, {18896, 3573}, {27447, 36863}, {27805, 75}, {27808, 40432}, {28659, 29055}, {32010, 4033}, {35544, 37134}, {40729, 4609}, {40738, 4505}, {52651, 670}
X(56241) = barycentric quotient X(i)/X(j) for these (i, j): {1, 20981}, {2, 4367}, {8, 3287}, {37, 7234}, {63, 22093}, {75, 4369}, {76, 4374}, {86, 18200}, {92, 54229}, {100, 172}, {101, 7122}, {190, 171}, {192, 24533}, {239, 4164}, {256, 649}, {257, 513}, {274, 17212}, {310, 16737}, {312, 3907}, {321, 2533}, {341, 4529}, {346, 4477}, {350, 4107}, {512, 21755}, {514, 53541}, {523, 16592}, {644, 2330}, {646, 7081}, {647, 22373}, {661, 4128}, {664, 7175}, {668, 894}, {670, 8033}, {693, 7200}, {694, 875}, {789, 40745}, {799, 17103}, {805, 18268}, {874, 385}, {893, 667}, {904, 1919}, {984, 45882}, {1016, 4579}, {1018, 20964}, {1332, 3955}, {1432, 43924}, {1577, 53559}, {1581, 3572}, {1897, 7119}, {1916, 876}, {1921, 14296}, {1934, 4444}, {1978, 1909}, {2238, 5027}, {3112, 18111}, {3570, 1580}, {3573, 1691}, {3661, 3805}, {3699, 2329}, {3700, 40608}, {3701, 4140}, {3783, 30654}, {3807, 40790}, {3863, 50514}, {3903, 6}, {3912, 53553}, {3948, 804}, {3952, 2295}, {4024, 21725}, {4033, 1215}, {4103, 21803}, {4110, 30584}, {4155, 2086}, {4358, 4922}, {4369, 7207}, {4391, 4459}, {4451, 650}, {4554, 7176}, {4562, 18787}, {4572, 7196}, {4583, 30669}, {4594, 81}, {4595, 51902}, {4603, 58}, {4671, 4774}, {4705, 21823}, {4835, 4790}, {6335, 7009}, {6386, 1920}, {7015, 22383}, {7018, 514}, {7019, 905}, {7035, 18047}, {7104, 1980}, {7249, 3669}, {7257, 27958}, {7260, 86}, {17493, 659}, {18743, 4504}, {18786, 8632}, {18829, 37128}, {20895, 28006}, {24004, 4434}, {27447, 43931}, {27569, 24381}, {27805, 1}, {27808, 3963}, {27853, 1966}, {29055, 604}, {30596, 4842}, {30670, 40746}, {32010, 1019}, {33946, 7184}, {35309, 40936}, {36863, 17752}, {37134, 741}, {37137, 56}, {39292, 36066}, {40432, 3733}, {40729, 669}, {40835, 7255}, {41209, 39276}, {42720, 4447}, {42721, 7267}, {43263, 4401}, {44187, 693}, {51614, 41534}, {52651, 512}, {52923, 51319}, {53332, 28369}, {53363, 4754}

X(56242) = X(6)X(23570)∩X(31)X(669)

Barycentrics    a^3*(b-c)*(a^2+b*c) : :

X(56242) lies on these lines: {6, 23570}, {31, 669}, {81, 50524}, {110, 24041}, {171, 24533}, {238, 25537}, {512, 5006}, {513, 8633}, {649, 1980}, {661, 5040}, {667, 50514}, {692, 41405}, {788, 8646}, {1021, 50544}, {1397, 7180}, {1580, 4367}, {1919, 8640}, {3063, 4507}, {3733, 9426}, {4164, 4369}, {4897, 24286}, {6373, 21005}, {7234, 20981}, {8635, 21758}, {8651, 23189}, {9256, 16612}, {9404, 17990}, {17123, 24747}, {18199, 53271}, {20979, 23568}, {21349, 21392}, {23301, 50302}, {25473, 32784}, {27982, 28007}, {31003, 32772}

X(56242) = midpoint of X(i) and X(j) for these {i,j}: {7252, 16874}, {8646, 22383}
X(56242) = isogonal conjugate of X(56241)
X(56242) = trilinear pole of line {21755, 22373}
X(56242) = perspector of circumconic {{A, B, C, X(172), X(604)}}
X(56242) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 56241}, {2, 27805}, {10, 4594}, {37, 7260}, {75, 3903}, {100, 7018}, {101, 44187}, {190, 257}, {256, 668}, {274, 56257}, {312, 37137}, {321, 4603}, {646, 1432}, {664, 4451}, {694, 27853}, {740, 18829}, {799, 52651}, {805, 35544}, {874, 1581}, {893, 1978}, {904, 6386}, {1178, 27808}, {1897, 7019}, {1916, 3570}, {1934, 3573}, {3596, 29055}, {3699, 7249}, {3807, 40738}, {3948, 37134}, {3952, 32010}, {4033, 40432}, {4505, 40763}, {4562, 17493}, {4583, 18786}, {4595, 27447}, {4602, 40729}, {4835, 53658}, {7239, 40835}, {18047, 40099}, {30670, 33931}, {51614, 52135}
X(56242) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 56241}, {206, 3903}, {1015, 44187}, {4369, 850}, {8054, 7018}, {16592, 561}, {19576, 874}, {32664, 27805}, {34467, 7019}, {38996, 52651}, {39025, 4451}, {39031, 3570}, {39043, 27853}, {40589, 7260}, {40597, 1978}, {55053, 257}
X(56242) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4565, 32}, {4579, 172}, {53628, 1333}
X(56242) = lies on inconic with perspector X(4579)
X(56242) = intersection, other than A, B, C, of circumconics {{A, B, C, X(31), X(1580)}}, {{A, B, C, X(110), X(669)}}, {{A, B, C, X(171), X(51864)}}, {{A, B, C, X(385), X(9111)}}, {{A, B, C, X(875), X(4367)}}, {{A, B, C, X(1215), X(40148)}}, {{A, B, C, X(2162), X(8033)}}, {{A, B, C, X(3287), X(7252)}}
X(56242) = barycentric product X(i)*X(j) for these (i, j): {1, 20981}, {19, 22093}, {31, 4369}, {32, 4374}, {48, 54229}, {101, 53541}, {110, 16592}, {163, 53559}, {171, 649}, {172, 513}, {292, 4164}, {385, 875}, {514, 7122}, {663, 7175}, {667, 894}, {669, 8033}, {692, 7200}, {1015, 4579}, {1019, 20964}, {1106, 4529}, {1333, 2533}, {1407, 4477}, {1408, 4140}, {1415, 4459}, {1438, 53553}, {1459, 7119}, {1580, 3572}, {1691, 876}, {1909, 1919}, {1911, 4107}, {1920, 1980}, {1933, 4444}, {2086, 36066}, {2162, 24533}, {2295, 3733}, {2329, 43924}, {2330, 3669}, {3063, 7176}, {3287, 56}, {3805, 40746}, {3907, 604}, {3955, 6591}, {4128, 662}, {4367, 6}, {4922, 9456}, {7234, 81}, {14296, 1922}, {16737, 1918}, {17103, 798}, {17212, 213}, {18047, 3248}, {18111, 1964}, {18200, 42}, {18268, 804}, {18787, 8632}, {21725, 4556}, {21755, 99}, {21823, 52935}, {22373, 648}, {22383, 7009}, {27958, 51641}, {28607, 4774}, {37128, 5027}, {38266, 4504}, {39179, 40936}, {40608, 4565}, {40745, 788}, {43929, 4447}, {43931, 51319}, {45882, 985}
X(56242) = barycentric quotient X(i)/X(j) for these (i, j): {6, 56241}, {31, 27805}, {32, 3903}, {58, 7260}, {171, 1978}, {172, 668}, {513, 44187}, {649, 7018}, {667, 257}, {669, 52651}, {875, 1916}, {876, 18896}, {894, 6386}, {1333, 4594}, {1397, 37137}, {1580, 27853}, {1691, 874}, {1918, 56257}, {1919, 256}, {1933, 3570}, {1980, 893}, {2206, 4603}, {2295, 27808}, {2330, 646}, {2533, 27801}, {3063, 4451}, {3287, 3596}, {3572, 1934}, {3907, 28659}, {4107, 18891}, {4128, 1577}, {4164, 1921}, {4367, 76}, {4369, 561}, {4374, 1502}, {4579, 31625}, {5027, 3948}, {7122, 190}, {7175, 4572}, {7200, 40495}, {7234, 321}, {8033, 4609}, {9426, 40729}, {14296, 44169}, {14602, 3573}, {16592, 850}, {17103, 4602}, {17212, 6385}, {18111, 18833}, {18200, 310}, {18268, 18829}, {20964, 4033}, {20981, 75}, {21725, 52623}, {21755, 523}, {21823, 4036}, {22093, 304}, {22373, 525}, {22383, 7019}, {24533, 6382}, {40745, 46132}, {45882, 33931}, {51319, 36863}, {53541, 3261}, {53559, 20948}, {54229, 1969}

X(56242) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7252, 16874, 512}, {8635, 21758, 50521}, {8646, 22383, 788}

X(56243) = KP4(X(9)) OF X(8) AND X(8)

Barycentrics    a*(a-b-c)*(a^2-2*a*b+b^2+c^2)*(a^2+b^2-2*a*c+c^2) : :

X(56243) lies on these lines: {6, 3692}, {9, 30681}, {19, 346}, {55, 30618}, {57, 345}, {63, 4437}, {169, 49782}, {200, 2195}, {312, 673}, {644, 1040}, {1024, 3239}, {1334, 2339}, {2291, 52778}, {2299, 62265}, {2321, 39943}, {3699, 6169}, {3719, 39273}, {4513, 17597}, {7077, 14935}, {7347, 13458}, {7348, 13425}

X(56243) = isogonal conjugate of X(28017)
X(56243) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 28017}, {6, 7195}, {7, 16502}, {34, 7289}, {56, 4000}, {57, 614}, {81, 40961}, {109, 48398}, {222, 1851}, {269, 2082}, {278, 1473}, {279, 7083}, {479, 30706}, {497, 1407}, {552, 21813}, {604, 3673}, {608, 17170}, {738, 4319}, {1014, 16583}, {1040, 1435}, {1119, 7124}, {1214, 4211}, {1396, 17441}, {1398, 27509}, {1402, 16750}, {1408, 53510}, {1412, 3914}, {1416, 51400}, {1427, 5324}, {1434, 40934}, {1633, 3669}, {3732, 43924}, {4565, 48403}, {4573, 50490}, {4617, 17115}, {6554, 7023}, {7177, 40987}
X(56243) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 4000}, {3, 28017}, {9, 7195}, {11, 48398}, {3161, 3673}, {5452, 614}, {6600, 2082}, {11517, 7289}, {24771, 497}, {40586, 40961}, {40599, 3914}, {40605, 16750}, {40609, 51400}, {55064, 48403}
X(56243) = X(i)-Ceva conjugate of X(j) for these {i, j}: {30701, 62262}
X(56243) = X(i)-cross conjugate of X(j) for these {i, j}: {9, 7131}, {521, 644}, {4105, 3699}
X(56243) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3744)}}, {{A, B, C, X(2), X(1261)}}, {{A, B, C, X(6), X(9)}}, {{A, B, C, X(8), X(1280)}}, {{A, B, C, X(21), X(6995)}}, {{A, B, C, X(33), X(4876)}}, {{A, B, C, X(63), X(1252)}}, {{A, B, C, X(78), X(10327)}}, {{A, B, C, X(92), X(34525)}}, {{A, B, C, X(200), X(312)}}, {{A, B, C, X(271), X(17784)}}, {{A, B, C, X(345), X(346)}}, {{A, B, C, X(521), X(1040)}}, {{A, B, C, X(1260), X(3719)}}, {{A, B, C, X(2287), X(18141)}}, {{A, B, C, X(3501), X(7079)}}, {{A, B, C, X(3610), X(3694)}}, {{A, B, C, X(3749), X(17597)}}, {{A, B, C, X(3886), X(3996)}}, {{A, B, C, X(4105), X(6168)}}, {{A, B, C, X(4183), X(37280)}}, {{A, B, C, X(4997), X(19605)}}, {{A, B, C, X(6557), X(41798)}}, {{A, B, C, X(7123), X(7131)}}, {{A, B, C, X(8817), X(62262)}}, {{A, B, C, X(17594), X(37540)}}
X(56243) = barycentric product X(i)*X(j) for these (i, j): {200, 8817}, {312, 7123}, {346, 7131}, {522, 52778}, {1037, 341}, {1041, 1265}, {2321, 40403}, {3596, 7084}, {3694, 40411}, {4163, 8269}, {14935, 7035}, {30701, 9}, {30705, 728}, {42384, 652}, {48070, 644}, {54967, 663}, {62262, 8}
X(56243) = barycentric quotient X(i)/X(j) for these (i, j): {1, 7195}, {6, 28017}, {8, 3673}, {9, 4000}, {33, 1851}, {41, 16502}, {42, 40961}, {55, 614}, {78, 17170}, {200, 497}, {210, 3914}, {212, 1473}, {219, 7289}, {220, 2082}, {333, 16750}, {480, 4319}, {644, 3732}, {650, 48398}, {728, 6554}, {1037, 269}, {1041, 1119}, {1253, 7083}, {1260, 1040}, {1334, 16583}, {1802, 7124}, {2299, 4211}, {2318, 17441}, {2321, 53510}, {2328, 5324}, {3501, 28110}, {3692, 27509}, {3693, 51400}, {3694, 18589}, {3710, 20235}, {3939, 1633}, {4041, 48403}, {4105, 17115}, {6602, 30706}, {7071, 40987}, {7084, 56}, {7123, 57}, {7131, 279}, {8269, 4626}, {8611, 21107}, {8817, 1088}, {14935, 244}, {17742, 41786}, {30701, 85}, {30705, 23062}, {40403, 1434}, {42384, 46404}, {48070, 24002}, {52370, 23620}, {52778, 664}, {54967, 4572}, {62262, 7}, {55337, 41785}

X(56244) = KP4(X(9)) OF X(8) AND X(142)

Barycentrics    a*(a-b-c)*(a^2+b^2-b*c+c^2-2*a*(b+c)) : :

X(56244) lies on these lines: {8, 9}, {21, 7259}, {45, 3721}, {63, 29627}, {75, 32088}, {85, 17336}, {190, 20880}, {220, 4511}, {644, 1212}, {1445, 32098}, {1759, 3730}, {2348, 3871}, {2975, 41391}, {3177, 28961}, {3219, 3912}, {3241, 16572}, {3294, 4115}, {3693, 4420}, {3731, 54392}, {3872, 4936}, {3957, 17745}, {4054, 30578}, {4384, 27065}, {5526, 34772}, {6559, 52344}, {6604, 37787}, {8545, 32086}, {10025, 28742}, {10039, 26793}, {12514, 39570}, {16284, 32100}, {17263, 32007}, {17350, 27253}, {24635, 28982}, {25242, 43984}, {27006, 40534}, {27529, 40869}, {30806, 32024}, {49466, 52354}

X(56244) = X(i)-isoconjugate-of-X(j) for these {i, j}: {56, 42326}
X(56244) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 42326}, {25006, 21617}
X(56244) = X(i)-Ceva conjugate of X(j) for these {i, j}: {17263, 3957}
X(56244) = intersection, other than A, B, C, of circumconics {{A, B, C, X(8), X(3957)}}, {{A, B, C, X(9), X(17745)}}, {{A, B, C, X(21), X(5853)}}, {{A, B, C, X(346), X(17263)}}, {{A, B, C, X(390), X(62286)}}, {{A, B, C, X(3717), X(52344)}}, {{A, B, C, X(24393), X(32635)}}
X(56244) = barycentric product X(i)*X(j) for these (i, j): {200, 32007}, {3699, 42325}, {3957, 8}, {17263, 9}, {17745, 312}
X(56244) = barycentric quotient X(i)/X(j) for these (i, j): {9, 42326}, {3957, 7}, {17263, 85}, {17745, 57}, {32007, 1088}, {42325, 3676}
X(56244) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 1334, 33950}, {9, 55337, 8}, {190, 32008, 20880}, {644, 1212, 4861}

X(56246) = KP4(X(10)) OF X(2) AND X(8)

Barycentrics    (b+c)*(a^4+b^4-b^2*c^2-a^2*(2*b^2+c^2))*(a^4-b^2*c^2+c^4-a^2*(b^2+2*c^2)) : :

X(56246) lies on these lines: {2, 23112}, {10, 275}, {42, 42300}, {71, 8795}, {95, 306}, {190, 46138}, {313, 34385}, {333, 39277}, {3219, 4391}, {3682, 37872}, {3695, 17751}, {3936, 26942}, {19811, 34384}, {21011, 39286}, {52369, 56189}

X(56246) = isotomic conjugate of X(17167)
X(56246) = trilinear pole of line {2616, 4064}
X(56246) = X(i)-isoconjugate-of-X(j) for these {i, j}: {5, 1333}, {6, 18180}, {19, 44709}, {25, 16697}, {28, 216}, {31, 17167}, {51, 81}, {53, 1437}, {58, 1953}, {86, 2179}, {163, 21102}, {217, 286}, {274, 40981}, {284, 1393}, {343, 2203}, {513, 1625}, {593, 21807}, {649, 2617}, {667, 14570}, {849, 21011}, {905, 52604}, {1172, 30493}, {1396, 44707}, {1412, 7069}, {1444, 3199}, {1474, 44706}, {1790, 2181}, {2206, 14213}, {2299, 44708}, {5317, 5562}, {6591, 23181}, {14399, 36831}, {14569, 18604}, {17434, 52920}, {18108, 35319}, {22383, 35360}, {44715, 52955}, {52935, 55219}
X(56246) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 17167}, {6, 44709}, {9, 18180}, {10, 1953}, {37, 5}, {115, 21102}, {226, 44708}, {4075, 21011}, {5375, 2617}, {6505, 16697}, {6631, 14570}, {39026, 1625}, {40586, 51}, {40590, 1393}, {40591, 216}, {40599, 7069}, {40600, 2179}, {40603, 14213}, {51574, 44706}, {55065, 12077}
X(56246) = X(i)-cross conjugate of X(j) for these {i, j}: {21012, 10}, {24082, 4632}, {52623, 190}
X(56246) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(11109)}}, {{A, B, C, X(4), X(7573)}}, {{A, B, C, X(9), X(52561)}}, {{A, B, C, X(10), X(306)}}, {{A, B, C, X(27), X(65)}}, {{A, B, C, X(37), X(19811)}}, {{A, B, C, X(71), X(4055)}}, {{A, B, C, X(72), X(3074)}}, {{A, B, C, X(81), X(18097)}}, {{A, B, C, X(92), X(38955)}}, {{A, B, C, X(95), X(275)}}, {{A, B, C, X(190), X(3219)}}, {{A, B, C, X(226), X(34234)}}, {{A, B, C, X(321), X(333)}}, {{A, B, C, X(469), X(3597)}}, {{A, B, C, X(1441), X(40417)}}, {{A, B, C, X(1751), X(4674)}}, {{A, B, C, X(2167), X(2190)}}, {{A, B, C, X(2322), X(3694)}}, {{A, B, C, X(17277), X(32863)}}, {{A, B, C, X(18082), X(40394)}}, {{A, B, C, X(19874), X(34255)}}, {{A, B, C, X(21011), X(21012)}}, {{A, B, C, X(30588), X(40420)}}
X(56246) = barycentric product X(i)*X(j) for these (i, j): {1, 56189}, {10, 95}, {275, 306}, {276, 71}, {313, 54}, {1441, 44687}, {1826, 34386}, {1978, 2623}, {2148, 27801}, {2167, 321}, {2616, 668}, {3682, 8795}, {4079, 55218}, {4600, 8901}, {15412, 190}, {15523, 39287}, {18315, 52623}, {18831, 4064}, {20336, 2190}, {21012, 31617}, {21035, 41488}, {34384, 42}, {34388, 35196}, {39182, 4568}, {40071, 8882}, {40440, 72}, {52396, 8884}
X(56246) = barycentric quotient X(i)/X(j) for these (i, j): {1, 18180}, {2, 17167}, {3, 44709}, {10, 5}, {37, 1953}, {42, 51}, {54, 58}, {63, 16697}, {65, 1393}, {71, 216}, {72, 44706}, {73, 30493}, {95, 86}, {97, 1790}, {100, 2617}, {101, 1625}, {190, 14570}, {210, 7069}, {213, 2179}, {275, 27}, {276, 44129}, {306, 343}, {313, 311}, {321, 14213}, {523, 21102}, {594, 21011}, {756, 21807}, {1214, 44708}, {1331, 23181}, {1824, 2181}, {1826, 53}, {1897, 35360}, {1918, 40981}, {2148, 1333}, {2167, 81}, {2169, 1437}, {2190, 28}, {2200, 217}, {2318, 44707}, {2333, 3199}, {2616, 513}, {2623, 649}, {3678, 35194}, {3682, 5562}, {4024, 12077}, {4028, 41588}, {4036, 2618}, {4055, 418}, {4062, 41586}, {4064, 6368}, {4079, 55219}, {8750, 52604}, {8804, 42459}, {8882, 1474}, {8884, 8747}, {8901, 3120}, {15412, 514}, {15414, 30805}, {16030, 17187}, {16813, 52919}, {18082, 17500}, {18315, 4556}, {20336, 18695}, {21011, 36412}, {21012, 233}, {21016, 27371}, {21043, 41221}, {21859, 35307}, {23286, 1459}, {34384, 310}, {34386, 17206}, {35196, 60}, {38808, 44698}, {39182, 10566}, {39287, 52394}, {40071, 28706}, {40440, 286}, {41267, 27374}, {43768, 18653}, {44687, 21}, {46148, 35319}, {52320, 52321}, {52369, 42698}, {52396, 52347}, {52623, 18314}, {53012, 8798}, {53576, 4466}, {54034, 2206}, {55218, 52612}, {55230, 15451}, {56189, 75}

X(56247) = KP4(X(10)) OF X(2) AND X(42)

Barycentrics    (-2*a*b^2*c+b^2*c^2+a^2*(b^2+c^2))*(-2*a*b*c^2+b^2*c^2+a^2*(b^2+c^2)) : :

X(56247) lies on these lines: {7, 26752}, {8, 39746}, {75, 31276}, {86, 26042}, {1575, 6384}, {1740, 25311}, {17350, 20979}, {17792, 27498}, {21264, 56212}, {26048, 39721}, {27044, 27494}

X(56247) = isogonal conjugate of X(23538)
X(56247) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 23538}, {6, 18194}, {28, 22439}, {56, 39250}, {58, 21345}, {81, 23652}, {1333, 21257}, {2162, 14823}, {2206, 21435}
X(56247) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 39250}, {3, 23538}, {9, 18194}, {10, 21345}, {37, 21257}, {40586, 23652}, {40591, 22439}, {40603, 21435}
X(56247) = X(i)-cross conjugate of X(j) for these {i, j}: {23886, 190}, {27091, 2}, {50516, 668}
X(56247) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(32033)}}, {{A, B, C, X(2), X(7)}}, {{A, B, C, X(6), X(192)}}, {{A, B, C, X(8), X(26752)}}, {{A, B, C, X(43), X(1740)}}, {{A, B, C, X(190), X(17350)}}, {{A, B, C, X(264), X(40098)}}, {{A, B, C, X(274), X(31276)}}, {{A, B, C, X(291), X(2998)}}, {{A, B, C, X(308), X(330)}}, {{A, B, C, X(321), X(26042)}}, {{A, B, C, X(749), X(38262)}}, {{A, B, C, X(1221), X(52654)}}, {{A, B, C, X(1376), X(17792)}}, {{A, B, C, X(1581), X(30701)}}, {{A, B, C, X(1964), X(30650)}}, {{A, B, C, X(2186), X(54123)}}, {{A, B, C, X(2221), X(3210)}}, {{A, B, C, X(3596), X(9229)}}, {{A, B, C, X(4000), X(33891)}}, {{A, B, C, X(4360), X(4393)}}, {{A, B, C, X(4492), X(39968)}}, {{A, B, C, X(4699), X(21264)}}, {{A, B, C, X(9295), X(9309)}}, {{A, B, C, X(13476), X(36957)}}, {{A, B, C, X(17316), X(26048)}}, {{A, B, C, X(17490), X(28358)}}, {{A, B, C, X(17743), X(17786)}}, {{A, B, C, X(23051), X(40738)}}, {{A, B, C, X(31360), X(40099)}}, {{A, B, C, X(32020), X(39742)}}, {{A, B, C, X(34248), X(51973)}}, {{A, B, C, X(39738), X(39983)}}
X(56247) = barycentric quotient X(i)/X(j) for these (i, j): {1, 18194}, {6, 23538}, {9, 39250}, {10, 21257}, {37, 21345}, {42, 23652}, {43, 14823}, {71, 22439}, {321, 21435}

X(56248) = KP4(X(10)) OF X(2) AND X(100)

Barycentrics    (a-b)*(a-c)*(a^2*(b-c)-b^2*c+c^3+a*b*(b+c))*(-b^3+a^2*(b-c)+b*c^2-a*c*(b+c)) : :

X(56248) lies on these lines: {100, 46541}, {190, 47793}, {3888, 48243}, {4552, 17906}, {4553, 48204}, {14543, 21362}, {24004, 25268}, {26685, 27136}, {36872, 37828}, {44040, 52746}

X(56248) = isotomic conjugate of X(47796)
X(56248) = trilinear pole of line {72, 950}
X(56248) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 48281}, {31, 47796}, {57, 48387}, {108, 39006}, {404, 649}, {514, 44085}, {604, 20293}, {667, 32939}, {849, 21721}, {1415, 44311}, {1919, 44139}
X(56248) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 47796}, {9, 48281}, {1146, 44311}, {3161, 20293}, {4075, 21721}, {5375, 404}, {5452, 48387}, {6631, 32939}, {9296, 44139}, {38983, 39006}
X(56248) = X(i)-cross conjugate of X(j) for these {i, j}: {652, 8}, {22071, 59}, {25078, 765}, {42312, 7}, {47794, 2}
X(56248) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(190)}}, {{A, B, C, X(37), X(40519)}}, {{A, B, C, X(100), X(1332)}}, {{A, B, C, X(281), X(3939)}}, {{A, B, C, X(345), X(1813)}}, {{A, B, C, X(514), X(47793)}}, {{A, B, C, X(644), X(40117)}}, {{A, B, C, X(645), X(655)}}, {{A, B, C, X(646), X(651)}}, {{A, B, C, X(648), X(51562)}}, {{A, B, C, X(650), X(40523)}}, {{A, B, C, X(653), X(3699)}}, {{A, B, C, X(662), X(36804)}}, {{A, B, C, X(666), X(38340)}}, {{A, B, C, X(789), X(42363)}}, {{A, B, C, X(941), X(34071)}}, {{A, B, C, X(1783), X(30730)}}, {{A, B, C, X(1897), X(42362)}}, {{A, B, C, X(2406), X(28826)}}, {{A, B, C, X(3952), X(37218)}}, {{A, B, C, X(4033), X(8050)}}, {{A, B, C, X(4554), X(4606)}}, {{A, B, C, X(4566), X(51566)}}, {{A, B, C, X(4572), X(5936)}}, {{A, B, C, X(4612), X(31628)}}, {{A, B, C, X(4627), X(43069)}}, {{A, B, C, X(8709), X(54458)}}, {{A, B, C, X(9058), X(36099)}}, {{A, B, C, X(9067), X(54982)}}, {{A, B, C, X(15455), X(37212)}}, {{A, B, C, X(17279), X(42720)}}, {{A, B, C, X(47794), X(47796)}}
X(56248) = barycentric product X(i)*X(j) for these (i, j): {40518, 7017}, {44040, 664}
X(56248) = barycentric quotient X(i)/X(j) for these (i, j): {1, 48281}, {2, 47796}, {8, 20293}, {55, 48387}, {100, 404}, {190, 32939}, {522, 44311}, {594, 21721}, {652, 39006}, {668, 44139}, {692, 44085}, {40518, 222}, {44040, 522}, {52609, 42705}

X(56249) = KP4(X(10)) OF X(75) AND X(1)

Barycentrics    b*c*(b+c)*(a^2-b*c+a*(b+c)) : :

X(56249) lies on these lines: {2, 18040}, {8, 18147}, {9, 29395}, {10, 75}, {37, 4033}, {42, 17393}, {45, 29712}, {63, 29551}, {71, 17336}, {86, 668}, {142, 18150}, {190, 29705}, {192, 21858}, {239, 18046}, {274, 1268}, {306, 5233}, {308, 39717}, {310, 31341}, {312, 48630}, {314, 32025}, {319, 17751}, {321, 6539}, {322, 18738}, {334, 40004}, {344, 27108}, {350, 4651}, {391, 41316}, {594, 3948}, {756, 28593}, {894, 29388}, {1100, 25298}, {1213, 3963}, {1654, 17790}, {1698, 18148}, {1909, 16709}, {1964, 25120}, {2322, 6335}, {3263, 31117}, {3293, 4360}, {3617, 44140}, {3661, 18137}, {3701, 42714}, {3728, 21238}, {3739, 18143}, {3759, 41233}, {3765, 17303}, {3766, 21714}, {3770, 28604}, {3834, 30044}, {3875, 31855}, {3952, 21865}, {3975, 17289}, {3992, 18697}, {4022, 20340}, {4036, 20954}, {4089, 33943}, {4103, 22012}, {4110, 4664}, {4150, 30854}, {4358, 17229}, {4359, 18136}, {4361, 29764}, {4384, 18044}, {4687, 17786}, {4699, 18144}, {4710, 50298}, {4751, 20917}, {6384, 28650}, {6542, 25660}, {15523, 20932}, {16696, 27102}, {16815, 18073}, {16828, 31997}, {16832, 18065}, {17148, 46838}, {17227, 30090}, {17228, 20923}, {17231, 29982}, {17233, 30830}, {17237, 20892}, {17239, 20891}, {17256, 17787}, {17258, 40875}, {17260, 29396}, {17261, 24004}, {17322, 26115}, {17394, 24524}, {17445, 17793}, {17788, 20654}, {18057, 33931}, {18082, 39044}, {18135, 42696}, {18146, 50088}, {18151, 21011}, {18739, 19804}, {20336, 52353}, {20646, 20659}, {20711, 23498}, {20930, 30758}, {20944, 21729}, {20952, 21720}, {20953, 21055}, {21591, 21689}, {21611, 21721}, {21612, 21722}, {22172, 41683}, {22343, 24487}, {24530, 26048}, {25107, 27633}, {25255, 52609}, {26042, 41838}, {27792, 31993}, {28654, 41809}, {30829, 37651}, {34021, 55239}, {39996, 50116}, {44153, 49524}

X(56249) = isotomic conjugate of X(39949)
X(56249) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 39949}, {32, 39747}, {58, 40148}, {596, 2206}, {667, 34594}, {1333, 39798}, {1576, 40086}, {1919, 37205}, {2194, 20615}, {3733, 40519}
X(56249) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 39949}, {10, 40148}, {37, 39798}, {594, 37}, {1214, 20615}, {4359, 1125}, {4858, 40086}, {6376, 39747}, {6631, 34594}, {9296, 37205}, {21827, 16604}, {40603, 596}
X(56249) = X(i)-Ceva conjugate of X(j) for these {i, j}: {274, 321}, {308, 4043}, {668, 20295}, {1268, 75}, {18140, 3995}
X(56249) = X(i)-cross conjugate of X(j) for these {i, j}: {4075, 3995}, {4132, 4033}
X(56249) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(18133)}}, {{A, B, C, X(10), X(3293)}}, {{A, B, C, X(37), X(726)}}, {{A, B, C, X(75), X(3995)}}, {{A, B, C, X(76), X(18140)}}, {{A, B, C, X(86), X(20295)}}, {{A, B, C, X(256), X(4057)}}, {{A, B, C, X(310), X(30594)}}, {{A, B, C, X(313), X(40039)}}, {{A, B, C, X(321), X(1269)}}, {{A, B, C, X(595), X(31359)}}, {{A, B, C, X(756), X(21035)}}, {{A, B, C, X(798), X(22201)}}, {{A, B, C, X(1441), X(3264)}}, {{A, B, C, X(1921), X(20949)}}, {{A, B, C, X(3159), X(39949)}}, {{A, B, C, X(3971), X(34832)}}, {{A, B, C, X(4129), X(6381)}}, {{A, B, C, X(4222), X(16062)}}, {{A, B, C, X(5224), X(32911)}}, {{A, B, C, X(6376), X(28650)}}, {{A, B, C, X(16606), X(25121)}}, {{A, B, C, X(41683), X(49493)}}, {{A, B, C, X(42027), X(50117)}}
X(56249) = barycentric product X(i)*X(j) for these (i, j): {10, 18140}, {37, 40087}, {274, 4075}, {313, 32911}, {321, 4360}, {349, 3871}, {1978, 4132}, {3293, 76}, {3948, 40093}, {3995, 75}, {4129, 668}, {20295, 4033}, {20949, 3952}, {27801, 595}, {27808, 4063}, {32018, 4065}, {40071, 4222}
X(56249) = barycentric quotient X(i)/X(j) for these (i, j): {2, 39949}, {10, 39798}, {37, 40148}, {75, 39747}, {190, 34594}, {226, 20615}, {313, 40013}, {321, 596}, {595, 1333}, {668, 37205}, {1018, 40519}, {1089, 40085}, {1577, 40086}, {2220, 2206}, {3293, 6}, {3871, 284}, {3995, 1}, {4033, 8050}, {4063, 3733}, {4065, 1100}, {4075, 37}, {4129, 513}, {4132, 649}, {4222, 1474}, {4360, 81}, {18140, 86}, {20295, 1019}, {20949, 7192}, {21208, 16726}, {27044, 18792}, {29398, 5253}, {32911, 58}, {40087, 274}, {40093, 37128}, {47793, 3737}, {48307, 7252}
X(56249) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 30473, 18040}, {10, 313, 75}, {37, 21900, 22201}, {75, 18133, 39995}, {75, 6376, 18133}, {594, 3948, 4043}, {1909, 28653, 16709}, {3739, 52043, 18143}, {4967, 6381, 1269}, {21022, 21699, 10}

X(56250) = KP4(X(10)) OF X(75) AND X(43)

Barycentrics    b*c*(b+c)*(-(b^2*c^2)+a^3*(b+c)+a^2*(b^2-b*c+c^2)) : :

X(56250) lies on these lines: {1, 18148}, {10, 75}, {42, 17149}, {65, 20716}, {334, 51870}, {350, 17152}, {668, 3293}, {714, 7148}, {1086, 30045}, {1237, 2292}, {1909, 16705}, {1918, 52138}, {3159, 27808}, {3210, 40598}, {3501, 29423}, {3666, 18136}, {3735, 18050}, {3948, 4415}, {3952, 25307}, {4033, 20691}, {4043, 21024}, {4424, 27801}, {4485, 37598}, {4642, 35544}, {4651, 25280}, {6384, 43223}, {18046, 41240}, {18057, 22275}, {18135, 21281}, {18140, 56191}, {18739, 20917}, {19998, 25278}, {20255, 29983}, {21858, 30473}, {21884, 25614}, {25303, 29822}, {25350, 30054}, {29454, 49997}, {29511, 37555}, {31008, 40418}, {34020, 34063}

X(56250) = X(i)-Dao conjugate of X(j) for these {i, j}: {6378, 16606}, {20891, 3741}, {21025, 17448}
X(56250) = X(i)-Ceva conjugate of X(j) for these {i, j}: {668, 25300}, {31008, 37}, {34020, 56185}, {40418, 75}
X(56250) = intersection, other than A, B, C, of circumconics {{A, B, C, X(65), X(726)}}, {{A, B, C, X(75), X(34063)}}, {{A, B, C, X(76), X(34020)}}, {{A, B, C, X(4080), X(20943)}}, {{A, B, C, X(6381), X(40515)}}, {{A, B, C, X(25300), X(33296)}}
X(56250) = barycentric product X(i)*X(j) for these (i, j): {10, 34020}, {321, 34063}, {34086, 37}, {56185, 75}
X(56250) = barycentric quotient X(i)/X(j) for these (i, j): {25300, 18197}, {25302, 18206}, {34020, 86}, {34063, 81}, {34086, 274}, {56185, 1}
X(56250) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 6376, 56249}

X(56251) = KP4(X(10)) OF X(75) AND X(75)

Barycentrics    b^2*(a^2+b^2)*c^2*(b+c)*(a^2+c^2) : :

X(56251) lies on these lines: {10, 18833}, {42, 308}, {76, 17141}, {83, 41233}, {181, 34388}, {291, 310}, {334, 16891}, {561, 18057}, {689, 28482}, {693, 1920}, {756, 28593}, {1240, 52394}, {1500, 3948}, {1909, 17176}, {1978, 7018}, {2333, 46104}, {2887, 18090}, {3963, 21327}, {4377, 21345}, {6187, 20566}, {7148, 16889}, {8024, 31111}, {17027, 18089}, {17751, 20022}, {17990, 17995}, {28595, 35532}, {32781, 35539}

X(56251) = isotomic conjugate of X(17187)
X(56251) = trilinear pole of line {4079, 4129}
X(56251) = X(i)-isoconjugate-of-X(j) for these {i, j}: {28, 20775}, {31, 17187}, {32, 16696}, {38, 2206}, {39, 1333}, {58, 1964}, {81, 3051}, {86, 1923}, {110, 50521}, {163, 21123}, {274, 41331}, {560, 16887}, {593, 21814}, {667, 1634}, {688, 52935}, {757, 41267}, {849, 21035}, {1401, 2194}, {1408, 3688}, {1412, 40972}, {1437, 1843}, {1444, 27369}, {1474, 4020}, {1501, 16703}, {1576, 2530}, {1980, 4576}, {2084, 4556}, {2203, 3917}, {2210, 46159}, {4623, 9494}, {9247, 17171}, {14574, 48084}, {14575, 16747}, {16702, 41272}, {16947, 33299}, {22383, 35325}, {46160, 52434}
X(56251) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 17187}, {10, 1964}, {37, 39}, {115, 21123}, {244, 50521}, {1214, 1401}, {4075, 21035}, {4858, 2530}, {6374, 16887}, {6376, 16696}, {6631, 1634}, {36901, 16892}, {40586, 3051}, {40591, 20775}, {40599, 40972}, {40600, 1923}, {40603, 38}, {40607, 41267}, {41884, 58}, {51574, 4020}, {55065, 3005}
X(56251) = X(i)-Ceva conjugate of X(j) for these {i, j}: {308, 56186}
X(56251) = X(i)-cross conjugate of X(j) for these {i, j}: {10, 18082}, {4024, 1978}, {4151, 4033}, {21022, 10}
X(56251) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(37678)}}, {{A, B, C, X(10), X(42)}}, {{A, B, C, X(37), X(28593)}}, {{A, B, C, X(75), X(3995)}}, {{A, B, C, X(76), X(18152)}}, {{A, B, C, X(86), X(27041)}}, {{A, B, C, X(226), X(31002)}}, {{A, B, C, X(308), X(40016)}}, {{A, B, C, X(310), X(321)}}, {{A, B, C, X(313), X(20566)}}, {{A, B, C, X(661), X(43687)}}, {{A, B, C, X(1920), X(1978)}}, {{A, B, C, X(2296), X(18832)}}, {{A, B, C, X(3112), X(18833)}}, {{A, B, C, X(4024), X(4039)}}, {{A, B, C, X(4080), X(6384)}}, {{A, B, C, X(7034), X(32926)}}, {{A, B, C, X(18097), X(27067)}}, {{A, B, C, X(21022), X(21035)}}
X(56251) = barycentric product X(i)*X(j) for these (i, j): {10, 308}, {190, 52618}, {306, 46104}, {313, 83}, {1240, 27067}, {3112, 321}, {4024, 689}, {4036, 4593}, {4079, 42371}, {4577, 52623}, {10566, 27808}, {16894, 3115}, {18070, 668}, {18082, 76}, {18097, 3596}, {18098, 561}, {18099, 44187}, {18833, 37}, {21011, 41488}, {21022, 31622}, {27801, 82}, {28654, 52394}, {32085, 40071}, {37204, 4705}, {40016, 42}, {44173, 4628}, {55240, 6386}, {56186, 75}
X(56251) = barycentric quotient X(i)/X(j) for these (i, j): {2, 17187}, {10, 39}, {37, 1964}, {42, 3051}, {71, 20775}, {72, 4020}, {75, 16696}, {76, 16887}, {82, 1333}, {83, 58}, {190, 1634}, {210, 40972}, {213, 1923}, {226, 1401}, {251, 2206}, {264, 17171}, {306, 3917}, {308, 86}, {313, 141}, {321, 38}, {335, 46159}, {349, 3665}, {523, 21123}, {561, 16703}, {594, 21035}, {661, 50521}, {689, 4610}, {756, 21814}, {850, 16892}, {1089, 3954}, {1237, 16720}, {1500, 41267}, {1577, 2530}, {1799, 1790}, {1826, 1843}, {1897, 35325}, {1918, 41331}, {1969, 16747}, {1978, 4576}, {2321, 3688}, {2333, 27369}, {3112, 81}, {3701, 33299}, {3952, 46148}, {4010, 46387}, {4024, 3005}, {4028, 3787}, {4033, 4553}, {4036, 8061}, {4037, 4093}, {4039, 8623}, {4079, 688}, {4080, 46150}, {4150, 3313}, {4456, 23208}, {4552, 46153}, {4577, 4556}, {4580, 1459}, {4593, 52935}, {4628, 1576}, {4705, 2084}, {6386, 55239}, {7141, 21016}, {10566, 3733}, {14618, 21108}, {15523, 8041}, {16889, 2275}, {18070, 513}, {18082, 6}, {18083, 26892}, {18084, 1473}, {18085, 26889}, {18097, 56}, {18098, 31}, {18099, 172}, {18105, 1919}, {18107, 16695}, {18359, 46160}, {18833, 274}, {20022, 17209}, {20927, 41582}, {20948, 48084}, {21021, 40936}, {21094, 9019}, {21803, 21752}, {27067, 1193}, {27801, 1930}, {27808, 4568}, {28654, 15523}, {30713, 3703}, {32085, 1474}, {34055, 1437}, {34294, 3122}, {37204, 4623}, {39998, 17193}, {40016, 310}, {40071, 3933}, {41013, 17442}, {42371, 52612}, {46104, 27}, {52376, 849}, {52394, 593}, {52570, 17200}, {52618, 514}, {52623, 826}, {53581, 9494}, {55240, 667}, {56186, 1}, {56245, 2194}, {56246, 16030}

X(56252) = KP4(X(10)) OF X(75) AND X(100)

Barycentrics    (a-b)*b*(a-c)*c*(-b^3+b*c^2+a*c*(-b+c)+a^2*(b+c))*(a*b*(b-c)+a^2*(b+c)+c*(b^2-c^2)) : :

X(56252) lies on these lines: {334, 51870}, {668, 56194}, {1332, 37218}, {2051, 18061}, {2397, 4033}, {4391, 21859}, {18133, 54121}, {20028, 40039}, {20566, 56249}, {21580, 53332}, {33116, 46880}

X(56252) = isotomic conjugate of X(21173)
X(56252) = trilinear pole of line {321, 908}
X(56252) = X(i)-isoconjugate-of-X(j) for these {i, j}: {25, 23187}, {31, 21173}, {32, 17496}, {513, 20986}, {572, 649}, {667, 2975}, {1415, 11998}, {1576, 53566}, {1919, 14829}, {2194, 51662}, {3063, 17074}, {3733, 52139}, {6591, 22118}, {24237, 32739}, {32674, 38344}
X(56252) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 21173}, {75, 27346}, {1146, 11998}, {1214, 51662}, {4858, 53566}, {5375, 572}, {6376, 17496}, {6505, 23187}, {6631, 2975}, {9296, 14829}, {10001, 17074}, {35072, 38344}, {39026, 20986}, {40619, 24237}, {40624, 34589}
X(56252) = X(i)-cross conjugate of X(j) for these {i, j}: {35519, 75}
X(56252) = intersection, other than A, B, C, of circumconics {{A, B, C, X(10), X(21859)}}, {{A, B, C, X(75), X(664)}}, {{A, B, C, X(85), X(31624)}}, {{A, B, C, X(101), X(31359)}}, {{A, B, C, X(190), X(53332)}}, {{A, B, C, X(334), X(668)}}, {{A, B, C, X(811), X(35174)}}, {{A, B, C, X(4554), X(21580)}}, {{A, B, C, X(4572), X(53647)}}, {{A, B, C, X(4595), X(6376)}}, {{A, B, C, X(6540), X(13136)}}, {{A, B, C, X(7257), X(36804)}}, {{A, B, C, X(18743), X(41314)}}, {{A, B, C, X(33931), X(42719)}}, {{A, B, C, X(40014), X(46406)}}
X(56252) = barycentric product X(i)*X(j) for these (i, j): {190, 54121}, {1978, 34434}, {2051, 668}, {20028, 4033}, {27808, 53083}, {51870, 799}, {56188, 75}, {56194, 76}
X(56252) = barycentric quotient X(i)/X(j) for these (i, j): {2, 21173}, {63, 23187}, {75, 17496}, {100, 572}, {101, 20986}, {190, 2975}, {226, 51662}, {521, 38344}, {522, 11998}, {664, 17074}, {668, 14829}, {693, 24237}, {1018, 52139}, {1331, 22118}, {1577, 53566}, {2051, 513}, {3952, 21061}, {4033, 17751}, {4103, 14973}, {4391, 34589}, {4552, 37558}, {4605, 20617}, {6335, 11109}, {6376, 27346}, {20028, 1019}, {20954, 26847}, {34434, 649}, {35519, 40624}, {46880, 3737}, {51870, 661}, {53083, 3733}, {53702, 909}, {54121, 514}, {56188, 1}, {56194, 6}

X(56253) = KP4(X(10)) OF X(75) AND X(145)

Barycentrics    b*c*(b+c)*(a^2-2*b*c+a*(b+c)) : :

X(56253) lies on these lines: {2, 18065}, {10, 75}, {71, 25728}, {142, 30044}, {306, 3452}, {314, 25280}, {322, 46937}, {350, 4685}, {519, 18147}, {594, 4044}, {668, 3879}, {730, 25120}, {1213, 4377}, {1441, 52353}, {1743, 41316}, {2321, 3948}, {2893, 36926}, {3008, 18044}, {3214, 3875}, {3679, 44140}, {3701, 18697}, {3760, 42696}, {3761, 19870}, {3765, 5750}, {3882, 56079}, {3912, 30473}, {3950, 4033}, {3963, 5257}, {3971, 35544}, {3975, 17353}, {3992, 20336}, {4043, 4058}, {4096, 42711}, {4125, 42714}, {4360, 50587}, {4416, 17790}, {4464, 50590}, {4494, 17257}, {4506, 17334}, {4656, 30713}, {4710, 50290}, {4718, 21858}, {4723, 17863}, {4780, 4783}, {7179, 30636}, {16828, 52716}, {17121, 41233}, {17286, 28809}, {17751, 32099}, {17786, 30830}, {17787, 50093}, {18040, 29571}, {18046, 50114}, {18136, 24177}, {18137, 29594}, {18144, 24199}, {18145, 50099}, {18739, 24175}, {20892, 50092}, {20930, 33942}, {25140, 35539}, {25590, 44147}, {25660, 29574}, {27076, 27633}, {29696, 56080}, {29705, 50118}, {31060, 48628}, {36856, 53541}, {44139, 50116}, {44153, 49529}

X(56253) = X(i)-isoconjugate-of-X(j) for these {i, j}: {667, 8690}, {849, 56192}, {1333, 39956}, {2194, 56155}, {2206, 34860}
X(56253) = X(i)-Dao conjugate of X(j) for these {i, j}: {37, 39956}, {1214, 56155}, {2321, 9}, {3175, 17749}, {4075, 56192}, {6631, 8690}, {40603, 34860}
X(56253) = X(i)-Ceva conjugate of X(j) for these {i, j}: {85, 321}, {18135, 3175}
X(56253) = intersection, other than A, B, C, of circumconics {{A, B, C, X(10), X(3214)}}, {{A, B, C, X(37), X(49447)}}, {{A, B, C, X(75), X(3175)}}, {{A, B, C, X(76), X(18135)}}, {{A, B, C, X(726), X(4139)}}, {{A, B, C, X(1266), X(3668)}}, {{A, B, C, X(1269), X(7018)}}, {{A, B, C, X(3596), X(30636)}}, {{A, B, C, X(3718), X(30568)}}, {{A, B, C, X(3915), X(42285)}}, {{A, B, C, X(3971), X(41886)}}, {{A, B, C, X(4106), X(39995)}}, {{A, B, C, X(4186), X(16062)}}, {{A, B, C, X(4357), X(28387)}}, {{A, B, C, X(4383), X(5224)}}, {{A, B, C, X(6376), X(27432)}}, {{A, B, C, X(19945), X(21963)}}, {{A, B, C, X(42027), X(49493)}}
X(56253) = barycentric product X(i)*X(j) for these (i, j): {10, 18135}, {313, 4383}, {321, 3875}, {349, 3913}, {1441, 30568}, {1978, 4139}, {3175, 75}, {3214, 76}, {4033, 4106}, {21963, 31625}, {27432, 6376}, {27801, 3915}, {27808, 4498}, {27813, 52353}, {28387, 3596}, {40071, 4186}
X(56253) = barycentric quotient X(i)/X(j) for these (i, j): {10, 39956}, {190, 8690}, {226, 56155}, {313, 40012}, {321, 34860}, {594, 56192}, {1089, 56123}, {1441, 42304}, {3175, 1}, {3214, 6}, {3217, 2194}, {3875, 81}, {3913, 284}, {3915, 1333}, {4106, 1019}, {4139, 649}, {4186, 1474}, {4383, 58}, {4498, 3733}, {16946, 2206}, {18135, 86}, {20317, 3737}, {21963, 1015}, {27432, 87}, {28387, 56}, {30568, 21}, {42312, 7252}
X(56253) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {313, 56249, 10}, {3264, 18133, 3663}, {3596, 6376, 4357}

X(56254) = KP4(X(37)) OF X(1) AND X(9)

Barycentrics    a*(b+c)*(a^4+b^4-b^2*c^2-a^2*(2*b^2+c^2))*(a^4-b^2*c^2+c^4-a^2*(b^2+2*c^2)) : :

X(56254) lies on these lines: {2, 22457}, {12, 860}, {21, 1807}, {35, 522}, {37, 2190}, {54, 72}, {95, 7523}, {96, 321}, {100, 1141}, {201, 758}, {228, 7412}, {933, 43659}, {1157, 48698}, {2148, 21078}, {3695, 17751}, {3949, 21061}, {4996, 51255}, {5251, 55091}, {6356, 41804}, {8901, 27687}, {10902, 22002}, {16030, 37247}, {23067, 37154}

X(56254) = isogonal conjugate of X(18180)
X(56254) = trilinear pole of line {2616, 2623}
X(56254) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 18180}, {4, 44709}, {5, 58}, {6, 17167}, {19, 16697}, {21, 1393}, {27, 216}, {28, 44706}, {29, 30493}, {51, 86}, {53, 1790}, {81, 1953}, {110, 21102}, {217, 44129}, {274, 2179}, {310, 40981}, {311, 2206}, {343, 1474}, {513, 2617}, {514, 1625}, {593, 21011}, {649, 14570}, {757, 21807}, {1014, 7069}, {1172, 44708}, {1333, 14213}, {1444, 2181}, {1459, 35360}, {2203, 18695}, {3199, 17206}, {4025, 52604}, {4243, 35363}, {4556, 12077}, {4610, 55219}, {5562, 8747}, {7649, 23181}, {8798, 44698}, {10566, 35319}, {11125, 36831}, {17187, 17500}, {17434, 52919}, {35194, 52375}, {35196, 41279}, {44715, 52954}
X(56254) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 18180}, {6, 16697}, {9, 17167}, {10, 5}, {37, 14213}, {244, 21102}, {5375, 14570}, {36033, 44709}, {39026, 2617}, {40586, 1953}, {40591, 44706}, {40600, 51}, {40603, 311}, {40607, 21807}, {40611, 1393}, {51574, 343}, {55065, 2618}
X(56254) = X(i)-Ceva conjugate of X(j) for these {i, j}: {95, 56246}
X(56254) = X(i)-cross conjugate of X(j) for these {i, j}: {4036, 100}, {42443, 1}
X(56254) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2975)}}, {{A, B, C, X(3), X(7412)}}, {{A, B, C, X(4), X(1006)}}, {{A, B, C, X(9), X(3191)}}, {{A, B, C, X(10), X(21)}}, {{A, B, C, X(12), X(37)}}, {{A, B, C, X(25), X(7523)}}, {{A, B, C, X(28), X(1400)}}, {{A, B, C, X(35), X(100)}}, {{A, B, C, X(42), X(26890)}}, {{A, B, C, X(54), X(95)}}, {{A, B, C, X(65), X(104)}}, {{A, B, C, X(73), X(45766)}}, {{A, B, C, X(90), X(13576)}}, {{A, B, C, X(98), X(1175)}}, {{A, B, C, X(267), X(53707)}}, {{A, B, C, X(321), X(42700)}}, {{A, B, C, X(947), X(2695)}}, {{A, B, C, X(1389), X(15232)}}, {{A, B, C, X(1476), X(53114)}}, {{A, B, C, X(1621), X(6763)}}, {{A, B, C, X(1826), X(26878)}}, {{A, B, C, X(1903), X(44861)}}, {{A, B, C, X(2167), X(2190)}}, {{A, B, C, X(2318), X(4183)}}, {{A, B, C, X(2346), X(39130)}}, {{A, B, C, X(3701), X(45393)}}, {{A, B, C, X(3962), X(38058)}}, {{A, B, C, X(4036), X(35194)}}, {{A, B, C, X(4222), X(37247)}}, {{A, B, C, X(4649), X(24053)}}, {{A, B, C, X(4674), X(15446)}}, {{A, B, C, X(5251), X(5260)}}, {{A, B, C, X(10308), X(15320)}}, {{A, B, C, X(10693), X(51870)}}, {{A, B, C, X(15179), X(31503)}}, {{A, B, C, X(18180), X(42443)}}, {{A, B, C, X(37733), X(52383)}}, {{A, B, C, X(42027), X(56137)}}, {{A, B, C, X(43743), X(56104)}}
X(56254) = barycentric product X(i)*X(j) for these (i, j): {1, 56246}, {6, 56189}, {10, 2167}, {37, 95}, {100, 15412}, {190, 2616}, {213, 34384}, {226, 44687}, {228, 276}, {275, 72}, {321, 54}, {1141, 42701}, {1824, 34386}, {2148, 313}, {2190, 306}, {2623, 668}, {3990, 8795}, {3998, 8884}, {4567, 8901}, {16030, 56186}, {18315, 4036}, {18831, 55232}, {20336, 8882}, {21814, 41488}, {23286, 6335}, {26941, 56227}, {27801, 54034}, {35196, 6358}, {36134, 52623}, {39182, 4553}, {39277, 4053}, {39287, 3954}, {40440, 71}, {41013, 97}, {42700, 96}, {50487, 55218}, {53576, 5379}
X(56254) = barycentric quotient X(i)/X(j) for these (i, j): {1, 17167}, {3, 16697}, {6, 18180}, {10, 14213}, {37, 5}, {42, 1953}, {48, 44709}, {54, 81}, {71, 44706}, {72, 343}, {73, 44708}, {95, 274}, {97, 1444}, {100, 14570}, {101, 2617}, {213, 51}, {228, 216}, {275, 286}, {306, 18695}, {321, 311}, {661, 21102}, {692, 1625}, {756, 21011}, {906, 23181}, {1334, 7069}, {1400, 1393}, {1409, 30493}, {1500, 21807}, {1783, 35360}, {1824, 53}, {1918, 2179}, {2148, 58}, {2167, 86}, {2169, 1790}, {2190, 27}, {2205, 40981}, {2333, 2181}, {2616, 514}, {2623, 513}, {3198, 42459}, {3695, 42698}, {3990, 5562}, {3998, 52347}, {4024, 2618}, {4036, 18314}, {4705, 12077}, {8882, 28}, {8901, 16732}, {14533, 1437}, {15412, 693}, {16030, 16696}, {16035, 18603}, {18098, 17500}, {18315, 52935}, {18831, 55231}, {19210, 18604}, {20336, 28706}, {21011, 1087}, {21794, 2599}, {21807, 36412}, {21833, 41221}, {21839, 41586}, {21855, 45238}, {21874, 41588}, {23286, 905}, {34384, 6385}, {35196, 2185}, {36134, 4556}, {40440, 44129}, {41013, 324}, {42700, 39113}, {42701, 1273}, {42702, 44716}, {44687, 333}, {46088, 23224}, {50487, 55219}, {51255, 16698}, {52370, 44707}, {53562, 2600}, {54034, 1333}, {55232, 6368}, {56189, 76}, {56246, 75}
X(56254) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2167, 44687, 54}

X(56255) = KP4(X(37)) OF X(1) AND X(10)

Barycentrics    a*(b+c)*(a^2+b*(b-c)-a*(2*b+c))*(a^2+c*(-b+c)-a*(b+2*c)) : :

X(56255) lies on these lines: {9, 1174}, {33, 7322}, {37, 41539}, {57, 21453}, {210, 3294}, {226, 1334}, {312, 728}, {1018, 3925}, {1170, 25430}, {2284, 17194}, {2321, 4651}, {3247, 56232}, {3475, 3730}, {3501, 41867}, {4551, 21795}, {6606, 35144}, {6690, 35341}, {8049, 30949}, {8818, 17747}, {10382, 41509}, {16552, 41711}, {31435, 56207}, {31618, 40025}, {36483, 36800}, {47487, 56225}

X(56255) = isogonal conjugate of X(18164)
X(56255) = isotomic conjugate of X(16708)
X(56255) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 18164}, {3, 53238}, {6, 17169}, {21, 1418}, {27, 22053}, {31, 16708}, {32, 53236}, {56, 16713}, {57, 17194}, {58, 142}, {60, 52023}, {81, 354}, {86, 1475}, {110, 21104}, {284, 10481}, {552, 21795}, {593, 3925}, {662, 48151}, {757, 21808}, {1014, 1212}, {1019, 35338}, {1229, 1408}, {1233, 2206}, {1333, 20880}, {1412, 4847}, {1414, 21127}, {1434, 2293}, {1509, 52020}, {2193, 53237}, {2360, 13156}, {2488, 4573}, {3285, 53240}, {3286, 53241}, {4556, 55282}, {4565, 6362}, {4616, 10581}, {4637, 6608}, {5009, 53239}, {7192, 35326}, {7203, 35341}, {7252, 35312}, {17187, 18087}, {17206, 40983}, {35335, 39179}
X(56255) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 16713}, {2, 16708}, {3, 18164}, {9, 17169}, {10, 142}, {37, 20880}, {244, 21104}, {1084, 48151}, {5452, 17194}, {6376, 53236}, {36103, 53238}, {40586, 354}, {40590, 10481}, {40599, 4847}, {40600, 1475}, {40603, 1233}, {40607, 21808}, {40608, 21127}, {40611, 1418}, {40622, 23599}, {47345, 53237}, {55064, 6362}
X(56255) = X(i)-Ceva conjugate of X(j) for these {i, j}: {32008, 56157}
X(56255) = X(i)-cross conjugate of X(j) for these {i, j}: {523, 1018}, {4068, 1}, {4524, 4551}
X(56255) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1621)}}, {{A, B, C, X(9), X(33)}}, {{A, B, C, X(10), X(3870)}}, {{A, B, C, X(19), X(52555)}}, {{A, B, C, X(42), X(57)}}, {{A, B, C, X(65), X(10389)}}, {{A, B, C, X(84), X(56221)}}, {{A, B, C, X(523), X(3925)}}, {{A, B, C, X(728), X(1334)}}, {{A, B, C, X(756), X(3930)}}, {{A, B, C, X(846), X(3573)}}, {{A, B, C, X(885), X(17194)}}, {{A, B, C, X(1174), X(32008)}}, {{A, B, C, X(1400), X(7308)}}, {{A, B, C, X(1441), X(34784)}}, {{A, B, C, X(2238), X(6654)}}, {{A, B, C, X(2279), X(40147)}}, {{A, B, C, X(3681), X(4006)}}, {{A, B, C, X(3695), X(28594)}}, {{A, B, C, X(3731), X(21061)}}, {{A, B, C, X(3943), X(14628)}}, {{A, B, C, X(4068), X(18164)}}, {{A, B, C, X(4524), X(21795)}}, {{A, B, C, X(5260), X(39458)}}, {{A, B, C, X(5665), X(41506)}}, {{A, B, C, X(6605), X(42310)}}, {{A, B, C, X(7046), X(40779)}}, {{A, B, C, X(10390), X(15320)}}, {{A, B, C, X(16577), X(17747)}}, {{A, B, C, X(16606), X(39963)}}, {{A, B, C, X(18793), X(39954)}}, {{A, B, C, X(21039), X(42449)}}, {{A, B, C, X(21808), X(42438)}}, {{A, B, C, X(21809), X(21811)}}, {{A, B, C, X(39797), X(39961)}}, {{A, B, C, X(39948), X(40747)}}, {{A, B, C, X(43739), X(45100)}}
X(56255) = barycentric product X(i)*X(j) for these (i, j): {1, 56157}, {6, 56127}, {10, 2346}, {210, 21453}, {226, 6605}, {1170, 2321}, {1174, 321}, {1334, 31618}, {4041, 6606}, {4086, 53243}, {4705, 55281}, {10482, 1441}, {10509, 4515}, {32008, 37}, {40443, 53008}, {41013, 47487}, {56118, 65}
X(56255) = barycentric quotient X(i)/X(j) for these (i, j): {1, 17169}, {2, 16708}, {6, 18164}, {9, 16713}, {10, 20880}, {19, 53238}, {37, 142}, {42, 354}, {55, 17194}, {65, 10481}, {75, 53236}, {210, 4847}, {213, 1475}, {225, 53237}, {228, 22053}, {321, 1233}, {512, 48151}, {661, 21104}, {756, 3925}, {872, 52020}, {1170, 1434}, {1174, 81}, {1334, 1212}, {1400, 1418}, {1500, 21808}, {1903, 13156}, {2171, 52023}, {2321, 1229}, {2346, 86}, {3668, 53242}, {3709, 21127}, {3930, 51384}, {4041, 6362}, {4515, 51972}, {4524, 6608}, {4551, 35312}, {4557, 35338}, {4674, 53240}, {4705, 55282}, {4878, 15185}, {6605, 333}, {6606, 4625}, {7064, 21039}, {7178, 23599}, {10482, 21}, {18098, 18087}, {18785, 53241}, {21039, 6067}, {21805, 51463}, {28594, 17672}, {32008, 274}, {47487, 1444}, {53243, 1414}, {55281, 4623}, {56118, 314}, {56127, 76}, {56157, 75}
X(56255) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2346, 6605, 1174}

X(56256) = KP4(X(37)) OF X(1) AND X(42)

Barycentrics    a*(b+c)*(a*b*(b-2*c)+b^2*c+a^2*(b+c))*(b*c^2+a*c*(-2*b+c)+a^2*(b+c)) : :

X(56256) lies on these lines: {1, 22220}, {10, 56197}, {75, 16569}, {596, 978}, {872, 41683}, {876, 6363}, {995, 39697}, {3294, 56240}, {4090, 42027}, {17795, 39714}

X(56256) = isogonal conjugate of X(18192)
X(56256) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 18192}, {6, 17178}, {27, 22066}, {58, 3840}, {81, 17448}, {86, 22343}, {593, 21025}, {757, 22167}, {1333, 20892}, {2162, 16722}, {17187, 18102}
X(56256) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 18192}, {9, 17178}, {10, 3840}, {37, 20892}, {40586, 17448}, {40600, 22343}, {40607, 22167}
X(56256) = X(i)-Ceva conjugate of X(j) for these {i, j}: {32011, 56197}
X(56256) = X(i)-cross conjugate of X(j) for these {i, j}: {50491, 1018}
X(56256) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}}, {{A, B, C, X(42), X(16569)}}, {{A, B, C, X(57), X(27809)}}, {{A, B, C, X(87), X(18082)}}, {{A, B, C, X(213), X(53676)}}, {{A, B, C, X(740), X(6363)}}, {{A, B, C, X(872), X(53581)}}, {{A, B, C, X(978), X(3293)}}, {{A, B, C, X(995), X(31855)}}, {{A, B, C, X(1400), X(18793)}}, {{A, B, C, X(2171), X(22220)}}, {{A, B, C, X(2998), X(39797)}}, {{A, B, C, X(3223), X(40147)}}, {{A, B, C, X(3551), X(13576)}}, {{A, B, C, X(3993), X(21892)}}, {{A, B, C, X(14624), X(52654)}}, {{A, B, C, X(20964), X(21830)}}, {{A, B, C, X(28248), X(42043)}}, {{A, B, C, X(39748), X(45988)}}, {{A, B, C, X(39972), X(52555)}}
X(56256) = barycentric product X(i)*X(j) for these (i, j): {1, 56197}, {32011, 37}
X(56256) = barycentric quotient X(i)/X(j) for these (i, j): {1, 17178}, {6, 18192}, {10, 20892}, {37, 3840}, {42, 17448}, {43, 16722}, {213, 22343}, {228, 22066}, {756, 21025}, {1500, 22167}, {18098, 18102}, {32011, 274}, {56197, 75}

X(56257) = KP4(X(37)) OF X(1) AND X(100)

Barycentrics    a*(a-b)*(a-c)*(b+c)*(b^2+a*c)*(a*b+c^2) : :

X(56257) lies on these lines: {37, 256}, {190, 4079}, {291, 21823}, {644, 3903}, {646, 3807}, {1432, 3970}, {4043, 44187}, {4053, 40873}, {4552, 7239}, {4606, 24052}, {7015, 21061}, {7018, 22015}, {7202, 36228}, {21295, 21834}, {21809, 55064}, {22003, 32041}

X(56257) = isogonal conjugate of X(18200)
X(56257) = isotomic conjugate of X(16737)
X(56257) = trilinear pole of line {210, 20691}
X(56257) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 18200}, {6, 17212}, {27, 22093}, {31, 16737}, {58, 4369}, {81, 4367}, {86, 20981}, {110, 7200}, {171, 1019}, {172, 7192}, {593, 2533}, {649, 17103}, {662, 53541}, {667, 8033}, {741, 4107}, {894, 3733}, {1014, 3287}, {1333, 4374}, {1412, 3907}, {1509, 7234}, {1790, 54229}, {2329, 7203}, {2330, 17096}, {3737, 7175}, {3955, 17925}, {4128, 4610}, {4140, 7341}, {4164, 37128}, {4459, 4565}, {4556, 53559}, {4579, 16726}, {4603, 7207}, {4623, 21755}, {4817, 40731}, {7009, 7254}, {7122, 7199}, {7176, 7252}, {7267, 43926}, {14296, 18268}, {16592, 52935}, {17187, 18111}, {18787, 50456}, {22373, 55231}, {27958, 43924}
X(56257) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 16737}, {3, 18200}, {9, 17212}, {10, 4369}, {37, 4374}, {244, 7200}, {1084, 53541}, {5375, 17103}, {6631, 8033}, {8299, 4107}, {35068, 14296}, {40586, 4367}, {40599, 3907}, {40600, 20981}, {55064, 4459}
X(56257) = X(i)-cross conjugate of X(j) for these {i, j}: {22280, 4551}, {22314, 4674}, {40501, 100}
X(56257) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(42363)}}, {{A, B, C, X(10), X(4572)}}, {{A, B, C, X(37), X(190)}}, {{A, B, C, X(42), X(34071)}}, {{A, B, C, X(101), X(4103)}}, {{A, B, C, X(256), X(4594)}}, {{A, B, C, X(644), X(646)}}, {{A, B, C, X(661), X(45661)}}, {{A, B, C, X(694), X(27805)}}, {{A, B, C, X(1581), X(3903)}}, {{A, B, C, X(2321), X(3939)}}, {{A, B, C, X(3799), X(40790)}}, {{A, B, C, X(3807), X(3862)}}, {{A, B, C, X(3952), X(36863)}}, {{A, B, C, X(4623), X(30571)}}, {{A, B, C, X(14624), X(56248)}}, {{A, B, C, X(29351), X(56221)}}, {{A, B, C, X(40519), X(52555)}}
X(56257) = barycentric product X(i)*X(j) for these (i, j): {10, 3903}, {42, 56241}, {190, 52651}, {256, 3952}, {1018, 257}, {1432, 30730}, {1500, 7260}, {1978, 40729}, {2321, 37137}, {4033, 893}, {4069, 7249}, {4451, 4551}, {4557, 7018}, {4594, 756}, {4603, 594}, {27805, 37}, {27808, 904}, {29055, 3701}, {30670, 3773}, {32010, 40521}, {37134, 4037}, {40432, 4103}
X(56257) = barycentric quotient X(i)/X(j) for these (i, j): {1, 17212}, {2, 16737}, {6, 18200}, {10, 4374}, {37, 4369}, {42, 4367}, {100, 17103}, {190, 8033}, {210, 3907}, {213, 20981}, {228, 22093}, {256, 7192}, {257, 7199}, {512, 53541}, {644, 27958}, {661, 7200}, {740, 14296}, {756, 2533}, {872, 7234}, {893, 1019}, {904, 3733}, {1018, 894}, {1334, 3287}, {1431, 7203}, {1432, 17096}, {1824, 54229}, {2238, 4107}, {3747, 4164}, {3774, 45882}, {3903, 86}, {3952, 1909}, {4033, 1920}, {4041, 4459}, {4069, 7081}, {4079, 16592}, {4103, 3963}, {4451, 18155}, {4515, 4529}, {4551, 7176}, {4552, 7196}, {4557, 171}, {4559, 7175}, {4594, 873}, {4603, 1509}, {4705, 53559}, {4849, 4504}, {7018, 52619}, {7116, 7254}, {7234, 7207}, {7239, 7187}, {18098, 18111}, {20683, 53553}, {21805, 4922}, {21809, 28006}, {21859, 4032}, {27805, 274}, {29055, 1014}, {30730, 17787}, {35309, 16720}, {36863, 27891}, {37137, 1434}, {40521, 1215}, {40729, 649}, {50487, 4128}, {52651, 514}, {53581, 21755}, {56183, 14006}, {56241, 310}

X(56258) = KP4(X(37)) OF X(10) AND X(2)

Barycentrics    (b+c)*(a^2+a*(-2*b+c)+b*(b+c))*(a^2+a*(b-2*c)+c*(b+c)) : :

X(56258) lies on these lines: {2, 32017}, {6, 145}, {25, 1261}, {37, 52353}, {42, 3950}, {75, 26997}, {111, 8706}, {192, 39957}, {251, 20056}, {321, 1427}, {967, 37639}, {1171, 31011}, {1400, 2321}, {2345, 39798}, {2350, 10453}, {3056, 40528}, {3952, 21809}, {3995, 56219}, {4024, 55263}, {4033, 27039}, {4140, 55261}, {4461, 42290}, {17178, 37128}, {17280, 39979}, {17281, 39982}, {20039, 20228}, {27145, 39981}, {30942, 40451}, {31325, 39951}, {40420, 56086}

X(56258) = isotomic conjugate of X(18600)
X(56258) = trilinear pole of line {14321, 512}
X(56258) = X(i)-isoconjugate-of-X(j) for these {i, j}: {27, 22344}, {31, 18600}, {56, 18163}, {58, 3752}, {81, 1201}, {86, 20228}, {110, 48334}, {284, 1122}, {593, 4642}, {604, 17183}, {645, 42336}, {662, 6363}, {757, 21796}, {849, 4415}, {1014, 2347}, {1019, 23845}, {1333, 3663}, {1396, 22072}, {1408, 3452}, {1412, 3057}, {1790, 1828}, {2194, 52563}, {2206, 26563}, {2360, 42549}, {3733, 21362}, {4565, 6615}, {7341, 21809}, {16947, 20895}, {27499, 38832}
X(56258) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 18163}, {2, 18600}, {10, 3752}, {37, 3663}, {244, 48334}, {1084, 6363}, {1214, 52563}, {3161, 17183}, {4075, 4415}, {6741, 21120}, {40586, 1201}, {40590, 1122}, {40599, 3057}, {40600, 20228}, {40603, 26563}, {40607, 21796}, {52872, 51415}, {55064, 6615}
X(56258) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1222, 56190}
X(56258) = X(i)-cross conjugate of X(j) for these {i, j}: {4041, 3952}, {27040, 2}, {56190, 56173}
X(56258) = intersection, other than A, B, C, of these circumconics: {{A, B, C, X(2), X(6)}}, {{A, B, C, X(4), X(11319)}}, {{A, B, C, X(7), X(18082)}}, {{A, B, C, X(8), X(17751)}}, {{A, B, C, X(10), X(145)}}, {{A, B, C, X(19), X(35058)}}, {{A, B, C, X(65), X(6553)}}, {{A, B, C, X(76), X(26770)}}, {{A, B, C, X(280), X(3701)}}, {{A, B, C, X(291), X(56256)}}, {{A, B, C, X(306), X(7172)}}, {{A, B, C, X(321), X(346)}}, {{A, B, C, X(330), X(18785)}}, {{A, B, C, X(523), X(9053)}}, {{A, B, C, X(594), X(3943)}}, {{A, B, C, X(966), X(37639)}}, {{A, B, C, X(1220), X(39458)}}, {{A, B, C, X(1826), X(4080)}}, {{A, B, C, X(2238), X(17178)}}, {{A, B, C, X(2298), X(39698)}}, {{A, B, C, X(2345), X(3995)}}, {{A, B, C, X(3293), X(15315)}}, {{A, B, C, X(3930), X(3963)}}, {{A, B, C, X(4029), X(5257)}}, {{A, B, C, X(4041), X(21809)}}, {{A, B, C, X(4058), X(4072)}}, {{A, B, C, X(4373), X(13576)}}, {{A, B, C, X(4651), X(10453)}}, {{A, B, C, X(4674), X(41446)}}, {{A, B, C, X(6539), X(17314)}}, {{A, B, C, X(9309), X(18793)}}, {{A, B, C, X(15320), X(36606)}}, {{A, B, C, X(15523), X(20056)}}, {{A, B, C, X(17340), X(40085)}}, {{A, B, C, X(18098), X(39694)}}, {{A, B, C, X(18600), X(27040)}}, {{A, B, C, X(19998), X(30942)}}, {{A, B, C, X(23617), X(32017)}}, {{A, B, C, X(27145), X(37657)}}, {{A, B, C, X(30710), X(56255)}}, {{A, B, C, X(30712), X(40718)}}, {{A, B, C, X(31503), X(35577)}}, {{A, B, C, X(38247), X(40747)}}
X(56258) = barycentric product X(i)*X(j) for these (i, j): {10, 1222}, {226, 52549}, {313, 51476}, {523, 8706}, {1261, 1441}, {1476, 3701}, {2321, 40420}, {3710, 40446}, {23617, 321}, {30713, 3451}, {32017, 37}, {56173, 8}, {56190, 75}
X(56258) = barycentric quotient X(i)/X(j) for these (i, j): {2, 18600}, {8, 17183}, {9, 18163}, {10, 3663}, {37, 3752}, {42, 1201}, {65, 1122}, {210, 3057}, {213, 20228}, {226, 52563}, {228, 22344}, {321, 26563}, {512, 6363}, {594, 4415}, {661, 48334}, {756, 4642}, {1018, 21362}, {1222, 86}, {1261, 21}, {1334, 2347}, {1476, 1014}, {1500, 21796}, {1824, 1828}, {1903, 42549}, {2318, 22072}, {2321, 3452}, {3451, 1412}, {3700, 21120}, {3701, 20895}, {3943, 51415}, {3950, 45204}, {3952, 21272}, {4033, 21580}, {4041, 6615}, {4082, 6736}, {4140, 28006}, {4557, 23845}, {4574, 23113}, {4849, 45219}, {6057, 21031}, {6613, 4616}, {8706, 99}, {16606, 27499}, {23617, 81}, {30730, 25268}, {32017, 274}, {40420, 1434}, {40451, 17205}, {40528, 18191}, {44729, 14284}, {51476, 58}, {51641, 42336}, {52549, 333}, {56173, 7}, {56190, 1}
X(56258) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1222, 52549, 23617}

X(56259) = KP4(X(37)) OF X(10) AND X(9)

Barycentrics    a*(b+c)*(a^4-a^3*c+b*(b-c)^2*(b+c)+a*c*(b+c)^2-a^2*(2*b^2-b*c+c^2))*(a^4-a^3*b+(b-c)^2*c*(b+c)+a*b*(b+c)^2-a^2*(b^2-b*c+2*c^2)) : :

X(56259) lies on these lines: {1, 1167}, {3, 40527}, {19, 1802}, {65, 3191}, {72, 52384}, {75, 936}, {158, 200}, {225, 2318}, {596, 997}, {2214, 3553}, {3333, 13476}, {3668, 3682}, {7982, 34434}, {8580, 39708}, {9623, 31359}, {21031, 52383}, {25091, 50196}, {30144, 39697}

X(56259) = X(i)-isoconjugate-of-X(j) for these {i, j}: {21, 37566}, {28, 1071}, {57, 40979}, {58, 1210}, {81, 1108}, {86, 40958}, {286, 23204}, {593, 21933}, {1014, 1864}, {1226, 2206}, {1333, 17862}, {2360, 52571}, {7192, 53288}, {41562, 52375}
X(56259) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 1210}, {37, 17862}, {5452, 40979}, {40586, 1108}, {40591, 1071}, {40600, 40958}, {40603, 1226}, {40611, 37566}
X(56259) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}}, {{A, B, C, X(9), X(3191)}}, {{A, B, C, X(42), X(936)}}, {{A, B, C, X(72), X(2321)}}, {{A, B, C, X(84), X(13576)}}, {{A, B, C, X(200), X(1802)}}, {{A, B, C, X(201), X(1089)}}, {{A, B, C, X(758), X(21031)}}, {{A, B, C, X(937), X(1400)}}, {{A, B, C, X(943), X(56255)}}, {{A, B, C, X(997), X(3293)}}, {{A, B, C, X(1167), X(40424)}}, {{A, B, C, X(1214), X(6769)}}, {{A, B, C, X(3680), X(38955)}}, {{A, B, C, X(3701), X(56101)}}, {{A, B, C, X(7952), X(51497)}}, {{A, B, C, X(7982), X(37558)}}, {{A, B, C, X(18793), X(39946)}}, {{A, B, C, X(21061), X(45032)}}, {{A, B, C, X(30144), X(31855)}}, {{A, B, C, X(30457), X(56146)}}, {{A, B, C, X(38271), X(41506)}}, {{A, B, C, X(39130), X(42470)}}, {{A, B, C, X(43531), X(52518)}}
X(56259) = barycentric product X(i)*X(j) for these (i, j): {10, 40399}, {37, 40424}, {1167, 321}, {3710, 40397}, {40444, 72}
X(56259) = barycentric quotient X(i)/X(j) for these (i, j): {10, 17862}, {37, 1210}, {42, 1108}, {55, 40979}, {71, 1071}, {213, 40958}, {321, 1226}, {756, 21933}, {1167, 81}, {1334, 1864}, {1400, 37566}, {1903, 52571}, {2200, 23204}, {21801, 1532}, {21871, 6260}, {21872, 41561}, {40399, 86}, {40424, 274}, {40444, 286}, {40527, 17219}

X(56260) = KP4(X(37)) OF X(10) AND X(10)

Barycentrics    a*(b+c)*(a^2-2*a*b+b^2+c^2)*(a^2+b^2-2*a*c+c^2) : :

X(56260) lies on these lines: {1, 39951}, {2, 30701}, {6, 3692}, {25, 200}, {42, 3991}, {111, 52778}, {251, 3935}, {306, 1427}, {346, 52223}, {393, 7101}, {967, 5337}, {1009, 2350}, {1018, 17441}, {1171, 40403}, {1400, 3694}, {1500, 56219}, {1880, 2321}, {3108, 3957}, {3228, 54967}, {3700, 3967}, {3938, 25066}, {3965, 53088}, {5347, 46010}, {8580, 21448}, {8817, 42290}, {16081, 42384}, {29817, 39389}, {39798, 44798}

X(56260) = isotomic conjugate of X(16750)
X(56260) = perspector of circumconic {{A, B, C, X(52778), X(54967)}}
X(56260) = X(i)-isoconjugate-of-X(j) for these {i, j}: {21, 28017}, {27, 1473}, {28, 7289}, {31, 16750}, {57, 5324}, {58, 4000}, {63, 4211}, {81, 614}, {86, 16502}, {110, 48398}, {284, 7195}, {497, 1412}, {593, 3914}, {757, 16583}, {849, 53510}, {873, 21750}, {1014, 2082}, {1019, 1633}, {1040, 1396}, {1333, 3673}, {1434, 7083}, {1474, 17170}, {1509, 40934}, {1790, 1851}, {2185, 40961}, {3732, 3733}, {4556, 48403}, {4610, 50490}, {4637, 17115}, {6628, 21813}, {22057, 36419}
X(56260) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 16750}, {10, 4000}, {37, 3673}, {244, 48398}, {3162, 4211}, {4075, 53510}, {5452, 5324}, {40586, 614}, {40590, 7195}, {40591, 7289}, {40599, 497}, {40600, 16502}, {40607, 16583}, {40611, 28017}, {51574, 17170}
X(56260) = X(i)-cross conjugate of X(j) for these {i, j}: {656, 1018}, {4524, 3952}
X(56260) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(39731)}}, {{A, B, C, X(2), X(6)}}, {{A, B, C, X(10), X(3870)}}, {{A, B, C, X(65), X(1280)}}, {{A, B, C, X(72), X(17742)}}, {{A, B, C, X(200), X(306)}}, {{A, B, C, X(210), X(321)}}, {{A, B, C, X(656), X(17441)}}, {{A, B, C, X(765), X(40033)}}, {{A, B, C, X(1009), X(14004)}}, {{A, B, C, X(1088), X(41683)}}, {{A, B, C, X(1089), X(4006)}}, {{A, B, C, X(1214), X(40910)}}, {{A, B, C, X(1826), X(34525)}}, {{A, B, C, X(2318), X(3998)}}, {{A, B, C, X(3294), X(3555)}}, {{A, B, C, X(3696), X(4651)}}, {{A, B, C, X(3931), X(28594)}}, {{A, B, C, X(3935), X(15523)}}, {{A, B, C, X(3952), X(3967)}}, {{A, B, C, X(3995), X(44798)}}, {{A, B, C, X(7123), X(30701)}}, {{A, B, C, X(13576), X(42361)}}, {{A, B, C, X(18082), X(21453)}}, {{A, B, C, X(21840), X(37593)}}, {{A, B, C, X(34892), X(38825)}}, {{A, B, C, X(42471), X(43672)}}, {{A, B, C, X(45744), X(45791)}}, {{A, B, C, X(51564), X(56257)}}
X(56260) = barycentric product X(i)*X(j) for these (i, j): {10, 56179}, {210, 8817}, {226, 56243}, {313, 7084}, {321, 7123}, {512, 54967}, {523, 52778}, {1018, 48070}, {1037, 3701}, {1041, 3710}, {2321, 7131}, {3949, 40411}, {30701, 37}, {30705, 4515}, {40403, 594}, {42384, 647}
X(56260) = barycentric quotient X(i)/X(j) for these (i, j): {2, 16750}, {10, 3673}, {25, 4211}, {37, 4000}, {42, 614}, {55, 5324}, {65, 7195}, {71, 7289}, {72, 17170}, {181, 40961}, {210, 497}, {213, 16502}, {228, 1473}, {594, 53510}, {661, 48398}, {756, 3914}, {872, 40934}, {1018, 3732}, {1037, 1014}, {1334, 2082}, {1400, 28017}, {1500, 16583}, {1824, 1851}, {2318, 1040}, {3690, 17441}, {3694, 27509}, {3695, 20235}, {3930, 51400}, {3949, 18589}, {3991, 41785}, {4006, 17671}, {4515, 6554}, {4524, 17115}, {4557, 1633}, {4705, 48403}, {7064, 40965}, {7084, 58}, {7109, 21750}, {7123, 81}, {7131, 1434}, {8269, 4616}, {14935, 18191}, {30701, 274}, {40403, 1509}, {42384, 6331}, {48070, 7199}, {50487, 50490}, {52370, 7124}, {52778, 99}, {54967, 670}, {55232, 21107}, {56179, 86}, {56243, 333}
X(56260) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {56179, 56243, 7123}

X(56261) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(3) AND X(4)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^6-a^5*c+2*a^3*c^3-a^4*(2*b^2+c^2)+(-(b^2*c)+c^3)^2+a*c*(b^4-c^4)+a^2*(b^4+4*b^2*c^2-c^4))*(a^6-a^5*b+2*a^3*b^3-a^4*(b^2+2*c^2)+(b^3-b*c^2)^2+a^2*(-b^4+4*b^2*c^2+c^4)+a*(-b^5+b*c^4)) : :

X(56261) lies on these lines: {1, 1941}, {3, 158}, {4, 255}, {273, 1804}, {281, 2289}, {318, 1013}, {771, 43764}, {2193, 8748}, {5722, 36123}, {7040, 7531}, {36055, 37695}, {36607, 37234}, {51281, 51282}

X(56261) = trilinear pole of line {3064, 36054}
X(56261) = X(i)-isoconjugate-of-X(j) for these {i, j}: {770, 1813}
X(56261) = X(i)-cross conjugate of X(j) for these {i, j}: {13734, 1}
X(56261) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(243)}}, {{A, B, C, X(3), X(21)}}, {{A, B, C, X(4), X(29)}}, {{A, B, C, X(7), X(18850)}}, {{A, B, C, X(8), X(1217)}}, {{A, B, C, X(77), X(1294)}}, {{A, B, C, X(78), X(40448)}}, {{A, B, C, X(79), X(18848)}}, {{A, B, C, X(80), X(264)}}, {{A, B, C, X(87), X(90)}}, {{A, B, C, X(276), X(17743)}}, {{A, B, C, X(277), X(34234)}}, {{A, B, C, X(1039), X(8884)}}, {{A, B, C, X(1061), X(1300)}}, {{A, B, C, X(5560), X(14860)}}, {{A, B, C, X(7319), X(18855)}}, {{A, B, C, X(13478), X(31623)}}, {{A, B, C, X(14621), X(23582)}}, {{A, B, C, X(23707), X(55918)}}, {{A, B, C, X(40801), X(52133)}}
X(56261) = barycentric product X(i)*X(j) for these (i, j): {44426, 771}
X(56261) = barycentric quotient X(i)/X(j) for these (i, j): {771, 6516}, {18344, 770}

X(56262) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(7) AND X(8)

Barycentrics    a*(a+b-c)*(a-b+c)*(a^4-4*a^3*c-4*a*c^3-2*a^2*(b^2-3*c^2)+(b^2-c^2)^2)*(a^4-4*a^3*b-4*a*b^3+a^2*(6*b^2-2*c^2)+(b^2-c^2)^2) : :

X(56262) lies on the Feuerbach hyperbola and on these lines: {8, 37787}, {9, 2078}, {57, 3254}, {80, 15299}, {100, 15348}, {104, 3358}, {294, 8557}, {518, 56101}, {885, 46006}, {1156, 30223}, {1320, 7672}, {1445, 6601}, {2801, 55966}, {3243, 6596}, {3333, 34485}, {3870, 34894}, {4321, 7284}, {5784, 37579}, {7160, 34486}, {7330, 55918}, {8545, 34919}, {11372, 46435}, {15175, 15298}, {21390, 23893}, {36976, 54408}, {37550, 43740}, {41575, 56089}

X(56262) = isogonal conjugate of X(54408)
X(56262) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 54408}, {6, 52457}, {57, 34526}
X(56262) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 54408}, {9, 52457}, {5452, 34526}
X(56262) = X(i)-cross conjugate of X(j) for these {i, j}: {30199, 100}, {33925, 1}
X(56262) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(19), X(1037)}}, {{A, B, C, X(57), X(59)}}, {{A, B, C, X(77), X(82)}}, {{A, B, C, X(273), X(56179)}}, {{A, B, C, X(765), X(1088)}}, {{A, B, C, X(1440), X(23617)}}, {{A, B, C, X(2161), X(52013)}}, {{A, B, C, X(2990), X(55937)}}, {{A, B, C, X(3333), X(34486)}}, {{A, B, C, X(7045), X(55927)}}, {{A, B, C, X(18815), X(39959)}}, {{A, B, C, X(34234), X(39273)}}, {{A, B, C, X(41431), X(41441)}}, {{A, B, C, X(42019), X(55105)}}
X(56262) = barycentric product X(i)*X(j) for these (i, j): {4554, 46006}, {34525, 7}
X(56262) = barycentric quotient X(i)/X(j) for these (i, j): {1, 52457}, {6, 54408}, {55, 34526}, {34525, 8}, {46006, 650}

X(56263) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(8) AND X(9)

Barycentrics    (a^4+a^3*(4*b-2*c)-10*a^2*b*(b-c)+(b-c)^3*(b+c)+2*a*(2*b^3+5*b^2*c-8*b*c^2+c^3))*(a^4-2*a^3*(b-2*c)+10*a^2*(b-c)*c-(b-c)^3*(b+c)+2*a*(b^3-8*b^2*c+5*b*c^2+2*c^3)) : :

X(56263) lies on the Feuerbach hyperbola and on these lines: {1, 54228}, {8, 15726}, {80, 36991}, {516, 4900}, {518, 56090}, {527, 3680}, {971, 1000}, {1156, 5435}, {1320, 5851}, {3254, 9812}, {3667, 23893}, {4866, 43174}, {5856, 56097}, {7995, 45830}, {9814, 14986}, {15733, 56089}, {18490, 36996}, {34862, 55918}, {34894, 52804}, {38454, 56091}

X(56263) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 36973}, {1253, 36888}
X(56263) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 36973}, {17113, 36888}
X(56263) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(144), X(10509)}}, {{A, B, C, X(479), X(513)}}, {{A, B, C, X(516), X(6006)}}, {{A, B, C, X(527), X(3667)}}, {{A, B, C, X(900), X(5851)}}, {{A, B, C, X(1014), X(53086)}}, {{A, B, C, X(15733), X(30198)}}, {{A, B, C, X(22334), X(56155)}}, {{A, B, C, X(23062), X(42483)}}, {{A, B, C, X(28217), X(38454)}}, {{A, B, C, X(34234), X(55937)}}, {{A, B, C, X(41441), X(52803)}}
X(56263) = barycentric quotient X(i)/X(j) for these (i, j): {1, 36973}, {279, 36888}

X(56264) = KIMBERLING-PAVLOV X(2)-CONJUGATE OF X(7) AND X(8)

Barycentrics    (a+b-c)*(a-b+c)*(a^2+3*b^2-2*a*c+c^2)*(a^2-2*a*b+b^2+3*c^2) : :

X(56264) lies on these lines: {2, 6559}, {7, 346}, {8, 279}, {69, 10509}, {75, 23062}, {85, 341}, {318, 1847}, {1043, 1434}, {2322, 15149}, {2481, 5274}, {3160, 49466}, {3663, 10322}, {3672, 21450}, {5281, 40419}, {6556, 7185}, {7172, 17093}, {7176, 32003}, {7233, 40217}, {10004, 24349}, {13577, 17784}, {18821, 41075}, {29616, 51351}, {29627, 40719}, {37223, 43762}

X(56264) = isotomic conjugate of X(390)
X(56264) = trilinear pole of line {3239, 3676}
X(56264) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 390}, {32, 30854}, {41, 5222}, {55, 7290}, {663, 35280}, {1106, 28057}, {1253, 3598}, {1415, 14330}, {2194, 3755}
X(56264) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 390}, {223, 7290}, {1146, 14330}, {1214, 3755}, {3160, 5222}, {6376, 30854}, {6552, 28057}, {17113, 3598}
X(56264) = X(i)-cross conjugate of X(j) for these {i, j}: {2550, 2}, {4762, 4554}, {39959, 39749}
X(56264) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(693)}}, {{A, B, C, X(7), X(85)}}, {{A, B, C, X(8), X(75)}}, {{A, B, C, X(92), X(42361)}}, {{A, B, C, X(291), X(14484)}}, {{A, B, C, X(330), X(2481)}}, {{A, B, C, X(390), X(2550)}}, {{A, B, C, X(479), X(42304)}}, {{A, B, C, X(518), X(40779)}}, {{A, B, C, X(961), X(5665)}}, {{A, B, C, X(3600), X(3668)}}, {{A, B, C, X(7131), X(43736)}}, {{A, B, C, X(7241), X(8801)}}, {{A, B, C, X(30806), X(42697)}}
X(56264) = barycentric product X(i)*X(j) for these (i, j): {21446, 75}, {24002, 37223}, {39749, 7}, {39959, 85}, {41075, 918}, {52013, 76}
X(56264) = barycentric quotient X(i)/X(j) for these (i, j): {2, 390}, {7, 5222}, {57, 7290}, {75, 30854}, {226, 3755}, {279, 3598}, {346, 28057}, {522, 14330}, {553, 4989}, {651, 35280}, {21446, 1}, {21450, 2082}, {24002, 30804}, {32560, 4326}, {37223, 644}, {39749, 8}, {39959, 9}, {41075, 666}, {52013, 6}

X(56265) = KIMBERLING-PAVLOV X(2)-CONJUGATE OF X(9) AND X(9)

Barycentrics    (a^3*(b-c)+b*(b-c)^2*c+a*(b-c)*(b+c)^2-a^2*(2*b^2+b*c-2*c^2))*(a^3*(b-c)-b*(b-c)^2*c+a*(b-c)*(b+c)^2+a^2*(-2*b^2+b*c+2*c^2)) : :
X(56265) = -3*X[2]+2*X[40593]

X(56265) lies on these lines: {2, 40593}, {7, 14943}, {9, 3177}, {192, 28071}, {200, 1721}, {281, 26125}, {282, 41246}, {346, 17786}, {4183, 56014}, {6605, 51352}, {7110, 25521}, {17261, 21218}, {19605, 40719}, {20906, 28132}, {23617, 27340}, {30695, 56200}, {42483, 43983}

X(56265) = isogonal conjugate of X(20995)
X(56265) = isotomic conjugate of X(3177)
X(56265) = anticomplement of X(40593)
X(56265) = trilinear pole of line {4885, 17072}
X(56265) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 20995}, {6, 1742}, {19, 20793}, {31, 3177}, {32, 20935}, {41, 31526}, {55, 34497}, {58, 21856}, {354, 38835}, {692, 21195}, {1333, 21084}, {2175, 40593}, {2223, 51846}
X(56265) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 3177}, {3, 20995}, {6, 20793}, {9, 1742}, {10, 21856}, {37, 21084}, {223, 34497}, {1086, 21195}, {3160, 31526}, {6376, 20935}, {40593, 40593}
X(56265) = X(i)-cross conjugate of X(j) for these {i, j}: {85, 2}
X(56265) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(9)}}, {{A, B, C, X(7), X(14189)}}, {{A, B, C, X(92), X(335)}}, {{A, B, C, X(189), X(1821)}}, {{A, B, C, X(192), X(54121)}}, {{A, B, C, X(330), X(2481)}}, {{A, B, C, X(522), X(43971)}}, {{A, B, C, X(7155), X(18031)}}, {{A, B, C, X(7361), X(30690)}}, {{A, B, C, X(14942), X(23618)}}
X(56265) = barycentric product X(i)*X(j) for these (i, j): {4397, 53632}, {43750, 8}
X(56265) = barycentric quotient X(i)/X(j) for these (i, j): {1, 1742}, {2, 3177}, {3, 20793}, {6, 20995}, {7, 31526}, {10, 21084}, {37, 21856}, {57, 34497}, {75, 20935}, {85, 40593}, {514, 21195}, {673, 51846}, {1174, 38835}, {43750, 7}, {53632, 934}
X(56265) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 46706, 3177}

X(56266) = KIMBERLING-PAVLOV X(3)-CONJUGATE OF X(2) AND X(3)

Barycentrics    a^2*(a^2-b^2-c^2)*(2*a^4+2*b^4-b^2*c^2-c^4-a^2*(4*b^2+c^2))*(2*a^4-b^4-b^2*c^2+2*c^4-a^2*(b^2+4*c^2)) : :

X(56266) lies on these lines: {2, 340}, {3, 323}, {23, 40801}, {276, 43768}, {376, 18317}, {394, 52437}, {577, 14919}, {1217, 3146}, {1297, 7492}, {1993, 52703}, {1995, 14489}, {3090, 14938}, {3292, 54032}, {3346, 50693}, {3523, 46412}, {3525, 22268}, {5158, 11004}, {10303, 22270}, {15066, 51545}, {15421, 31296}, {18316, 18531}, {34225, 38435}, {34287, 43988}, {34897, 37188}, {51350, 54973}

X(56266) = trilinear pole of line {8552, 520}
X(56266) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 381}, {92, 34417}, {158, 5158}, {393, 18477}, {1096, 37638}, {1784, 51544}, {1969, 34416}, {1973, 44135}, {2181, 4993}, {8749, 18486}, {18487, 36119}, {32225, 36128}
X(56266) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 381}, {1147, 5158}, {1511, 18487}, {4550, 36430}, {6337, 44135}, {6503, 37638}, {22391, 34417}
X(56266) = X(i)-cross conjugate of X(j) for these {i, j}: {23039, 69}
X(56266) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(3)}}, {{A, B, C, X(68), X(13582)}}, {{A, B, C, X(69), X(323)}}, {{A, B, C, X(89), X(1795)}}, {{A, B, C, X(94), X(9289)}}, {{A, B, C, X(184), X(39955)}}, {{A, B, C, X(248), X(1383)}}, {{A, B, C, X(275), X(13472)}}, {{A, B, C, X(287), X(7578)}}, {{A, B, C, X(577), X(3284)}}, {{A, B, C, X(647), X(40103)}}, {{A, B, C, X(2052), X(13452)}}, {{A, B, C, X(2986), X(34386)}}, {{A, B, C, X(2987), X(55977)}}, {{A, B, C, X(2996), X(43756)}}, {{A, B, C, X(3292), X(52898)}}, {{A, B, C, X(3431), X(43530)}}, {{A, B, C, X(8796), X(16835)}}, {{A, B, C, X(11270), X(16080)}}, {{A, B, C, X(13579), X(15077)}}, {{A, B, C, X(20421), X(40384)}}, {{A, B, C, X(51336), X(52153)}}
X(56266) = barycentric product X(i)*X(j) for these (i, j): {311, 46091}, {394, 43530}, {3431, 69}, {14919, 46809}, {16263, 3964}, {18316, 52437}, {54959, 8552}
X(56266) = barycentric quotient X(i)/X(j) for these (i, j): {3, 381}, {69, 44135}, {97, 4993}, {184, 34417}, {255, 18477}, {394, 37638}, {577, 5158}, {1531, 18484}, {3167, 21970}, {3284, 18487}, {3292, 32225}, {3431, 4}, {5158, 36430}, {14575, 34416}, {14919, 46808}, {16263, 1093}, {18316, 6344}, {18877, 51544}, {22115, 3581}, {43530, 2052}, {46091, 54}, {46809, 46106}, {47391, 40909}, {51394, 1531}, {51545, 1990}, {52437, 52149}, {54959, 46456}

X(56267) = KIMBERLING-PAVLOV X(3)-CONJUGATE OF X(2) AND X(6)

Barycentrics    (a^2-b^2-c^2)*(3*a^4+b^4-4*b^2*c^2+3*c^4-2*a^2*(2*b^2+c^2))*(3*a^4+3*b^4-4*b^2*c^2+c^4-2*a^2*(b^2+2*c^2)) : :

X(56267) lies on these lines: {2, 3167}, {6, 8797}, {20, 1972}, {68, 32972}, {69, 10607}, {95, 3620}, {141, 36948}, {155, 32987}, {182, 42351}, {193, 264}, {253, 401}, {287, 53783}, {394, 6340}, {524, 36889}, {1494, 11160}, {2987, 2996}, {3424, 46807}, {3580, 10603}, {5032, 55958}, {5921, 33971}, {6193, 32990}, {6330, 15258}, {6776, 42313}, {9007, 14977}, {11411, 32973}, {11898, 37188}, {12164, 32979}, {12429, 32982}, {13575, 45794}, {33272, 44665}, {37668, 46806}, {37779, 41896}, {40410, 51171}

X(56267) = isotomic conjugate of X(37174)
X(56267) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 51288}, {19, 1351}, {31, 37174}, {1007, 1973}
X(56267) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 37174}, {6, 1351}, {9, 51288}, {6337, 1007}, {6338, 10008}, {35067, 10011}
X(56267) = X(i)-cross conjugate of X(j) for these {i, j}: {11898, 69}, {37188, 2}
X(56267) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(69)}}, {{A, B, C, X(3), X(5050)}}, {{A, B, C, X(4), X(14912)}}, {{A, B, C, X(6), X(97)}}, {{A, B, C, X(20), X(401)}}, {{A, B, C, X(66), X(8796)}}, {{A, B, C, X(68), X(525)}}, {{A, B, C, X(193), X(394)}}, {{A, B, C, X(265), X(41895)}}, {{A, B, C, X(275), X(17040)}}, {{A, B, C, X(524), X(9007)}}, {{A, B, C, X(2052), X(16774)}}, {{A, B, C, X(3424), X(6776)}}, {{A, B, C, X(3519), X(14376)}}, {{A, B, C, X(4846), X(53101)}}, {{A, B, C, X(6090), X(14919)}}, {{A, B, C, X(6339), X(6504)}}, {{A, B, C, X(9028), X(9031)}}, {{A, B, C, X(9289), X(15077)}}, {{A, B, C, X(15316), X(28724)}}, {{A, B, C, X(15740), X(18845)}}, {{A, B, C, X(16081), X(34285)}}, {{A, B, C, X(18850), X(54973)}}, {{A, B, C, X(20080), X(37669)}}, {{A, B, C, X(30541), X(55978)}}, {{A, B, C, X(31626), X(34817)}}, {{A, B, C, X(34403), X(43681)}}, {{A, B, C, X(43537), X(47388)}}
X(56267) = barycentric product X(i)*X(j) for these (i, j): {69, 7612}, {394, 42298}, {3926, 47735}, {40819, 6340}
X(56267) = barycentric quotient X(i)/X(j) for these (i, j): {1, 51288}, {2, 37174}, {3, 1351}, {69, 1007}, {3564, 10011}, {3926, 10008}, {6391, 40809}, {6776, 9752}, {7612, 4}, {40819, 6353}, {42298, 2052}, {43718, 51338}, {47735, 393}

X(56268) = KIMBERLING-PAVLOV X(3)-CONJUGATE OF X(4) AND X(6)

Barycentrics    (a^2-b^2-c^2)*(a^6+(b^2-c^2)^2*(b^2+c^2)-a^4*(5*b^2+c^2)-a^2*(5*b^4-14*b^2*c^2+c^4))*(a^6+(b^2-c^2)^2*(b^2+c^2)-a^4*(b^2+5*c^2)-a^2*(b^4-14*b^2*c^2+5*c^4)) : :

X(56268) lies on the Jerabek hyperbola and on these lines: {3, 53021}, {4, 8681}, {6, 40132}, {64, 524}, {66, 9027}, {74, 20187}, {511, 35512}, {895, 37669}, {1177, 1660}, {2393, 43695}, {2854, 11744}, {3426, 3564}, {4846, 34382}, {6391, 18919}, {8057, 10097}, {9004, 43703}, {9007, 35364}, {10293, 14984}, {16051, 55977}, {18934, 42021}, {34383, 54962}, {40048, 47343}, {44495, 45011}

X(56268) = X(i)-isoconjugate-of-X(j) for these {i, j}: {162, 20186}
X(56268) = X(i)-Dao conjugate of X(j) for these {i, j}: {125, 20186}, {6338, 36895}
X(56268) = X(i)-cross conjugate of X(j) for these {i, j}: {6791, 525}
X(56268) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(4)}}, {{A, B, C, X(520), X(4176)}}, {{A, B, C, X(523), X(6340)}}, {{A, B, C, X(524), X(8057)}}, {{A, B, C, X(1265), X(34893)}}, {{A, B, C, X(2393), X(30211)}}, {{A, B, C, X(3564), X(9007)}}, {{A, B, C, X(3926), X(41909)}}, {{A, B, C, X(7056), X(34916)}}, {{A, B, C, X(8673), X(9027)}}, {{A, B, C, X(8675), X(34382)}}, {{A, B, C, X(9051), X(34381)}}, {{A, B, C, X(9516), X(42287)}}, {{A, B, C, X(41894), X(42484)}}
X(56268) = barycentric product X(i)*X(j) for these (i, j): {20187, 525}, {36878, 3926}
X(56268) = barycentric quotient X(i)/X(j) for these (i, j): {647, 20186}, {3926, 36895}, {6791, 53992}, {20187, 648}, {36878, 393}

X(56269) = KIMBERLING-PAVLOV X(3)-CONJUGATE OF X(7) AND X(7)

Barycentrics    a^2*(a-b-c)*(a^2-b^2-c^2)*(a^3+a^2*(b-c)+(b-c)^2*(b+c)+a*(b^2-2*b*c-c^2))*(a^3+a^2*(-b+c)+(b-c)^2*(b+c)+a*(-b^2-2*b*c+c^2)) : :

X(56269) lies on these lines: {6, 169}, {7, 2982}, {9, 40141}, {48, 4303}, {63, 45127}, {155, 45130}, {159, 2876}, {222, 22122}, {912, 2911}, {1172, 3193}, {1812, 27509}, {1814, 20806}, {2192, 15733}, {2193, 7124}, {2194, 7083}, {2219, 23604}, {8761, 15310}, {13397, 32726}, {14578, 15905}, {22132, 52431}, {27382, 52663}

X(56269) = trilinear pole of line {1946, 52306}
X(56269) = X(i)-isoconjugate-of-X(j) for these {i, j}: {4, 1708}, {27, 41538}, {34, 17776}, {92, 37579}, {158, 3173}, {225, 40571}, {226, 30733}, {273, 2911}, {278, 3811}, {281, 4341}, {653, 15313}, {1780, 40149}, {2052, 3215}, {4564, 5521}, {7115, 17877}, {14054, 40573}
X(56269) = X(i)-Dao conjugate of X(j) for these {i, j}: {1147, 3173}, {11517, 17776}, {22391, 37579}, {36033, 1708}, {40628, 17877}, {51473, 278}
X(56269) = X(i)-Ceva conjugate of X(j) for these {i, j}: {15474, 3}
X(56269) = X(i)-cross conjugate of X(j) for these {i, j}: {3271, 521}, {6056, 3}
X(56269) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(7)}}, {{A, B, C, X(6), X(48)}}, {{A, B, C, X(9), X(169)}}, {{A, B, C, X(58), X(78)}}, {{A, B, C, X(63), X(284)}}, {{A, B, C, X(72), X(1036)}}, {{A, B, C, X(77), X(13404)}}, {{A, B, C, X(255), X(1069)}}, {{A, B, C, X(269), X(36057)}}, {{A, B, C, X(345), X(2189)}}, {{A, B, C, X(348), X(2335)}}, {{A, B, C, X(394), X(2989)}}, {{A, B, C, X(521), X(1264)}}, {{A, B, C, X(608), X(32658)}}, {{A, B, C, X(1400), X(3694)}}, {{A, B, C, X(1820), X(2164)}}, {{A, B, C, X(2316), X(3692)}}, {{A, B, C, X(2359), X(2364)}}, {{A, B, C, X(2983), X(41081)}}, {{A, B, C, X(15733), X(55111)}}, {{A, B, C, X(28787), X(43740)}}
X(56269) = barycentric product X(i)*X(j) for these (i, j): {3, 43740}, {21, 28787}, {1259, 39267}, {2193, 43675}, {3719, 46886}, {11517, 46354}, {13397, 521}, {15474, 219}, {23604, 283}, {39943, 63}
X(56269) = barycentric quotient X(i)/X(j) for these (i, j): {48, 1708}, {184, 37579}, {212, 3811}, {219, 17776}, {228, 41538}, {577, 3173}, {603, 4341}, {1946, 15313}, {2193, 40571}, {2194, 30733}, {3271, 5521}, {6056, 11517}, {7004, 17877}, {13397, 18026}, {15474, 331}, {20967, 41609}, {23207, 14054}, {28787, 1441}, {39943, 92}, {43675, 52575}, {43740, 264}, {52425, 2911}, {52430, 3215}

X(56270) = KIMBERLING-PAVLOV X(4)-CONJUGATE OF X(2) AND X(4)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^4+b^4+4*b^2*c^2-5*c^4-2*a^2*(b^2-2*c^2))*(a^4-5*b^4+4*b^2*c^2+c^4+a^2*(4*b^2-2*c^2)) : :

X(56270) lies on the Kiepert hyperbola and on these lines: {2, 1990}, {3, 54660}, {4, 3426}, {5, 54763}, {27, 54587}, {29, 54790}, {30, 54667}, {76, 46106}, {98, 4232}, {193, 2986}, {235, 54604}, {262, 52284}, {275, 51990}, {297, 5485}, {324, 37874}, {340, 54774}, {381, 54838}, {393, 16080}, {458, 18842}, {467, 54930}, {468, 7612}, {469, 54689}, {470, 43542}, {471, 43543}, {472, 33603}, {473, 33602}, {475, 54727}, {671, 37174}, {1585, 14241}, {1586, 14226}, {1993, 41899}, {2394, 2501}, {2996, 3580}, {3424, 52301}, {3523, 40448}, {3535, 43536}, {3536, 54597}, {3542, 54498}, {3543, 54512}, {3839, 18554}, {4194, 54758}, {4196, 54740}, {4198, 54533}, {4200, 54757}, {4207, 54657}, {4213, 54885}, {5056, 13599}, {5068, 31363}, {5094, 14494}, {5125, 54787}, {5177, 54559}, {5702, 14361}, {6515, 43670}, {6620, 55009}, {6872, 54555}, {6995, 14458}, {7378, 14492}, {7391, 54640}, {7396, 54709}, {7408, 54519}, {7409, 54520}, {7500, 54610}, {7505, 54500}, {7518, 54526}, {7519, 54632}, {7607, 53857}, {7714, 54612}, {8796, 13567}, {8889, 54523}, {10301, 54845}, {11109, 54624}, {11331, 18840}, {13736, 54702}, {14004, 54690}, {14035, 54551}, {14063, 54828}, {14918, 43676}, {14920, 44877}, {15274, 53099}, {17555, 54786}, {17578, 54552}, {18316, 18533}, {18841, 52289}, {31099, 54919}, {32532, 52282}, {32971, 54682}, {32974, 54898}, {34767, 55276}, {35486, 54969}, {37122, 54486}, {37192, 54785}, {37337, 54529}, {37384, 54677}, {37388, 54499}, {37448, 54831}, {37460, 52168}, {40138, 43530}, {40890, 54651}, {50689, 54923}, {52253, 54772}, {52280, 54867}, {52288, 54616}, {52290, 53103}, {52293, 53098}, {54372, 54770}

X(56270) = polar conjugate of X(376)
X(56270) = trilinear pole of line {16231, 37984}
X(56270) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 376}, {63, 26864}, {163, 9007}, {255, 40138}, {4100, 47392}, {4575, 9209}, {9247, 44133}, {52147, 52430}
X(56270) = X(i)-Dao conjugate of X(j) for these {i, j}: {115, 9007}, {136, 9209}, {1249, 376}, {3162, 26864}, {6523, 40138}, {16253, 36427}
X(56270) = X(i)-Ceva conjugate of X(j) for these {i, j}: {36889, 52452}
X(56270) = X(i)-cross conjugate of X(j) for these {i, j}: {1596, 264}, {3426, 36889}, {34288, 52487}, {37643, 2}
X(56270) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(55982)}}, {{A, B, C, X(53), X(46952)}}, {{A, B, C, X(64), X(14919)}}, {{A, B, C, X(89), X(36121)}}, {{A, B, C, X(97), X(3532)}}, {{A, B, C, X(193), X(3580)}}, {{A, B, C, X(253), X(850)}}, {{A, B, C, X(297), X(4232)}}, {{A, B, C, X(393), X(1990)}}, {{A, B, C, X(394), X(43719)}}, {{A, B, C, X(1383), X(43717)}}, {{A, B, C, X(6995), X(11331)}}, {{A, B, C, X(10603), X(35142)}}, {{A, B, C, X(11738), X(40384)}}, {{A, B, C, X(13854), X(18384)}}, {{A, B, C, X(14528), X(31626)}}, {{A, B, C, X(34288), X(46808)}}
X(56270) = barycentric product X(i)*X(j) for these (i, j): {253, 52452}, {264, 3426}, {850, 9064}, {18027, 51990}, {36889, 4}
X(56270) = barycentric quotient X(i)/X(j) for these (i, j): {4, 376}, {25, 26864}, {264, 44133}, {393, 40138}, {523, 9007}, {1093, 47392}, {2052, 52147}, {2501, 9209}, {3426, 3}, {9064, 110}, {14593, 40348}, {18554, 1531}, {36889, 69}, {40138, 36427}, {47649, 5063}, {51385, 1515}, {51990, 577}, {52168, 47391}, {52452, 20}

X(56271) = KIMBERLING-PAVLOV X(4)-CONJUGATE OF X(3) AND X(3)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^10*(b^2-c^2)+b^2*c^2*(b^2-c^2)^4+a^2*(b^2-c^2)^3*(b^2+c^2)^2+a^8*(-4*b^4+b^2*c^2+4*c^4)+2*a^6*(3*b^6+b^4*c^2-b^2*c^4-3*c^6)-2*a^4*(2*b^8+b^6*c^2-2*b^4*c^4+b^2*c^6-2*c^8))*(a^10*(b^2-c^2)-b^2*c^2*(b^2-c^2)^4+a^2*(b^2-c^2)^3*(b^2+c^2)^2-a^8*(4*b^4+b^2*c^2-4*c^4)+2*a^6*(3*b^6+b^4*c^2-b^2*c^4-3*c^6)+a^4*(-4*b^8+2*b^6*c^2-4*b^4*c^4+2*b^2*c^6+4*c^8)) : :

X(56271) lies on the Jerabek hyperbola and on these lines: {3, 1075}, {54, 3168}, {64, 41365}, {68, 6761}, {73, 1148}, {393, 8612}, {450, 15316}, {1942, 3542}, {1987, 52011}, {13450, 43710}, {14528, 42457}, {19173, 43918}, {37070, 43908}

X(56271) = polar conjugate of X(46717)
X(56271) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 46717}, {63, 41373}, {255, 1075}, {2169, 41481}
X(56271) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 46717}, {3162, 41373}, {6523, 1075}, {14363, 41481}
X(56271) = X(i)-Ceva conjugate of X(j) for these {i, j}: {13855, 4}
X(56271) = X(i)-cross conjugate of X(j) for these {i, j}: {1093, 4}
X(56271) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(4)}}, {{A, B, C, X(158), X(7049)}}, {{A, B, C, X(254), X(1941)}}, {{A, B, C, X(450), X(3542)}}, {{A, B, C, X(1075), X(1093)}}, {{A, B, C, X(3168), X(13450)}}, {{A, B, C, X(32230), X(34449)}}
X(56271) = barycentric product X(i)*X(j) for these (i, j): {13855, 2052}, {34287, 4}
X(56271) = barycentric quotient X(i)/X(j) for these (i, j): {4, 46717}, {25, 41373}, {53, 41481}, {393, 1075}, {13855, 394}, {34287, 69}

X(56272) = KIMBERLING-PAVLOV X(5)-CONJUGATE OF X(4) AND X(4)

Barycentrics    b^2*c^2*(a^4-2*a^2*b^2+(b^2-c^2)^2)*(a^4-2*a^2*c^2+(b^2-c^2)^2)*(-(b^2-c^2)^2+a^2*(b^2+c^2)) : :
X(56272) = -3*X[568]+2*X[15231]

X(56272) lies on cubic K562 and on these lines: {3, 22261}, {4, 52}, {5, 45793}, {23, 11816}, {26, 2351}, {51, 40449}, {53, 41587}, {91, 52383}, {94, 96}, {216, 2165}, {311, 1209}, {338, 11585}, {343, 8800}, {565, 1154}, {568, 15231}, {2970, 12359}, {2980, 7517}, {3459, 53028}, {3613, 5576}, {7526, 16391}, {8797, 20563}, {10539, 44145}, {11799, 17703}, {15761, 15912}, {32379, 32734}, {34385, 39286}, {36747, 41244}, {40441, 41271}

X(56272) = X(i)-isoconjugate-of-X(j) for these {i, j}: {24, 2169}, {47, 54}, {275, 563}, {571, 2167}, {924, 36134}, {1147, 2190}, {1748, 14533}, {1993, 2148}, {18315, 55216}, {40440, 52435}, {44179, 54034}
X(56272) = X(i)-Dao conjugate of X(j) for these {i, j}: {5, 1147}, {137, 924}, {139, 15423}, {216, 1993}, {338, 6563}, {6663, 52}, {14363, 24}, {15450, 30451}, {17433, 44808}, {18402, 52416}, {34853, 54}, {37864, 54034}, {39019, 52584}, {40588, 571}, {52032, 9723}, {52869, 51393}
X(56272) = X(i)-Ceva conjugate of X(j) for these {i, j}: {847, 5}
X(56272) = X(i)-cross conjugate of X(j) for these {i, j}: {216, 324}
X(56272) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(5889)}}, {{A, B, C, X(4), X(5)}}, {{A, B, C, X(51), X(1209)}}, {{A, B, C, X(52), X(216)}}, {{A, B, C, X(94), X(324)}}, {{A, B, C, X(96), X(5962)}}, {{A, B, C, X(343), X(34853)}}, {{A, B, C, X(850), X(3519)}}, {{A, B, C, X(5562), X(6368)}}, {{A, B, C, X(8798), X(34802)}}, {{A, B, C, X(11442), X(53174)}}, {{A, B, C, X(18314), X(51481)}}
X(56272) = barycentric product X(i)*X(j) for these (i, j): {5, 5392}, {324, 68}, {343, 847}, {1953, 20571}, {2165, 311}, {12077, 46134}, {13450, 52350}, {14213, 91}, {14593, 28706}, {15415, 32734}, {18314, 925}, {20563, 53}, {30450, 6368}, {34385, 36412}, {39116, 8800}, {45793, 96}
X(56272) = barycentric quotient X(i)/X(j) for these (i, j): {5, 1993}, {51, 571}, {53, 24}, {68, 97}, {91, 2167}, {216, 1147}, {217, 52435}, {311, 7763}, {324, 317}, {343, 9723}, {847, 275}, {925, 18315}, {1820, 2169}, {1953, 47}, {2081, 44808}, {2165, 54}, {2351, 14533}, {3199, 44077}, {5392, 95}, {6368, 52584}, {11062, 52416}, {12077, 924}, {13450, 11547}, {14213, 44179}, {14569, 8745}, {14576, 52432}, {14593, 8882}, {15451, 30451}, {18180, 18605}, {18314, 6563}, {20563, 34386}, {30450, 18831}, {32734, 14586}, {35360, 41679}, {36145, 36134}, {36412, 52}, {40981, 52436}, {41221, 47421}, {41536, 34756}, {45793, 39113}, {47731, 8883}, {51513, 6753}, {52945, 51393}, {53174, 51776}, {53245, 31635}, {55219, 34952}, {55250, 2616}
X(56272) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {847, 5392, 68}

X(56273) = X(3)-VERTEX CONJUGATE OF X(9)

Barycentrics    a*(a^6-a^4*(b-c)^2-2*a^5*(b+c)+(b-c)^4*(b+c)^2-a^2*(b^2-c^2)^2+4*a^3*(b^3-2*b*c^2+c^3)-2*a*(b^5-b^4*c+4*b^3*c^2-5*b*c^4+c^5))*(a^6-a^4*(b-c)^2-2*a^5*(b+c)+(b-c)^4*(b+c)^2-a^2*(b^2-c^2)^2+4*a^3*(b^3-2*b^2*c+c^3)-2*a*(b^5-5*b^4*c+4*b^2*c^3-b*c^4+c^5)) : :

X(56273) lies on the Feuerbach hyperbola and on these lines: {1, 1035}, {4, 207}, {8, 1490}, {9, 3197}, {21, 8726}, {34, 7149}, {57, 30500}, {79, 12676}, {80, 1750}, {84, 1467}, {90, 7992}, {514, 43737}, {515, 6601}, {517, 42470}, {1000, 18446}, {1768, 55966}, {1864, 38308}, {1870, 38268}, {2800, 34894}, {2829, 3254}, {2900, 12641}, {2950, 45393}, {3427, 54366}, {3577, 15239}, {3911, 55964}, {6245, 10429}, {6282, 56101}, {7091, 12114}, {7160, 7971}, {7966, 56038}, {10305, 12246}, {10396, 17649}, {12664, 38271}, {28234, 56089}

X(56273) = isogonal conjugate of X(6282)
X(56273) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 9}
X(56273) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(3), X(937)}}, {{A, B, C, X(28), X(40)}}, {{A, B, C, X(34), X(64)}}, {{A, B, C, X(57), X(30503)}}, {{A, B, C, X(78), X(40446)}}, {{A, B, C, X(102), X(269)}}, {{A, B, C, X(103), X(998)}}, {{A, B, C, X(282), X(36123)}}, {{A, B, C, X(514), X(1422)}}, {{A, B, C, X(515), X(2751)}}, {{A, B, C, X(516), X(30199)}}, {{A, B, C, X(971), X(28292)}}, {{A, B, C, X(1243), X(39393)}}, {{A, B, C, X(1295), X(53086)}}, {{A, B, C, X(2217), X(54197)}}, {{A, B, C, X(2291), X(3426)}}, {{A, B, C, X(2324), X(8748)}}, {{A, B, C, X(2800), X(2826)}}, {{A, B, C, X(2829), X(3887)}}, {{A, B, C, X(3900), X(7008)}}, {{A, B, C, X(8917), X(47645)}}, {{A, B, C, X(28234), X(30198)}}, {{A, B, C, X(40836), X(44692)}}, {{A, B, C, X(43672), X(56136)}}
X(56273) = barycentric quotient X(i)/X(j) for these (i, j): {6, 6282}

X(56274) = KIMBERLING-PAVLOV X(7)-CONJUGATE OF X(2) AND X(7)

Barycentrics    (a+b-c)*(a-b+c)*(a^2-2*a*b+b^2+4*a*c+4*b*c-5*c^2)*(a^2+4*a*b-5*b^2-2*a*c+4*b*c+c^2) : :

X(56274) lies on these lines: {2, 1323}, {7, 55922}, {75, 37780}, {145, 51567}, {903, 51351}, {2400, 21183}, {3911, 42318}, {4373, 26015}, {9436, 36588}, {11019, 20121}, {31527, 31721}

X(56274) = X(i)-isoconjugate-of-X(j) for these {i, j}: {41, 6172}, {55, 35445}, {59, 23056}
X(56274) = X(i)-Dao conjugate of X(j) for these {i, j}: {223, 35445}, {3160, 6172}, {6615, 23056}, {40615, 46919}
X(56274) = X(i)-cross conjugate of X(j) for these {i, j}: {21314, 7}, {55922, 55948}
X(56274) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(7)}}, {{A, B, C, X(80), X(56088)}}, {{A, B, C, X(89), X(43736)}}, {{A, B, C, X(279), X(1323)}}, {{A, B, C, X(693), X(10405)}}, {{A, B, C, X(1000), X(43672)}}, {{A, B, C, X(3062), X(41798)}}
X(56274) = barycentric product X(i)*X(j) for these (i, j): {55922, 85}, {55948, 7}
X(56274) = barycentric quotient X(i)/X(j) for these (i, j): {7, 6172}, {57, 35445}, {2170, 23056}, {3676, 46919}, {23062, 47374}, {55922, 9}, {55948, 8}

X(56275) = KIMBERLING-PAVLOV X(7)-CONJUGATE OF X(8) AND X(8)

Barycentrics    (a+b-c)*(a-b+c)*(a^4-4*a^3*(b-c)+(b-c)^4-4*a*(b-c)*(b+c)^2+2*a^2*(3*b^2+2*b*c-5*c^2))*(a^4+4*a^3*(b-c)+(b-c)^4+4*a*(b-c)*(b+c)^2+a^2*(-10*b^2+4*b*c+6*c^2)) : :

X(56275) lies on the Feuerbach hyperbola and on these lines: {1, 3599}, {7, 10939}, {8, 31527}, {9, 2124}, {279, 3062}, {347, 42015}, {2898, 7319}, {5543, 10390}, {7320, 31526}, {10481, 31507}

X(56275) = X(i)-isoconjugate-of-X(j) for these {i, j}: {9, 1615}, {41, 30695}, {55, 2951}, {220, 2124}, {1253, 31527}, {3939, 17427}, {6602, 17113}
X(56275) = X(i)-Dao conjugate of X(j) for these {i, j}: {223, 2951}, {478, 1615}, {3160, 30695}, {17113, 31527}, {40617, 17427}
X(56275) = X(i)-cross conjugate of X(j) for these {i, j}: {479, 7}, {8917, 42483}
X(56275) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(277), X(38254)}}, {{A, B, C, X(479), X(2124)}}, {{A, B, C, X(2125), X(8917)}}
X(56275) = barycentric product X(i)*X(j) for these (i, j): {85, 8917}, {1088, 2125}, {42483, 7}
X(56275) = barycentric quotient X(i)/X(j) for these (i, j): {7, 30695}, {56, 1615}, {57, 2951}, {269, 2124}, {279, 31527}, {479, 17113}, {2125, 200}, {3022, 17426}, {3669, 17427}, {8917, 9}, {42483, 8}
X(56275) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3160, 15913, 2124}

X(56276) = KIMBERLING-PAVLOV X(8)-CONJUGATE OF X(1) AND X(1)

Barycentrics    (a-b-c)*(a^2*(b-c)+b*c*(b+c)+a*(b^2-b*c-c^2))*(a^2*(b-c)-b*c*(b+c)+a*(b^2+b*c-c^2)) : :

X(56276) lies on the Feuerbach hyperbola and on these lines: {1, 979}, {2, 45989}, {4, 36926}, {7, 2899}, {21, 27538}, {84, 5205}, {104, 13732}, {190, 38286}, {941, 3161}, {2478, 43749}, {3239, 3249}, {3296, 30947}, {3701, 7155}, {4518, 43748}, {4876, 27523}, {5192, 24349}, {5558, 8055}, {7080, 9365}, {9780, 24451}, {26093, 33144}, {28997, 45254}, {38271, 51284}

X(56276) = X(i)-isoconjugate-of-X(j) for these {i, j}: {34, 20805}, {56, 978}, {57, 21769}, {604, 3210}, {1106, 19582}, {1407, 3169}, {1412, 21857}, {4564, 16614}
X(56276) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 978}, {3161, 3210}, {5452, 21769}, {6552, 19582}, {11517, 20805}, {24771, 3169}, {40599, 21857}
X(56276) = X(i)-Ceva conjugate of X(j) for these {i, j}: {979, 8}
X(56276) = X(i)-cross conjugate of X(j) for these {i, j}: {341, 8}
X(56276) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(29), X(56180)}}, {{A, B, C, X(280), X(9369)}}, {{A, B, C, X(318), X(4518)}}, {{A, B, C, X(2319), X(39976)}}, {{A, B, C, X(2899), X(5423)}}, {{A, B, C, X(3701), X(43534)}}, {{A, B, C, X(4076), X(56146)}}, {{A, B, C, X(5205), X(7080)}}
X(56276) = barycentric product X(i)*X(j) for these (i, j): {312, 979}, {4391, 53625}, {39694, 8}, {39701, 6557}
X(56276) = barycentric quotient X(i)/X(j) for these (i, j): {8, 3210}, {9, 978}, {55, 21769}, {200, 3169}, {210, 21857}, {219, 20805}, {346, 19582}, {979, 57}, {3271, 16614}, {6557, 27835}, {39694, 7}, {39701, 5435}, {53625, 651}
X(56276) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {39694, 39701, 979}

X(56277) = KIMBERLING-PAVLOV X(8)-CONJUGATE OF X(4) AND X(4)

Barycentrics    (a-b-c)*(a^3+b^3+a^2*(b-3*c)+b^2*c+b*c^2+c^3+a*(b^2-3*c^2))*(a^3+b^3+b^2*c+b*c^2+c^3+a^2*(-3*b+c)+a*(-3*b^2+c^2)) : :

X(56277) lies on the Feuerbach hyperbola and on these lines: {1, 26065}, {4, 2899}, {7, 19582}, {104, 42469}, {941, 25082}, {989, 4339}, {1476, 15375}, {2298, 3161}, {2481, 30022}, {5423, 56276}, {5556, 8055}, {7319, 36926}

X(56277) = isotomic conjugate of X(31598)
X(56277) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 28039}, {31, 31598}, {34, 42461}, {56, 1722}, {604, 30699}, {608, 8897}, {1106, 2899}
X(56277) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 1722}, {2, 31598}, {9, 28039}, {3161, 30699}, {6552, 2899}, {11517, 42461}
X(56277) = X(i)-cross conjugate of X(j) for these {i, j}: {1265, 8}
X(56277) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(280), X(4518)}}, {{A, B, C, X(960), X(34820)}}, {{A, B, C, X(1265), X(2899)}}, {{A, B, C, X(8851), X(9375)}}
X(56277) = barycentric product X(i)*X(j) for these (i, j): {312, 39946}, {4391, 53629}, {39696, 8}, {42469, 7017}
X(56277) = barycentric quotient X(i)/X(j) for these (i, j): {1, 28039}, {2, 31598}, {8, 30699}, {9, 1722}, {78, 8897}, {219, 42461}, {346, 2899}, {15375, 1407}, {39696, 7}, {39946, 57}, {42469, 222}, {53629, 651}

X(56278) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(4) AND X(4)

Barycentrics    a*(a-b-c)*(a^4-2*a^3*b-2*a^2*c^2+2*a*b^2*(b+c)-(b-c)^3*(b+c))*(a^4-2*a^2*b^2-2*a^3*c+(b-c)^3*(b+c)+2*a*c^2*(b+c)) : :

X(56278) lies on the Feuerbach hyperbola and on these lines: {1, 11517}, {4, 2900}, {7, 224}, {8, 10395}, {72, 90}, {78, 43740}, {80, 12625}, {84, 912}, {200, 6598}, {226, 5555}, {376, 10305}, {405, 7162}, {950, 30513}, {1000, 16845}, {1476, 3873}, {1490, 5840}, {2136, 3577}, {2481, 53652}, {3158, 5665}, {3487, 41540}, {3880, 56152}, {3913, 17098}, {3935, 7319}, {5436, 7160}, {5553, 18446}, {5758, 10309}, {6769, 56273}, {7149, 15500}, {14923, 17097}, {18232, 55918}, {21627, 43745}, {34489, 37301}

X(56278) = isogonal conjugate of X(34489)
X(56278) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 34489}, {34, 224}, {56, 12649}, {57, 1723}, {269, 2900}, {278, 3211}
X(56278) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 12649}, {3, 34489}, {1145, 51432}, {5452, 1723}, {6600, 2900}, {11517, 224}, {41540, 41565}
X(56278) = X(i)-Ceva conjugate of X(j) for these {i, j}: {39695, 39947}
X(56278) = X(i)-cross conjugate of X(j) for these {i, j}: {1260, 9}
X(56278) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(34), X(2316)}}, {{A, B, C, X(78), X(11517)}}, {{A, B, C, X(224), X(1260)}}, {{A, B, C, X(281), X(1257)}}, {{A, B, C, X(318), X(56136)}}, {{A, B, C, X(912), X(8058)}}, {{A, B, C, X(2184), X(18359)}}, {{A, B, C, X(2218), X(39943)}}, {{A, B, C, X(3737), X(39946)}}, {{A, B, C, X(7220), X(9398)}}, {{A, B, C, X(7367), X(42064)}}, {{A, B, C, X(10570), X(56179)}}, {{A, B, C, X(14942), X(40436)}}, {{A, B, C, X(34430), X(41505)}}, {{A, B, C, X(42019), X(56148)}}
X(56278) = barycentric product X(i)*X(j) for these (i, j): {312, 34430}, {345, 41505}, {39695, 9}, {39947, 8}, {53652, 650}
X(56278) = barycentric quotient X(i)/X(j) for these (i, j): {6, 34489}, {9, 12649}, {55, 1723}, {212, 3211}, {219, 224}, {220, 2900}, {34430, 57}, {39695, 85}, {39947, 7}, {41505, 278}, {53652, 4554}

X(56279) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(6) AND X(6)

Barycentrics    a*(a-b-c)*(a^2*(b-c)+b*c*(b+c)+a*(b^2-b*c-c^2))*(a^2*(b-c)-b*c*(b+c)+a*(b^2+b*c-c^2)) : :

X(56279) lies on these lines: {6, 979}, {9, 56276}, {57, 1999}, {284, 3208}, {333, 4110}, {2258, 3158}, {2291, 53625}, {2319, 2321}, {3500, 17786}, {4876, 51995}

X(56279) = X(i)-isoconjugate-of-X(j) for these {i, j}: {7, 21769}, {56, 3210}, {57, 978}, {269, 3169}, {278, 20805}, {1014, 21857}, {1407, 19582}, {4998, 16614}
X(56279) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 3210}, {5452, 978}, {6600, 3169}, {24771, 19582}
X(56279) = X(i)-Ceva conjugate of X(j) for these {i, j}: {39694, 979}
X(56279) = X(i)-cross conjugate of X(j) for these {i, j}: {346, 9}
X(56279) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(5255)}}, {{A, B, C, X(6), X(9)}}, {{A, B, C, X(281), X(3501)}}, {{A, B, C, X(314), X(7220)}}, {{A, B, C, X(983), X(7350)}}, {{A, B, C, X(1043), X(1120)}}, {{A, B, C, X(1261), X(2298)}}, {{A, B, C, X(2321), X(3208)}}, {{A, B, C, X(3900), X(30693)}}, {{A, B, C, X(7155), X(8851)}}, {{A, B, C, X(56154), X(56180)}}
X(56279) = barycentric product X(i)*X(j) for these (i, j): {1, 56276}, {8, 979}, {522, 53625}, {3680, 39701}, {39694, 9}
X(56279) = barycentric quotient X(i)/X(j) for these (i, j): {9, 3210}, {41, 21769}, {55, 978}, {200, 19582}, {212, 20805}, {220, 3169}, {979, 7}, {1334, 21857}, {3680, 27835}, {39694, 85}, {39701, 39126}, {53625, 664}, {56276, 75}

X(56280) = KIMBERLING-PAVLOV X(9)-CONJUGATE OF X(10) AND X(10)

Barycentrics    a*(a-b-c)*(a^4+b^4-c^4-a*b*c*(b+c)-a^2*b*(2*b+c))*(a^4-b^4+c^4-a*b*c*(b+c)-a^2*c*(b+2*c)) : :

X(56280) lies on these lines: {1, 52388}, {9, 41502}, {10, 451}, {35, 72}, {40, 37979}, {74, 16132}, {78, 35193}, {307, 1442}, {1717, 56141}, {3694, 52405}, {3710, 4420}, {7110, 38336}

X(56280) = trilinear pole of line {8611, 9404}
X(56280) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 18625}, {34, 52362}, {56, 2475}, {57, 1781}, {65, 229}, {608, 28754}, {1042, 52360}, {1400, 52361}, {1427, 40582}, {37583, 41495}
X(56280) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 2475}, {9, 18625}, {5452, 1781}, {11517, 52362}, {40582, 52361}, {40602, 229}
X(56280) = X(i)-cross conjugate of X(j) for these {i, j}: {2328, 9}, {44782, 8}
X(56280) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(35)}}, {{A, B, C, X(9), X(10)}}, {{A, B, C, X(21), X(191)}}, {{A, B, C, X(65), X(2341)}}, {{A, B, C, X(90), X(2166)}}, {{A, B, C, X(200), X(56278)}}, {{A, B, C, X(285), X(3255)}}, {{A, B, C, X(522), X(1098)}}, {{A, B, C, X(1039), X(2364)}}, {{A, B, C, X(2287), X(6598)}}, {{A, B, C, X(7040), X(15446)}}, {{A, B, C, X(7161), X(52409)}}, {{A, B, C, X(7281), X(9398)}}, {{A, B, C, X(15175), X(36626)}}, {{A, B, C, X(15910), X(52344)}}, {{A, B, C, X(19605), X(26702)}}
X(56280) = barycentric product X(i)*X(j) for these (i, j): {312, 34435}, {54454, 9}
X(56280) = barycentric quotient X(i)/X(j) for these (i, j): {1, 18625}, {9, 2475}, {21, 52361}, {55, 1781}, {78, 28754}, {219, 52362}, {284, 229}, {2287, 52360}, {2328, 40582}, {34435, 57}, {54454, 85}

X(56281) = KIMBERLING-PAVLOV X(10)-CONJUGATE OF X(1) AND X(10)

Barycentrics    (b+c)*(a^2*(b-2*c)-2*b*c*(b+c)+a*(b^2-2*c^2))*(a^2*(2*b-c)+2*b*c*(b+c)+a*(2*b^2-c^2)) : :

X(56281) lies on these lines: {1, 3994}, {65, 49980}, {596, 30942}, {740, 56160}, {897, 51285}, {1089, 41683}, {3632, 34434}, {4671, 39697}, {13476, 49532}, {29822, 56221}

X(56281) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}}, {{A, B, C, X(1089), X(4024)}}, {{A, B, C, X(5561), X(18082)}}
X(56281) = barycentric product X(i)*X(j) for these (i, j): {10, 55953}, {321, 55926}
X(56281) = barycentric quotient X(i)/X(j) for these (i, j): {55926, 81}, {55953, 86}

X(56282) = KIMBERLING-PAVLOV X(10)-CONJUGATE OF X(4) AND X(4)

Barycentrics    -((b+c)*(-(a^2*c)+b^2*(b+c)+a*(b^2-c^2))*(a^2*b-c^2*(b+c)+a*(b^2-c^2))) : :

X(56282) lies on the Kiepert hyperbola and on these lines: {2, 3670}, {4, 2901}, {10, 4016}, {37, 43531}, {72, 1751}, {76, 42714}, {98, 29014}, {226, 3159}, {321, 3454}, {519, 54676}, {912, 13478}, {2051, 39566}, {3175, 54928}, {3743, 40718}, {4444, 23875}, {14534, 15376}, {22035, 43672}, {42471, 44040}

X(56282) = trilinear pole of line {21719, 21721}
X(56282) = X(i)-isoconjugate-of-X(j) for these {i, j}: {28, 42463}, {58, 1724}, {81, 5301}, {163, 29013}, {849, 2901}, {1333, 3187}, {2206, 18147}
X(56282) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 1724}, {37, 3187}, {115, 29013}, {4075, 2901}, {40586, 5301}, {40591, 42463}, {40603, 18147}, {55065, 50329}
X(56282) = X(i)-cross conjugate of X(j) for these {i, j}: {3695, 10}
X(56282) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(313)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(34), X(4674)}}, {{A, B, C, X(37), X(1089)}}, {{A, B, C, X(65), X(3454)}}, {{A, B, C, X(525), X(29016)}}, {{A, B, C, X(596), X(1441)}}, {{A, B, C, X(740), X(23875)}}, {{A, B, C, X(6757), X(42027)}}, {{A, B, C, X(14208), X(28787)}}
X(56282) = barycentric product X(i)*X(j) for these (i, j): {10, 39700}, {15376, 28654}, {29014, 850}
X(56282) = barycentric quotient X(i)/X(j) for these (i, j): {10, 3187}, {37, 1724}, {42, 5301}, {71, 42463}, {321, 18147}, {523, 29013}, {594, 2901}, {4024, 50329}, {4064, 52599}, {15376, 593}, {29014, 110}, {39700, 86}

X(56283) = KIMBERLING-PAVLOV X(11)-CONJUGATE OF X(1) AND X(1)

Barycentrics    (a+b)*(b-c)^3*(a+c)*(-a+b+c)^2 : :

X(56283) lies on these lines: {1, 523}, {21, 884}, {28, 2401}, {140, 14838}, {512, 34434}, {513, 4292}, {514, 942}, {522, 960}, {764, 4089}, {1043, 7253}, {1393, 7178}, {1434, 7192}, {1577, 4187}, {2283, 3658}, {2424, 8747}, {3575, 54244}, {3700, 33299}, {3884, 4151}, {3900, 6737}, {4124, 21132}, {4833, 5327}, {6003, 20420}, {6842, 39212}, {8042, 23764}, {10006, 33528}, {14010, 40213}, {15914, 18191}, {24006, 37368}, {37298, 45671}

X(56283) = perspector of circumconic {{A, B, C, X(16727), X(17197)}}
X(56283) = X(i)-isoconjugate-of-X(j) for these {i, j}: {37, 4619}, {59, 4551}, {765, 53321}, {1018, 1262}, {1020, 1252}, {1110, 4566}, {1400, 31615}, {2149, 4552}, {3952, 24027}, {4033, 23979}, {4069, 7339}, {4557, 7045}, {4559, 4564}, {4574, 7128}, {7012, 23067}, {21859, 52378}
X(56283) = X(i)-Dao conjugate of X(j) for these {i, j}: {513, 53321}, {514, 4566}, {522, 3952}, {650, 4552}, {661, 1020}, {3239, 52609}, {4988, 4605}, {6608, 4069}, {6615, 4551}, {17115, 4557}, {40582, 31615}, {40589, 4619}, {40620, 1275}, {40625, 4998}, {55067, 4564}, {55068, 765}
X(56283) = X(i)-Ceva conjugate of X(j) for these {i, j}: {3737, 11}, {7192, 17197}
X(56283) = X(i)-cross conjugate of X(j) for these {i, j}: {1090, 11}, {42462, 40213}
X(56283) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(11)}}, {{A, B, C, X(341), X(1146)}}, {{A, B, C, X(885), X(42462)}}, {{A, B, C, X(1086), X(1847)}}, {{A, B, C, X(2170), X(34434)}}
X(56283) = barycentric product X(i)*X(j) for these (i, j): {1, 40213}, {11, 4560}, {21, 40166}, {261, 55195}, {341, 8042}, {645, 7336}, {1019, 24026}, {1021, 1111}, {1043, 6545}, {1086, 7253}, {1090, 662}, {1146, 7192}, {1412, 23104}, {1434, 23615}, {1565, 17926}, {2310, 7199}, {3737, 4858}, {4573, 5532}, {14010, 2401}, {14616, 46384}, {14936, 52619}, {15411, 2969}, {15419, 42069}, {16726, 4397}, {16727, 3900}, {17096, 4081}, {17197, 522}, {17205, 3239}, {17219, 3064}, {17925, 2968}, {18155, 2170}, {18191, 4391}, {21132, 333}, {21666, 7254}, {21789, 23989}, {23090, 2973}, {23100, 2328}, {23978, 3733}, {26856, 523}, {34387, 7252}, {39277, 52325}, {42455, 81}, {42462, 86}
X(56283) = barycentric quotient X(i)/X(j) for these (i, j): {11, 4552}, {21, 31615}, {58, 4619}, {244, 1020}, {261, 55194}, {764, 1427}, {1015, 53321}, {1019, 7045}, {1021, 765}, {1043, 6632}, {1086, 4566}, {1090, 1577}, {1146, 3952}, {2170, 4551}, {2310, 1018}, {2968, 52609}, {2969, 52607}, {3119, 4069}, {3120, 4605}, {3270, 4574}, {3271, 4559}, {3733, 1262}, {3737, 4564}, {3937, 52610}, {4081, 30730}, {4516, 21859}, {4560, 4998}, {5532, 3700}, {6545, 3668}, {7117, 23067}, {7192, 1275}, {7252, 59}, {7253, 1016}, {7336, 7178}, {8042, 269}, {14010, 2397}, {14936, 4557}, {16726, 934}, {16727, 4569}, {17197, 664}, {17205, 658}, {17926, 15742}, {18191, 651}, {21132, 226}, {21143, 1042}, {21789, 1252}, {23104, 30713}, {23189, 44717}, {23615, 2321}, {23978, 27808}, {24026, 4033}, {26856, 99}, {36197, 40521}, {40166, 1441}, {40213, 75}, {42455, 321}, {42462, 10}, {46384, 758}, {52316, 17757}, {52335, 4103}, {52338, 40663}, {55195, 12}

X(56284) = KIMBERLING-PAVLOV X(11)-CONJUGATE OF X(9) AND X(9)

Barycentrics    (a-b-c)*(b-c)^3*(a^2+b*(b-c)-a*(2*b+c))*(a^2+c*(-b+c)-a*(b+2*c)) : :
X(56284) = -3*X[42454]+X[42462]

X(56284) lies on these lines: {9, 6362}, {513, 52819}, {514, 5572}, {522, 40659}, {523, 885}, {2488, 13476}, {10509, 23351}, {21104, 21346}, {21132, 21133}, {42454, 42462}, {52305, 56283}

X(56284) = X(i)-isoconjugate-of-X(j) for these {i, j}: {59, 35338}, {1110, 35312}, {1212, 4619}, {1262, 35341}, {1475, 31615}, {4564, 35326}, {35310, 52378}
X(56284) = X(i)-Dao conjugate of X(j) for these {i, j}: {514, 35312}, {6615, 35338}, {35509, 51384}
X(56284) = intersection, other than A, B, C, of circumconics {{A, B, C, X(9), X(11)}}, {{A, B, C, X(885), X(42462)}}, {{A, B, C, X(1086), X(23062)}}, {{A, B, C, X(2170), X(13476)}}
X(56284) = barycentric product X(i)*X(j) for these (i, j): {1170, 42455}, {2346, 40166}, {10482, 23100}, {10509, 23615}, {21132, 32008}, {21453, 42462}, {56118, 6545}
X(56284) = barycentric quotient X(i)/X(j) for these (i, j): {764, 1418}, {1086, 35312}, {2170, 35338}, {2310, 35341}, {2346, 31615}, {3271, 35326}, {4516, 35310}, {6545, 10481}, {7336, 21104}, {21132, 142}, {23615, 51972}, {40166, 20880}, {42455, 1229}, {42462, 4847}, {52305, 51384}, {52316, 51416}, {52338, 51463}, {55195, 3925}, {56118, 6632}, {56283, 16713}

X(56285) = KIMBERLING-PAVLOV X(12)-CONJUGATE OF X(10) AND X(10)

Barycentrics    b*(a+b-c)*c*(a-b+c)*(b+c)^2*(a^2+b^2-c^2)*(a^2-b^2+c^2) : :

X(56285) lies on these lines: {4, 80}, {10, 201}, {12, 7140}, {33, 158}, {34, 92}, {46, 91}, {65, 1867}, {78, 20928}, {108, 2372}, {273, 1268}, {278, 1224}, {286, 18812}, {313, 52575}, {331, 334}, {407, 40663}, {429, 51870}, {498, 1068}, {594, 8736}, {756, 1091}, {1089, 7141}, {1109, 1254}, {1118, 7102}, {1393, 4858}, {1441, 54346}, {1733, 7098}, {1784, 6198}, {1824, 1882}, {1826, 2171}, {1835, 56133}, {1873, 56132}, {1874, 18082}, {1893, 53861}, {1902, 42385}, {1935, 14206}, {1940, 7009}, {4092, 7314}, {4552, 5552}, {5136, 30147}, {6354, 26955}, {6796, 22342}, {10950, 37239}, {11499, 23067}, {13411, 23710}, {14213, 37591}, {17871, 37550}, {18026, 35162}, {18815, 24883}, {20832, 32626}, {23290, 24006}

X(56285) = polar conjugate of X(2185)
X(56285) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 60}, {11, 47390}, {21, 1437}, {48, 2185}, {58, 283}, {63, 2150}, {78, 849}, {81, 2193}, {110, 23189}, {184, 261}, {212, 757}, {219, 593}, {222, 7054}, {249, 7117}, {250, 1364}, {255, 270}, {284, 1790}, {332, 2206}, {394, 2189}, {577, 46103}, {603, 1098}, {652, 4556}, {763, 52370}, {1101, 7004}, {1172, 18604}, {1260, 7341}, {1265, 7342}, {1333, 1812}, {1408, 1792}, {1412, 2327}, {1439, 23609}, {1444, 2194}, {1459, 4636}, {1474, 6514}, {1509, 52425}, {1789, 17104}, {1798, 4267}, {1805, 1806}, {1808, 5009}, {1946, 52935}, {2326, 7125}, {3049, 55196}, {3737, 4575}, {4558, 7252}, {4560, 32661}, {4565, 23090}, {4612, 22383}, {5546, 7254}, {6061, 7053}, {6064, 22096}, {7058, 52411}, {7305, 20753}, {9247, 52379}, {14575, 18021}, {17880, 23995}, {23224, 52914}, {23357, 26932}, {30606, 32659}, {35196, 44709}, {52380, 52407}
X(56285) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 283}, {37, 1812}, {136, 3737}, {244, 23189}, {523, 7004}, {1214, 1444}, {1249, 2185}, {2171, 23114}, {3162, 2150}, {4075, 78}, {6523, 270}, {7952, 1098}, {15267, 603}, {18314, 17880}, {21233, 22400}, {23050, 6061}, {36103, 60}, {39053, 52935}, {39060, 4610}, {40586, 2193}, {40590, 1790}, {40599, 2327}, {40603, 332}, {40607, 212}, {40611, 1437}, {40837, 757}, {47345, 81}, {51574, 6514}, {55064, 23090}, {55065, 521}
X(56285) = X(i)-Ceva conjugate of X(j) for these {i, j}: {40149, 8736}, {41013, 12}
X(56285) = X(i)-cross conjugate of X(j) for these {i, j}: {2171, 6358}, {2970, 24006}
X(56285) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(24006)}}, {{A, B, C, X(10), X(12)}}, {{A, B, C, X(33), X(756)}}, {{A, B, C, X(91), X(6757)}}, {{A, B, C, X(201), X(2171)}}, {{A, B, C, X(1825), X(7012)}}, {{A, B, C, X(2800), X(6370)}}, {{A, B, C, X(8818), X(54972)}}
X(56285) = barycentric product X(i)*X(j) for these (i, j): {4, 6358}, {10, 40149}, {12, 92}, {19, 34388}, {42, 52575}, {57, 7141}, {75, 8736}, {108, 52623}, {158, 26942}, {181, 1969}, {201, 2052}, {225, 321}, {226, 41013}, {273, 594}, {318, 6354}, {331, 756}, {338, 7012}, {1089, 278}, {1091, 46103}, {1109, 46102}, {1118, 52369}, {1254, 7017}, {1426, 30713}, {1441, 1826}, {1446, 53008}, {1824, 349}, {1847, 6057}, {1880, 313}, {2171, 264}, {2970, 4564}, {4036, 653}, {4064, 54240}, {4086, 52607}, {6046, 7101}, {6521, 7066}, {7140, 85}, {14618, 4551}, {18026, 4024}, {21859, 46107}, {23994, 7115}, {24006, 4552}, {27808, 55208}, {28654, 34}, {37790, 4013}, {44426, 4605}, {46404, 4705}, {52938, 55232}, {55197, 811}
X(56285) = barycentric quotient X(i)/X(j) for these (i, j): {4, 2185}, {10, 1812}, {12, 63}, {19, 60}, {25, 2150}, {33, 7054}, {34, 593}, {37, 283}, {42, 2193}, {65, 1790}, {72, 6514}, {73, 18604}, {92, 261}, {108, 4556}, {115, 7004}, {158, 46103}, {181, 48}, {201, 394}, {210, 2327}, {225, 81}, {226, 1444}, {264, 52379}, {273, 1509}, {278, 757}, {281, 1098}, {318, 7058}, {321, 332}, {331, 873}, {338, 17880}, {393, 270}, {429, 17185}, {594, 78}, {608, 849}, {653, 52935}, {661, 23189}, {756, 219}, {762, 2318}, {811, 55196}, {872, 52425}, {1089, 345}, {1091, 26942}, {1096, 2189}, {1109, 26932}, {1254, 222}, {1365, 3942}, {1400, 1437}, {1425, 7125}, {1426, 1412}, {1435, 7341}, {1441, 17206}, {1500, 212}, {1783, 4636}, {1824, 284}, {1825, 40214}, {1826, 21}, {1847, 552}, {1857, 2326}, {1865, 54356}, {1877, 30576}, {1880, 58}, {1897, 4612}, {1969, 18021}, {2149, 47390}, {2171, 3}, {2197, 255}, {2321, 1792}, {2332, 23609}, {2333, 2194}, {2501, 3737}, {2643, 7117}, {2970, 4858}, {3690, 2289}, {3695, 3719}, {3708, 1364}, {3949, 1259}, {4017, 7254}, {4024, 521}, {4036, 6332}, {4041, 23090}, {4077, 15419}, {4079, 1946}, {4086, 15411}, {4092, 34591}, {4103, 4571}, {4551, 4558}, {4552, 4592}, {4559, 4575}, {4605, 6516}, {4705, 652}, {6046, 7177}, {6057, 3692}, {6058, 3949}, {6354, 77}, {6356, 7183}, {6358, 69}, {6535, 3694}, {7012, 249}, {7064, 1802}, {7066, 6507}, {7079, 6061}, {7115, 1101}, {7140, 9}, {7141, 312}, {7143, 7099}, {7147, 7053}, {7235, 20769}, {7314, 37755}, {8736, 1}, {8754, 2170}, {8818, 1789}, {14618, 18155}, {16732, 17219}, {18026, 4610}, {21043, 53560}, {21794, 52408}, {21853, 1800}, {21859, 1331}, {21871, 1819}, {24006, 4560}, {26942, 326}, {27808, 55207}, {28654, 3718}, {34388, 304}, {35307, 23181}, {37755, 1804}, {38462, 30606}, {40149, 86}, {40521, 4587}, {41013, 333}, {44113, 4282}, {46102, 24041}, {46404, 4623}, {52369, 1264}, {52567, 22097}, {52575, 310}, {52577, 5324}, {52607, 1414}, {52623, 35518}, {52938, 55231}, {53008, 2287}, {55197, 656}, {55206, 21789}, {55208, 3733}, {55230, 36054}, {55234, 23224}
X(56285) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {40149, 41013, 225}

X(56286) = KP2(X(1)) OF X(5) AND X(12)

Barycentrics    a*(a+b-c)*(a-b+c)*(a^7-a*b^2*c^2*(b+c)^2-2*a^5*(b^2+b*c+c^2)+(b-c)^2*(b+c)^3*(b^2+b*c+c^2)+a^3*(b^2+b*c+c^2)^2+a^4*(b^3+b^2*c+b*c^2+c^3)-a^2*(2*b^5+3*b^4*c+b^3*c^2+b^2*c^3+3*b*c^4+2*c^5)) : :

X(56286) lies on these lines: {1, 49}, {5, 2595}, {12, 14985}, {110, 2599}, {201, 1325}, {484, 37230}, {501, 16577}, {1726, 37523}, {1762, 7066}, {2070, 35194}, {2594, 21381}, {2957, 7173}, {4225, 21368}, {11101, 52391}

X(56287) = KP2(X(1)) OF X(7) AND X(8)

Barycentrics    a*(a+b-c)*(a-b+c)*(a^4+4*a*b^2*c+(b^2-c^2)^2-2*a^2*(b^2+c^2))*(a^4+4*a*b*c^2+(b^2-c^2)^2-2*a^2*(b^2+c^2)) : :

X(56287) lies on these lines: {7, 5552}, {8, 34413}, {40, 1804}, {46, 269}, {57, 53995}, {63, 55110}, {77, 3359}, {479, 55015}, {1014, 3193}, {1068, 1119}, {7040, 7330}, {13437, 52419}, {13459, 52420}

X(56287) = isogonal conjugate of X(30223)
X(56287) = trilinear pole of line {3669, 46389}
X(56287) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 30223}, {4, 19354}, {6, 53994}, {9, 3554}, {41, 54284}, {55, 3086}, {284, 24005}, {607, 26871}, {836, 8748}, {1436, 38015}, {1519, 2342}, {2194, 17869}, {13456, 38003}
X(56287) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 30223}, {9, 53994}, {223, 3086}, {478, 3554}, {1214, 17869}, {3160, 54284}, {36033, 19354}, {40590, 24005}
X(56287) = X(i)-cross conjugate of X(j) for these {i, j}: {6129, 651}
X(56287) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(46)}}, {{A, B, C, X(7), X(57)}}, {{A, B, C, X(8), X(40)}}, {{A, B, C, X(9), X(59)}}, {{A, B, C, X(19), X(1037)}}, {{A, B, C, X(21), X(51498)}}, {{A, B, C, X(63), X(1804)}}, {{A, B, C, X(75), X(77)}}, {{A, B, C, X(78), X(775)}}, {{A, B, C, X(88), X(1440)}}, {{A, B, C, X(103), X(39943)}}, {{A, B, C, X(282), X(8759)}}, {{A, B, C, X(291), X(1041)}}, {{A, B, C, X(342), X(7128)}}, {{A, B, C, X(347), X(40399)}}, {{A, B, C, X(484), X(5119)}}, {{A, B, C, X(921), X(7163)}}, {{A, B, C, X(972), X(6601)}}, {{A, B, C, X(1155), X(54408)}}, {{A, B, C, X(1156), X(53086)}}, {{A, B, C, X(1167), X(42464)}}, {{A, B, C, X(1259), X(47849)}}, {{A, B, C, X(1697), X(5128)}}, {{A, B, C, X(1937), X(8769)}}, {{A, B, C, X(2160), X(52013)}}, {{A, B, C, X(3336), X(3338)}}, {{A, B, C, X(3345), X(43740)}}, {{A, B, C, X(7012), X(56179)}}, {{A, B, C, X(8809), X(18815)}}, {{A, B, C, X(9372), X(39956)}}, {{A, B, C, X(55076), X(56139)}}
X(56287) = barycentric product X(i)*X(j) for these (i, j): {1, 34401}, {223, 34413}, {42019, 85}, {52385, 837}, {53995, 75}
X(56287) = barycentric quotient X(i)/X(j) for these (i, j): {1, 53994}, {6, 30223}, {7, 54284}, {40, 38015}, {48, 19354}, {56, 3554}, {57, 3086}, {65, 24005}, {77, 26871}, {226, 17869}, {837, 1896}, {1465, 1519}, {22341, 836}, {34401, 75}, {34413, 34404}, {37755, 26955}, {42019, 9}, {52419, 40650}, {53995, 1}

X(56288) = KP2(X(1)) OF X(8) AND X(10)

Barycentrics    a*(a^3-b^3-c^3+a^2*(b+c)-a*(b^2+b*c+c^2)) : :
X(56288) = -2*X[2646]+3*X[17549], -3*X[37298]+2*X[37737]

X(56288) lies on these lines: {1, 89}, {2, 46}, {3, 3417}, {4, 1748}, {5, 5057}, {7, 37550}, {8, 20}, {9, 5128}, {10, 191}, {12, 17768}, {21, 65}, {30, 5086}, {31, 986}, {35, 758}, {36, 3878}, {38, 5255}, {42, 1046}, {55, 3868}, {56, 3877}, {57, 3616}, {58, 4424}, {60, 2651}, {71, 1761}, {72, 74}, {78, 165}, {79, 3822}, {81, 3931}, {92, 6197}, {109, 283}, {140, 51409}, {142, 9782}, {144, 7080}, {145, 4305}, {149, 10916}, {171, 2292}, {190, 3701}, {200, 3951}, {221, 17080}, {224, 37105}, {226, 14450}, {227, 651}, {238, 24443}, {307, 27535}, {329, 3359}, {355, 48363}, {377, 3474}, {386, 49500}, {390, 10936}, {391, 54420}, {392, 5253}, {404, 960}, {405, 36279}, {411, 6001}, {442, 20292}, {452, 1708}, {474, 9352}, {498, 31053}, {516, 6734}, {517, 2975}, {518, 3871}, {519, 6763}, {535, 37710}, {548, 10609}, {551, 3337}, {595, 3670}, {644, 21872}, {649, 5592}, {662, 37294}, {672, 3496}, {748, 24174}, {813, 52085}, {894, 26115}, {896, 4642}, {908, 6684}, {912, 11491}, {920, 6872}, {942, 1621}, {944, 24467}, {946, 5180}, {956, 12702}, {958, 37567}, {962, 5709}, {970, 42448}, {976, 3550}, {982, 3915}, {993, 5903}, {997, 4188}, {999, 3890}, {1001, 5221}, {1005, 44547}, {1006, 34339}, {1042, 1758}, {1054, 27627}, {1098, 1325}, {1104, 54315}, {1125, 3336}, {1159, 17571}, {1191, 17595}, {1193, 17596}, {1203, 17012}, {1259, 5584}, {1319, 5330}, {1320, 11260}, {1334, 3509}, {1376, 3876}, {1385, 5303}, {1399, 54292}, {1400, 9791}, {1406, 1443}, {1441, 8822}, {1442, 1444}, {1445, 52653}, {1452, 4194}, {1453, 36277}, {1454, 3485}, {1468, 4650}, {1571, 17756}, {1697, 3241}, {1698, 4338}, {1706, 3929}, {1707, 54418}, {1709, 3146}, {1714, 33131}, {1727, 10572}, {1737, 5046}, {1738, 26998}, {1756, 26699}, {1757, 3214}, {1759, 3730}, {1760, 2550}, {1766, 24280}, {1768, 4297}, {1776, 1837}, {1780, 17521}, {1788, 2478}, {1817, 40660}, {1836, 2476}, {2077, 31806}, {2093, 19860}, {2094, 11037}, {2098, 11194}, {2099, 3897}, {2136, 20053}, {2185, 46441}, {2245, 5051}, {2287, 4047}, {2646, 17549}, {2650, 37573}, {2800, 4996}, {2802, 5288}, {2893, 20291}, {2949, 2950}, {3008, 10899}, {3052, 37549}, {3057, 54391}, {3085, 5905}, {3160, 7183}, {3178, 32949}, {3185, 16451}, {3244, 37563}, {3245, 5258}, {3256, 15556}, {3295, 3873}, {3303, 3889}, {3305, 19877}, {3306, 5550}, {3333, 38314}, {3338, 3622}, {3339, 4512}, {3434, 6361}, {3436, 5657}, {3486, 34744}, {3501, 5282}, {3556, 11337}, {3559, 40149}, {3562, 18607}, {3576, 11682}, {3584, 14526}, {3612, 17548}, {3617, 31295}, {3625, 5541}, {3634, 35595}, {3647, 3754}, {3649, 6690}, {3650, 17757}, {3652, 18480}, {3654, 37430}, {3671, 15932}, {3679, 4333}, {3681, 3927}, {3683, 3812}, {3685, 16574}, {3695, 33078}, {3698, 5302}, {3702, 14829}, {3721, 17735}, {3727, 33863}, {3743, 17019}, {3746, 3874}, {3753, 5260}, {3757, 50404}, {3814, 5445}, {3821, 27678}, {3831, 32930}, {3832, 54370}, {3833, 25542}, {3870, 54422}, {3872, 7991}, {3884, 4973}, {3885, 12513}, {3895, 6762}, {3896, 56018}, {3899, 4881}, {3904, 53300}, {3911, 41012}, {3914, 24883}, {3920, 5264}, {3924, 54354}, {3925, 18253}, {3935, 5904}, {3953, 40091}, {3958, 54316}, {3962, 56176}, {3980, 31339}, {3983, 15481}, {4018, 24929}, {4031, 51723}, {4066, 51285}, {4193, 24703}, {4197, 5880}, {4202, 33068}, {4252, 37614}, {4278, 18417}, {4292, 24987}, {4294, 12649}, {4301, 5536}, {4302, 49168}, {4304, 41575}, {4318, 37591}, {4385, 32933}, {4427, 7283}, {4450, 5015}, {4458, 42657}, {4641, 4646}, {4651, 46519}, {4660, 36568}, {4676, 5192}, {4744, 5426}, {4757, 5425}, {4847, 5493}, {4850, 16466}, {4855, 35242}, {4921, 50083}, {4930, 19704}, {4968, 32939}, {5010, 22836}, {5011, 16552}, {5122, 17614}, {5172, 45288}, {5174, 52414}, {5175, 5775}, {5176, 5690}, {5183, 5836}, {5204, 5289}, {5217, 12635}, {5223, 43178}, {5230, 24248}, {5231, 9589}, {5248, 5902}, {5259, 5883}, {5278, 5342}, {5284, 5439}, {5292, 33134}, {5440, 31663}, {5442, 6681}, {5506, 51073}, {5530, 41011}, {5603, 6892}, {5692, 25440}, {5693, 6796}, {5697, 8666}, {5711, 28606}, {5714, 10585}, {5770, 12116}, {5774, 50044}, {5784, 30295}, {5791, 33108}, {5794, 17579}, {5815, 37427}, {5884, 10902}, {5887, 6905}, {6051, 37633}, {6061, 10536}, {6260, 9809}, {6350, 8251}, {6735, 12527}, {6737, 12512}, {6836, 14647}, {6840, 12616}, {6845, 11680}, {6894, 12617}, {6909, 14110}, {6912, 7686}, {6937, 11681}, {6942, 45770}, {6960, 12608}, {6996, 24633}, {7082, 54361}, {7262, 24440}, {7288, 37789}, {7292, 24046}, {7384, 28940}, {7411, 9943}, {7483, 39542}, {7504, 17605}, {7580, 9961}, {7677, 37566}, {7701, 31673}, {8256, 34606}, {8258, 29631}, {8582, 51090}, {8583, 53056}, {8616, 28082}, {9678, 38235}, {9785, 11240}, {9802, 21627}, {9812, 12705}, {10032, 50821}, {10039, 20060}, {10164, 27385}, {10198, 31019}, {10248, 11372}, {10268, 10884}, {10306, 37287}, {10381, 22080}, {10395, 45043}, {10449, 32929}, {10528, 20078}, {10529, 30305}, {10624, 26015}, {11009, 51111}, {11015, 15338}, {11101, 51290}, {11239, 28610}, {11246, 25466}, {11263, 11552}, {11344, 37541}, {11495, 41228}, {11500, 12528}, {11507, 20846}, {11523, 35445}, {11570, 14798}, {11571, 39778}, {12005, 34486}, {12436, 24564}, {12572, 24982}, {12672, 37623}, {12680, 13243}, {12688, 36002}, {13145, 22937}, {13407, 17483}, {13465, 18524}, {13587, 31165}, {14868, 35997}, {14974, 26242}, {15228, 47033}, {15254, 17536}, {15298, 20059}, {15507, 28238}, {15678, 16141}, {15777, 26888}, {15803, 19861}, {15829, 35262}, {16062, 32950}, {16138, 33697}, {16454, 31359}, {16678, 23844}, {16823, 20367}, {16865, 54318}, {17021, 27785}, {17100, 46684}, {17484, 21077}, {17531, 25917}, {17566, 25681}, {17577, 28534}, {17594, 19767}, {17606, 37375}, {17613, 31793}, {17647, 37256}, {17739, 56024}, {17748, 32843}, {17781, 21075}, {18193, 28011}, {18228, 26062}, {18249, 26060}, {18357, 19919}, {18360, 35193}, {18398, 29817}, {18419, 34489}, {18421, 51576}, {20057, 31393}, {20067, 45287}, {20070, 41338}, {20290, 27558}, {20653, 33082}, {20992, 38286}, {21078, 37508}, {21384, 41319}, {21677, 26750}, {21853, 38871}, {21935, 24851}, {22060, 35614}, {22344, 37620}, {23537, 33102}, {23661, 54107}, {24159, 29681}, {24231, 28027}, {24390, 28174}, {24468, 28194}, {24475, 37621}, {24850, 54331}, {25082, 42316}, {25522, 31224}, {25581, 33949}, {26027, 28950}, {26030, 27064}, {26127, 40998}, {26131, 50307}, {26364, 27131}, {26562, 33821}, {26689, 33828}, {26842, 51706}, {26934, 49687}, {27059, 50314}, {27129, 28734}, {27383, 37560}, {27509, 45040}, {28916, 37416}, {29958, 51377}, {30852, 31423}, {31159, 51113}, {31803, 44425}, {31938, 41853}, {32912, 50581}, {32917, 49598}, {33100, 54355}, {33862, 37733}, {34610, 36977}, {35238, 38901}, {36643, 40131}, {37298, 37737}, {37534, 54445}, {41013, 52344}, {48924, 49716}, {50194, 51683}, {54289, 54295}, {54320, 54400}

X(56288) = midpoint of X(i) and X(j) for these {i,j}: {12702, 26321}, {6763, 11010}
X(56288) = reflection of X(i) in X(j) for these {i,j}: {1, 5267}, {11009, 51111}, {11015, 15338}, {20060, 10039}, {2975, 3916}, {21740, 3}, {3585, 10}, {3871, 37568}, {31159, 51113}, {34772, 35}, {37733, 33862}, {4861, 2975}, {52367, 6734}
X(56288) = anticomplement of X(12047)
X(56288) = perspector of circumconic {{A, B, C, X(4604), X(44327)}}
X(56288) = X(i)-Dao conjugate of X(j) for these {i, j}: {12047, 12047}
X(56288) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {52185, 8}
X(56288) = intersection, other than A, B, C, of circumconics {{A, B, C, X(74), X(84)}}, {{A, B, C, X(89), X(189)}}, {{A, B, C, X(280), X(2320)}}, {{A, B, C, X(502), X(17097)}}, {{A, B, C, X(1442), X(41013)}}, {{A, B, C, X(1444), X(52344)}}, {{A, B, C, X(4420), X(5379)}}
X(56288) = barycentric product X(i)*X(j) for these (i, j): {1, 33066}, {312, 34043}
X(56288) = barycentric quotient X(i)/X(j) for these (i, j): {33066, 75}, {34043, 57}
X(56288) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 14988, 21740}, {3, 3869, 4511}, {10, 1770, 2475}, {10, 191, 3219}, {31, 986, 5262}, {35, 758, 34772}, {40, 1158, 20}, {40, 1782, 3101}, {40, 54290, 63}, {46, 12514, 2}, {57, 5250, 3616}, {58, 4424, 17016}, {65, 4640, 21}, {71, 1761, 5279}, {72, 3579, 100}, {100, 11684, 72}, {191, 2475, 18259}, {191, 484, 10}, {392, 37582, 5253}, {516, 6734, 52367}, {517, 2975, 4861}, {517, 3916, 2975}, {518, 37568, 3871}, {595, 3670, 7191}, {672, 3496, 33950}, {896, 4642, 5247}, {908, 6684, 27529}, {956, 12702, 14923}, {960, 1155, 404}, {962, 5744, 10527}, {1125, 3336, 27003}, {1468, 37598, 17015}, {1571, 54406, 17756}, {1788, 5698, 2478}, {1836, 26066, 2476}, {2093, 31424, 19860}, {3306, 31435, 5550}, {3339, 4512, 54392}, {3579, 11684, 4420}, {3622, 23958, 3338}, {3647, 3754, 5251}, {3683, 3812, 5047}, {3743, 37559, 17019}, {3746, 3874, 3957}, {3746, 4880, 3874}, {3753, 31445, 5260}, {3884, 4973, 5563}, {3895, 6762, 20050}, {3899, 7280, 30144}, {3927, 5687, 3681}, {3929, 41348, 1706}, {3983, 15481, 32635}, {4018, 24929, 34195}, {4650, 37598, 1468}, {4757, 35016, 5425}, {5177, 18231, 9780}, {5692, 37572, 25440}, {5697, 8666, 38460}, {5884, 10902, 18444}, {7280, 30144, 4881}, {12515, 16139, 3579}, {15338, 44669, 11015}, {17594, 54421, 19767}, {17784, 54398, 8}, {24703, 24914, 4193}, {41229, 54286, 3617}

X(56289) = X(12)-CEVA CONJUGATE OF X(1)

Barycentrics    a*(a^6+a^5*(b+c)-a^4*(b^2+c^2)-(b^2-c^2)^2*(b^2+b*c+c^2)+a^2*(b^2+b*c+c^2)^2-a*(b^5-4*b^3*c^2-4*b^2*c^3+c^5)) : :

X(56289) lies on these lines: {1, 60}, {5, 2607}, {9, 6537}, {10, 191}, {12, 14985}, {35, 228}, {57, 40655}, {65, 1046}, {655, 1091}, {1048, 4551}, {1400, 1781}, {1761, 5341}, {2938, 3579}, {2940, 13589}, {3336, 24880}, {3337, 50757}, {3460, 7951}, {3496, 20607}, {3841, 24342}, {4647, 34997}, {6757, 39137}, {6763, 54335}, {7701, 12368}, {10944, 36935}, {11010, 36171}, {14882, 38903}, {20369, 25446}, {24443, 39394}, {37710, 47270}, {50198, 52706}

X(56289) = reflection of X(i) in X(j) for these {i,j}: {1, 37816}
X(56289) = X(i)-Dao conjugate of X(j) for these {i, j}: {2185, 261}
X(56289) = X(i)-Ceva conjugate of X(j) for these {i, j}: {12, 1}, {14985, 50346}, {56286, 3460}
X(56289) = intersection, other than A, B, C, of circumconics {{A, B, C, X(267), X(3437)}}, {{A, B, C, X(502), X(759)}}, {{A, B, C, X(6757), X(21381)}}, {{A, B, C, X(17104), X(39137)}}
X(56289) = barycentric product X(i)*X(j) for these (i, j): {10, 47059}
X(56289) = barycentric quotient X(i)/X(j) for these (i, j): {47059, 86}
X(56289) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {191, 267, 484}

X(56290) = KP2(X(2)) OF X(3) AND X(5)

Barycentrics    a^8-b^2*c^2*(b^2-c^2)^2-2*a^6*(b^2+c^2)+a^4*(b^4+3*b^2*c^2+c^4) : :

X(56290) lies on these lines: {2, 6}, {3, 3164}, {5, 17035}, {20, 33971}, {30, 56022}, {52, 9792}, {53, 40853}, {95, 216}, {97, 324}, {98, 6467}, {110, 44088}, {112, 35928}, {140, 56021}, {147, 46442}, {148, 52069}, {194, 7503}, {264, 401}, {297, 41008}, {311, 4558}, {317, 52247}, {384, 26166}, {411, 18666}, {458, 15905}, {549, 39358}, {631, 56013}, {1235, 28723}, {1350, 20792}, {1879, 53507}, {1941, 26897}, {1968, 21447}, {1975, 10607}, {2322, 21940}, {2896, 26154}, {2905, 37354}, {3148, 3186}, {3284, 14767}, {3933, 26205}, {5063, 41760}, {5065, 40814}, {5158, 52712}, {5562, 9290}, {5889, 46866}, {5999, 12220}, {6389, 44134}, {6815, 20065}, {6905, 56014}, {7395, 7754}, {7399, 7762}, {7488, 19189}, {7509, 56015}, {7549, 56019}, {7550, 56016}, {7567, 56020}, {7767, 26155}, {7783, 14118}, {7785, 13160}, {7793, 17928}, {7839, 26216}, {7928, 26170}, {8743, 37186}, {9512, 20775}, {9863, 41757}, {10979, 47383}, {12167, 13860}, {14570, 44180}, {14712, 38323}, {15576, 15717}, {16081, 41890}, {16310, 53477}, {17364, 53821}, {19210, 37127}, {20477, 36748}, {22052, 46724}, {23115, 37337}, {23635, 37334}, {26179, 26221}, {26226, 31276}, {26873, 55021}, {26945, 55020}, {31859, 54994}, {32000, 37188}, {32002, 36412}, {32467, 45857}, {34664, 47286}, {35360, 54375}, {35921, 41676}, {35937, 42459}, {37457, 38294}, {37893, 39931}, {39352, 41005}, {41891, 42300}, {46760, 46832}

X(56290) = reflection of X(i) in X(j) for these {i,j}: {32002, 36412}, {46724, 22052}
X(56290) = isotomic conjugate of X(9290)
X(56290) = anticomplement of X(45198)
X(56290) = perspector of circumconic {{A, B, C, X(99), X(41208)}}
X(56290) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 9251}, {31, 9290}, {661, 1303}
X(56290) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 9290}, {9, 9251}, {36830, 1303}, {45198, 45198}
X(56290) = X(i)-Ceva conjugate of X(j) for these {i, j}: {5562, 8613}, {9291, 436}, {14941, 401}, {40448, 2}
X(56290) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {40402, 21270}, {40448, 6327}, {42333, 21275}
X(56290) = X(i)-cross conjugate of X(j) for these {i, j}: {1970, 436}
X(56290) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(43710)}}, {{A, B, C, X(6), X(1970)}}, {{A, B, C, X(69), X(54114)}}, {{A, B, C, X(81), X(1954)}}, {{A, B, C, X(343), X(1972)}}, {{A, B, C, X(394), X(40800)}}, {{A, B, C, X(3289), X(41890)}}, {{A, B, C, X(8795), X(9290)}}, {{A, B, C, X(13567), X(16081)}}
X(56290) = barycentric product X(i)*X(j) for these (i, j): {3, 9291}, {63, 9252}, {110, 42331}, {436, 69}, {1954, 75}, {1970, 76}, {21449, 343}, {27359, 34386}
X(56290) = barycentric quotient X(i)/X(j) for these (i, j): {1, 9251}, {2, 9290}, {110, 1303}, {436, 4}, {1954, 1}, {1970, 6}, {9252, 92}, {9291, 264}, {21449, 275}, {27359, 53}, {42331, 850}
X(56290) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 36413, 51171}, {2, 52058, 3329}, {3, 9308, 3164}, {95, 648, 216}, {97, 324, 8613}, {264, 577, 401}, {3164, 43980, 3}, {3180, 3181, 41628}, {3284, 14767, 36794}, {20477, 36748, 51350}, {40896, 51350, 20477}

X(56291) = ANTICOMPLEMENT OF X(261)

Barycentrics    a^5-b^5-b^4*c+b^3*c^2+b^2*c^3-b*c^4-c^5+a^4*(b+c)+a^2*(b+c)^3+a^3*(b^2+4*b*c+c^2)-a*(b^4-3*b^2*c^2+c^4) : :
X(56291) = -3*X[2]+2*X[261]

X(56291) lies on these lines: {1, 20558}, {2, 261}, {6, 26081}, {10, 894}, {75, 44370}, {86, 20337}, {148, 192}, {193, 5177}, {226, 1943}, {1029, 3995}, {1655, 18666}, {2895, 31025}, {3770, 17789}, {5207, 28369}, {5949, 19623}, {6646, 20349}, {7384, 17300}, {7785, 17379}, {17103, 27688}, {17234, 26147}, {17363, 20536}, {21287, 26110}, {24267, 25650}, {25978, 49745}, {26117, 50290}

X(56291) = anticomplement of X(261)
X(56291) = X(i)-Ceva conjugate of X(j) for these {i, j}: {12, 2}
X(56291) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {1, 35614}, {6, 21273}, {9, 54109}, {12, 6327}, {31, 2975}, {32, 18662}, {37, 20245}, {41, 54107}, {42, 3869}, {56, 17140}, {57, 17143}, {59, 21295}, {65, 17135}, {73, 20243}, {85, 54112}, {109, 17166}, {181, 8}, {201, 1370}, {213, 63}, {225, 20242}, {226, 17137}, {594, 21286}, {604, 4360}, {651, 17159}, {756, 3436}, {872, 144}, {1020, 4374}, {1042, 3873}, {1214, 18659}, {1254, 3434}, {1333, 18654}, {1334, 18750}, {1400, 75}, {1402, 1}, {1409, 17134}, {1415, 17161}, {1423, 34086}, {1425, 52365}, {1427, 20244}, {1441, 17138}, {1500, 329}, {1880, 17220}, {1903, 20246}, {2149, 99}, {2171, 69}, {2197, 4329}, {2333, 92}, {2357, 20220}, {3690, 52366}, {4079, 37781}, {4551, 512}, {4552, 17217}, {4559, 7192}, {4564, 4576}, {4705, 33650}, {6354, 21285}, {6358, 315}, {6378, 20348}, {7012, 53350}, {7109, 3177}, {7143, 36845}, {7147, 6604}, {7148, 20557}, {7235, 20554}, {8736, 21270}, {20616, 40007}, {21859, 20295}, {34388, 21275}, {50487, 39351}, {51641, 17154}, {55197, 21294}, {55230, 34188}, {56285, 11442}
X(56291) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1654, 6625, 894}, {14534, 46828, 2}, {17778, 54119, 1999}

X(56292) = KP2(X(3)) OF X(4) AND X(5)

Barycentrics    a^2*(a^8+b^8-b^6*c^2-b^2*c^6+c^8-4*a^6*(b^2+c^2)+a^4*(6*b^4+5*b^2*c^2+6*c^4)-4*a^2*(b^6+c^6)) : :
X(56292) = -3*X[3520]+2*X[11440]

X(56292) lies on these lines: {2, 1199}, {3, 323}, {4, 155}, {5, 195}, {6, 3090}, {20, 16266}, {23, 156}, {24, 3167}, {26, 9544}, {30, 43605}, {49, 1154}, {51, 43598}, {52, 110}, {54, 5562}, {68, 7577}, {69, 7558}, {81, 6852}, {93, 56272}, {140, 15087}, {143, 13595}, {182, 7999}, {184, 7512}, {185, 43574}, {186, 1147}, {193, 2904}, {235, 19504}, {343, 12325}, {376, 1181}, {378, 12164}, {389, 3292}, {394, 631}, {399, 3627}, {511, 1614}, {524, 7552}, {546, 15052}, {549, 43845}, {567, 1493}, {568, 44802}, {569, 7550}, {576, 9781}, {578, 11459}, {632, 15037}, {648, 13450}, {1006, 22136}, {1092, 5890}, {1173, 5097}, {1204, 37948}, {1216, 5012}, {1351, 9925}, {1498, 33703}, {1568, 10112}, {1594, 3564}, {1656, 34545}, {1658, 9703}, {1986, 45172}, {1995, 37493}, {2070, 12316}, {2071, 34783}, {2072, 32358}, {2930, 12061}, {3060, 10539}, {3091, 11004}, {3146, 12112}, {3153, 44076}, {3410, 5576}, {3448, 13371}, {3470, 44769}, {3520, 11440}, {3525, 15066}, {3529, 11456}, {3533, 17811}, {3545, 17814}, {3549, 45794}, {3567, 9306}, {3574, 41171}, {3580, 9820}, {3581, 32171}, {3628, 15018}, {3832, 39522}, {3855, 10982}, {4994, 39530}, {5067, 5422}, {5133, 31831}, {5446, 52294}, {5448, 50435}, {5449, 41724}, {5504, 7722}, {5609, 51882}, {5651, 15024}, {5654, 16868}, {5663, 12086}, {5707, 6874}, {5818, 16473}, {5876, 7527}, {5891, 13434}, {5907, 15033}, {6090, 11432}, {6101, 6636}, {6102, 22115}, {6143, 12359}, {6238, 9637}, {6240, 12383}, {6241, 7464}, {6247, 12317}, {6353, 35603}, {6403, 52016}, {6515, 7505}, {6759, 37925}, {6776, 18948}, {6800, 37486}, {6832, 37685}, {6920, 36750}, {6946, 37509}, {7496, 32142}, {7502, 9704}, {7509, 11402}, {7525, 54048}, {7537, 40571}, {7540, 9143}, {7543, 56000}, {7547, 12429}, {7551, 56001}, {7553, 46818}, {7556, 9707}, {7574, 45731}, {7576, 31802}, {7691, 9706}, {7998, 13336}, {8537, 8681}, {8538, 15531}, {8883, 52032}, {8889, 17836}, {9705, 10282}, {9927, 54001}, {9936, 11442}, {10116, 51392}, {10263, 10540}, {10323, 19347}, {10605, 41427}, {10625, 23061}, {10984, 44832}, {11002, 13861}, {11064, 26879}, {11264, 51391}, {11381, 14094}, {11411, 37119}, {11424, 15058}, {11430, 45187}, {11464, 46730}, {11585, 43808}, {11660, 21284}, {11793, 13366}, {12038, 17506}, {12087, 13391}, {12111, 12364}, {12118, 34797}, {12121, 34798}, {12162, 13596}, {12163, 35473}, {12225, 12254}, {12227, 15035}, {12902, 18567}, {13340, 16661}, {13353, 15067}, {13409, 14152}, {13419, 24981}, {13431, 52675}, {13482, 43613}, {13491, 37477}, {14118, 18436}, {14157, 45186}, {14449, 18378}, {14611, 36160}, {14651, 39810}, {14831, 43572}, {14912, 20806}, {15026, 16042}, {15319, 50433}, {15331, 32608}, {15606, 22352}, {15704, 37496}, {15800, 23236}, {17538, 37483}, {17824, 34782}, {18533, 34966}, {18569, 34799}, {18583, 34939}, {18859, 45957}, {18912, 22151}, {18916, 37669}, {19150, 43150}, {19161, 22828}, {21844, 47391}, {22128, 26877}, {22139, 37120}, {22330, 32127}, {23039, 32046}, {26863, 46261}, {26869, 31282}, {26882, 37939}, {31074, 32140}, {31724, 32423}, {31804, 43590}, {31810, 34397}, {32609, 40640}, {34224, 46450}, {34864, 55039}, {35265, 37440}, {35471, 44752}, {37452, 43588}, {37489, 44879}, {37494, 38435}, {37943, 41587}, {38683, 47064}, {40111, 45735}, {41202, 41481}, {41758, 41759}, {43595, 43818}, {43614, 53863}

X(56292) = reflection of X(i) in X(j) for these {i,j}: {1614, 43844}, {12086, 37495}, {12088, 1614}, {3520, 34148}, {7488, 49}
X(56292) = X(i)-Ceva conjugate of X(j) for these {i, j}: {14860, 3}
X(56292) = intersection, other than A, B, C, of circumconics {{A, B, C, X(254), X(2383)}}, {{A, B, C, X(323), X(15319)}}
X(56292) = barycentric product X(i)*X(j) for these (i, j): {305, 41759}, {41758, 69}
X(56292) = barycentric quotient X(i)/X(j) for these (i, j): {41758, 4}, {41759, 25}
X(56292) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12161, 1199}, {5, 195, 1994}, {49, 1154, 7488}, {52, 41597, 110}, {54, 5562, 35921}, {110, 15801, 52}, {143, 18350, 13595}, {155, 36747, 11441}, {156, 6243, 23}, {184, 11412, 7512}, {195, 50461, 5}, {394, 7592, 631}, {511, 1614, 12088}, {511, 43844, 1614}, {578, 11459, 35500}, {1147, 5889, 186}, {1493, 11591, 567}, {1993, 11441, 36747}, {3060, 10539, 34484}, {3091, 11004, 36749}, {3146, 32139, 12112}, {3167, 12160, 24}, {3580, 9820, 14940}, {5562, 34986, 54}, {5663, 37495, 12086}, {5876, 37472, 7527}, {6102, 22115, 22467}, {6241, 13346, 7464}, {7691, 9706, 18475}, {7999, 11423, 182}, {9707, 17834, 7556}, {11411, 37645, 37119}, {11422, 11444, 569}, {11441, 36747, 4}, {11456, 37498, 3529}, {11585, 45968, 43808}, {11793, 13366, 43651}, {12111, 13352, 14865}, {13352, 15083, 12111}, {13754, 34148, 3520}, {15066, 36752, 3525}, {15067, 32136, 13353}, {15068, 36749, 3091}, {15801, 41597, 3518}, {16266, 18445, 20}, {23039, 32046, 37126}, {23061, 52525, 10625}, {32142, 37471, 7496}, {43595, 52069, 43818}

X(56293) = X(8)-CEVA CONJUGATE OF X(3)

Barycentrics    a^2*(a^2-b^2-c^2)*(a^6+2*a^3*b*c*(b+c)-2*a*b*(b-c)^2*c*(b+c)+a^4*(-3*b^2+2*b*c-3*c^2)-(b^2-c^2)^2*(b^2+c^2)+a^2*(b-c)^2*(3*b^2+4*b*c+3*c^2)) : :

X(56293) lies on these lines: {1, 90}, {3, 1364}, {6, 1210}, {8, 15501}, {33, 41560}, {55, 47371}, {68, 10523}, {72, 15524}, {78, 271}, {221, 2800}, {222, 1181}, {255, 39167}, {323, 20013}, {519, 22130}, {521, 5687}, {613, 34381}, {651, 7952}, {1071, 19354}, {1147, 8071}, {1158, 34052}, {1406, 1735}, {1498, 5930}, {1785, 8757}, {1993, 3562}, {2956, 34488}, {3075, 36754}, {6193, 10629}, {6238, 11508}, {6700, 17811}, {7352, 22766}, {8068, 14852}, {8069, 13754}, {10320, 12359}, {10321, 11411}, {12528, 15500}, {14793, 47391}, {15068, 15252}, {17814, 34048}, {18445, 23070}, {22117, 22136}, {22132, 22133}, {37194, 45046}, {40518, 44040}

X(56293) = midpoint of X(i) and X(j) for these {i,j}: {1069, 3157}
X(56293) = X(i)-isoconjugate-of-X(j) for these {i, j}: {4, 42464}, {19, 54451}
X(56293) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 54451}, {222, 7}, {36033, 42464}
X(56293) = X(i)-Ceva conjugate of X(j) for these {i, j}: {8, 3}, {15501, 46974}
X(56293) = intersection, other than A, B, C, of circumconics {{A, B, C, X(90), X(271)}}, {{A, B, C, X(36059), X(42019)}}
X(56293) = barycentric product X(i)*X(j) for these (i, j): {219, 31600}, {1158, 63}, {10692, 914}, {34052, 78}
X(56293) = barycentric quotient X(i)/X(j) for these (i, j): {3, 54451}, {48, 42464}, {1158, 92}, {10692, 37203}, {31600, 331}, {34052, 273}
X(56293) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {155, 3157, 3173}, {1069, 3157, 912}, {1433, 7078, 46974}, {7335, 40944, 3}

X(56294) = X(9)-CEVA CONJUGATE OF X(3)

Barycentrics    a^2*(a^2-b^2-c^2)*(a^5-a^4*(b+c)+2*a^2*(b-c)^2*(b+c)-(b-c)^2*(b+c)^3+a*(b-c)^2*(b^2+c^2)-2*a^3*(b^2-3*b*c+c^2)) : :

X(56294) lies on circumconic {{A, B, C, X(90), X(1433)}} and on these lines: {1, 90}, {3, 1433}, {6, 20310}, {55, 36059}, {219, 22117}, {222, 7004}, {521, 1376}, {971, 2192}, {1060, 15524}, {1200, 2280}, {1413, 34862}, {1422, 3358}, {1709, 34492}, {1993, 37782}, {3295, 47371}, {3938, 22130}, {3940, 7078}, {5452, 36054}, {7046, 13138}, {7952, 8757}, {10629, 18970}, {12915, 34381}, {15252, 34048}, {20793, 22139}

X(56294) = X(i)-Dao conjugate of X(j) for these {i, j}: {77, 85}
X(56294) = X(i)-Ceva conjugate of X(j) for these {i, j}: {9, 3}
X(56294) = barycentric product X(i)*X(j) for these (i, j): {3, 5942}, {1709, 63}, {34492, 78}
X(56294) = barycentric quotient X(i)/X(j) for these (i, j): {1709, 92}, {5942, 264}, {34492, 273}
X(56294) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 56293, 3157}, {7125, 40945, 3}

X(56295) = X(10)-CEVA CONJUGATE OF X(3)

Barycentrics    a^2*(a^2-b^2-c^2)*(a^6+a^5*(b+c)-a*(b-c)^2*(b+c)^3-a^4*(b^2-b*c+c^2)-(b^2-c^2)^2*(b^2+b*c+c^2)+a^2*(b^4+c^4)) : :

X(56295) lies on these lines: {5, 6}, {31, 6238}, {58, 13754}, {72, 23120}, {386, 1147}, {387, 6193}, {394, 41014}, {539, 3017}, {1069, 16466}, {1468, 7352}, {1834, 44665}, {1993, 11109}, {2594, 36059}, {2650, 3157}, {3192, 10539}, {3940, 7078}, {4055, 22139}, {4252, 12163}, {4255, 47391}, {4256, 12038}, {4257, 7689}, {5230, 10055}, {5449, 45939}, {7141, 44765}, {9820, 37662}, {10071, 11269}, {10573, 56293}, {11411, 37642}, {12118, 48837}, {12359, 37646}, {18755, 32661}, {22123, 22133}, {22145, 23070}, {37698, 47371}

X(56295) = X(i)-Dao conjugate of X(j) for these {i, j}: {1790, 86}
X(56295) = X(i)-Ceva conjugate of X(j) for these {i, j}: {10, 3}
X(56295) = barycentric product X(i)*X(j) for these (i, j): {1710, 63}
X(56295) = barycentric quotient X(i)/X(j) for these (i, j): {1710, 92}

X(56296) = KP2(X(4)) OF X(2) AND X(3)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^8+2*b^2*c^2*(b^2-c^2)^2-3*a^6*(b^2+c^2)-a^2*(b^2-c^2)^2*(b^2+c^2)+3*a^4*(b^4+c^4)) : :

X(56296) lies on these lines: {2, 253}, {3, 1075}, {4, 3527}, {6, 275}, {22, 35360}, {24, 16035}, {25, 3168}, {51, 33971}, {92, 37543}, {107, 154}, {112, 35941}, {145, 3176}, {184, 37070}, {193, 6820}, {196, 21454}, {264, 10601}, {268, 7361}, {297, 6515}, {324, 458}, {343, 17907}, {381, 6761}, {389, 41365}, {393, 11433}, {394, 648}, {401, 3172}, {427, 41371}, {436, 11402}, {450, 3167}, {467, 37644}, {470, 42988}, {471, 42989}, {472, 36303}, {473, 36302}, {653, 6360}, {999, 1148}, {1033, 3164}, {1093, 1181}, {1260, 1897}, {1370, 44704}, {1498, 14249}, {1503, 52448}, {1559, 5656}, {1585, 7583}, {1586, 7584}, {1629, 17810}, {1656, 3462}, {1853, 15274}, {1896, 5706}, {1899, 6530}, {1990, 11547}, {1993, 46106}, {1994, 15262}, {2207, 40814}, {3060, 37200}, {3183, 3522}, {3295, 7049}, {3523, 41425}, {3534, 5667}, {5059, 15005}, {5523, 14715}, {6000, 41372}, {6524, 6776}, {6525, 11206}, {6529, 41376}, {6617, 46717}, {6759, 14363}, {6819, 43981}, {7592, 13450}, {8613, 15905}, {8778, 51350}, {8888, 15022}, {10002, 32064}, {11064, 46927}, {11331, 37636}, {11427, 40138}, {11456, 52661}, {14165, 26958}, {15004, 42400}, {17811, 52147}, {17821, 38808}, {19221, 53415}, {20477, 51936}, {26869, 52249}, {27377, 37192}, {34032, 54240}, {34545, 52253}, {34854, 39646}, {36751, 46760}, {36794, 41244}, {37067, 39575}, {37505, 45062}, {41370, 52281}, {41678, 43988}, {52283, 56015}

X(56296) = isogonal conjugate of X(18890)
X(56296) = polar conjugate of X(15318)
X(56296) = perspector of circumconic {{A, B, C, X(52779), X(53639)}}
X(56296) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 18890}, {48, 15318}, {63, 32319}, {810, 30441}, {1953, 14371}
X(56296) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 18890}, {53, 5}, {1249, 15318}, {3162, 32319}, {39062, 30441}
X(56296) = X(i)-Ceva conjugate of X(j) for these {i, j}: {95, 4}
X(56296) = X(i)-cross conjugate of X(j) for these {i, j}: {6759, 20477}
X(56296) = intersection, other than A, B, C, of circumconics {{A, B, C, X(253), X(8795)}}, {{A, B, C, X(275), X(1073)}}, {{A, B, C, X(394), X(34538)}}, {{A, B, C, X(2052), X(13157)}}
X(56296) = barycentric product X(i)*X(j) for these (i, j): {264, 6759}, {14363, 95}, {20477, 4}, {30442, 6331}, {51936, 76}, {52585, 648}
X(56296) = barycentric quotient X(i)/X(j) for these (i, j): {4, 15318}, {6, 18890}, {25, 32319}, {54, 14371}, {648, 30441}, {6759, 3}, {14363, 5}, {20477, 69}, {30442, 647}, {51936, 6}, {52585, 525}
X(56296) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 14361, 51358}, {2, 17037, 20213}, {2, 20217, 253}, {324, 5422, 458}, {648, 15466, 394}, {1249, 14361, 2}, {1990, 13567, 11547}, {3168, 41204, 25}, {5656, 36876, 1559}, {6525, 15258, 11206}, {11245, 14569, 4}

X(56297) = KP2(X(4)) OF X(2) AND X(5)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(2*a^8-5*a^6*(b^2+c^2)+a^2*(b^2-c^2)^2*(b^2+c^2)-(b^2-c^2)^2*(b^4+c^4)+a^4*(3*b^4+4*b^2*c^2+3*c^4)) : :

X(56297) lies on these lines: {2, 253}, {4, 11402}, {5, 3462}, {6, 11547}, {22, 44704}, {25, 41371}, {51, 42873}, {53, 275}, {97, 112}, {107, 10192}, {140, 1075}, {154, 15274}, {184, 6530}, {217, 19170}, {264, 37649}, {297, 1993}, {324, 14389}, {343, 648}, {393, 11427}, {394, 17907}, {427, 41204}, {436, 14569}, {441, 46717}, {458, 41361}, {467, 1994}, {468, 3168}, {472, 36302}, {473, 36303}, {549, 40664}, {597, 37873}, {1148, 15325}, {1559, 41372}, {1585, 3311}, {1586, 3312}, {1629, 5480}, {1853, 15576}, {1941, 6823}, {1990, 2052}, {2883, 51892}, {3176, 3622}, {3183, 15717}, {5068, 8888}, {5523, 52281}, {5667, 8703}, {6509, 23583}, {6524, 37070}, {6525, 35260}, {6747, 13366}, {6750, 37505}, {6819, 51171}, {8613, 42459}, {8746, 53477}, {8884, 45089}, {8887, 12242}, {10002, 11206}, {10282, 33549}, {10303, 41425}, {11064, 15466}, {11245, 52249}, {11433, 40138}, {13567, 14165}, {14249, 16252}, {14918, 41628}, {15005, 50693}, {15258, 32064}, {15262, 34545}, {18121, 53176}, {23332, 51939}, {34782, 38808}, {34986, 39569}, {38652, 40938}, {40684, 41366}, {41170, 52917}, {41203, 41588}, {41370, 52282}, {43462, 53506}, {45794, 56021}, {52147, 53415}, {52253, 56022}

X(56297) = polar conjugate of X(15319)
X(56297) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 15319}, {6748, 140}
X(56297) = X(i)-Ceva conjugate of X(j) for these {i, j}: {40410, 4}
X(56297) = intersection, other than A, B, C, of circumconics {{A, B, C, X(253), X(39286)}}, {{A, B, C, X(288), X(1073)}}, {{A, B, C, X(13157), X(34579)}}
X(56297) = barycentric product X(i)*X(j) for these (i, j): {10282, 264}, {33549, 40410}
X(56297) = barycentric quotient X(i)/X(j) for these (i, j): {4, 15319}, {10282, 3}, {33549, 140}
X(56297) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1249, 56296}, {2, 56296, 51358}, {154, 15274, 52448}, {467, 1994, 27377}, {1990, 23292, 2052}, {1994, 37766, 467}, {51266, 51273, 5}

X(56298) = KP2(X(4)) OF X(3) AND X(5)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^12+b^2*c^2*(b^2-c^2)^4-4*a^10*(b^2+c^2)+a^4*(b^2-c^2)^2*(b^4+c^4)+a^8*(6*b^4+9*b^2*c^2+6*c^4)-4*a^6*(b^6+b^4*c^2+b^2*c^4+c^6)) : :

X(56298) lies on these lines: {3, 1075}, {4, 6}, {5, 3462}, {24, 3168}, {51, 8884}, {54, 436}, {55, 7049}, {56, 1148}, {107, 10282}, {133, 14862}, {140, 51358}, {184, 1093}, {186, 47153}, {216, 40448}, {275, 8887}, {324, 13434}, {450, 1147}, {459, 3525}, {550, 5667}, {567, 37127}, {578, 2052}, {631, 14361}, {648, 5562}, {1092, 15466}, {1614, 52661}, {1629, 10110}, {2055, 8613}, {3176, 7967}, {3183, 3528}, {3518, 51887}, {3524, 41425}, {3544, 8888}, {5158, 13599}, {6524, 18925}, {6759, 14249}, {6952, 18687}, {7383, 46741}, {7395, 9308}, {7488, 35360}, {7567, 41083}, {9833, 52448}, {10112, 39569}, {11001, 15005}, {11202, 51877}, {11547, 39571}, {11587, 15912}, {15033, 44732}, {15318, 53852}, {15459, 38933}, {15781, 41481}, {16252, 51385}, {17401, 52011}, {18912, 52249}, {19169, 55084}, {20299, 51939}, {26883, 47392}, {32379, 52917}, {34148, 46106}, {37124, 43651}, {41203, 41587}, {42329, 51936}

X(56298) = X(i)-isoconjugate-of-X(j) for these {i, j}: {63, 8612}
X(56298) = X(i)-Dao conjugate of X(j) for these {i, j}: {3162, 8612}, {38976, 525}, {52280, 45198}
X(56298) = X(i)-Ceva conjugate of X(j) for these {i, j}: {216, 436}, {40448, 4}
X(56298) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(41373)}}, {{A, B, C, X(4), X(8613)}}, {{A, B, C, X(6), X(3463)}}, {{A, B, C, X(96), X(41204)}}
X(56298) = barycentric product X(i)*X(j) for these (i, j): {4, 8613}, {275, 51888}, {2052, 2055}
X(56298) = barycentric quotient X(i)/X(j) for these (i, j): {25, 8612}, {2055, 394}, {8613, 69}, {51888, 343}
X(56298) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 56296, 1075}, {4, 1498, 48364}, {5, 56297, 3462}, {54, 13450, 436}, {107, 38808, 10282}, {2055, 51888, 8613}, {3462, 6761, 5}, {10112, 39569, 43995}, {10282, 14363, 107}, {10982, 33971, 4}, {36302, 36303, 53}

X(56299) = X(9)-CEVA CONJUGATE OF X(4)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^7*(b+c)-b*(b-c)^4*c*(b+c)^2-a^3*(b-c)^2*(b+c)^3+a*(b-c)^2*(b+c)^3*(b^2+c^2)-a^2*(b^2-c^2)^2*(2*b^2-b*c+2*c^2)-a^6*(2*b^2+b*c+2*c^2)-a^5*(b^3+b^2*c+b*c^2+c^3)+a^4*(4*b^4+b^3*c-2*b^2*c^2+b*c^3+4*c^4)) : :

X(56299) lies on these lines: {4, 65}, {37, 1249}, {72, 1895}, {92, 5728}, {243, 1708}, {342, 5927}, {653, 7580}, {943, 7049}, {971, 44697}, {1075, 1712}, {1260, 1897}, {1784, 18397}, {1940, 10393}, {3168, 26000}, {3487, 7551}, {3651, 8762}, {5658, 40837}, {5729, 37279}, {5759, 44695}, {7046, 14361}, {7952, 40967}, {34032, 36127}, {36996, 55110}

X(56299) = X(i)-Dao conjugate of X(j) for these {i, j}: {273, 85}
X(56299) = X(i)-Ceva conjugate of X(j) for these {i, j}: {9, 4}
X(56299) = barycentric product X(i)*X(j) for these (i, j): {318, 51969}, {2947, 92}
X(56299) = barycentric quotient X(i)/X(j) for these (i, j): {2947, 63}, {51969, 77}
X(56299) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {12664, 47372, 4}

X(56300) = KP2(X(4)) OF X(9) AND X(10)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^7-a^6*(b+c)+b*(b-c)^2*c*(b+c)^3+a*b*c*(b^2-c^2)^2+a^3*(b+c)^2*(b^2+c^2)-a^5*(2*b^2+3*b*c+2*c^2)+a^4*(2*b^3-b^2*c-b*c^2+2*c^3)-a^2*(b^5-b^4*c-b*c^4+c^5)) : :

X(56300) lies on these lines: {1, 281}, {6, 158}, {9, 56299}, {19, 1148}, {65, 8748}, {92, 54358}, {196, 52819}, {219, 1895}, {243, 579}, {284, 1940}, {393, 18391}, {1118, 5802}, {1172, 2982}, {1449, 39585}, {1783, 3990}, {1857, 5746}, {1897, 3694}, {1990, 21933}, {5776, 47372}, {6520, 19350}, {30456, 36127}, {32674, 47345}

X(56300) = X(i)-Dao conjugate of X(j) for these {i, j}: {1838, 5249}
X(56300) = X(i)-Ceva conjugate of X(j) for these {i, j}: {40435, 4}
X(56300) = intersection, other than A, B, C, of circumconics {{A, B, C, X(282), X(40395)}}, {{A, B, C, X(2982), X(41087)}}
X(56300) = barycentric product X(i)*X(j) for these (i, j): {10536, 264}
X(56300) = barycentric quotient X(i)/X(j) for these (i, j): {10536, 3}
X(56300) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1249, 3176, 281}

X(56301) = X(10)-CEVA CONJUGATE OF X(4)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^6+3*a^5*(b+c)-a*(b-c)^2*(b+c)^3-a^2*(b+c)^2*(b^2+c^2)-(b^2-c^2)^2*(b^2+b*c+c^2)+a^4*(b^2+3*b*c+c^2)-2*a^3*(b^3+b^2*c+b*c^2+c^3)) : :

X(56301) lies on these lines: {1, 18679}, {4, 6}, {10, 56300}, {30, 44698}, {40, 52011}, {42, 4213}, {108, 38856}, {186, 47163}, {297, 56018}, {442, 41083}, {451, 3085}, {648, 1330}, {1068, 1148}, {1897, 3695}, {2322, 4205}, {3487, 18678}, {3651, 8885}, {5292, 7543}, {6998, 16318}, {7149, 12867}, {7380, 45141}, {7513, 48847}, {7554, 37642}, {7952, 40967}, {9308, 16062}, {10449, 17907}, {11109, 56297}, {17555, 56296}, {39591, 45766}

X(56301) = X(i)-isoconjugate-of-X(j) for these {i, j}: {63, 34440}
X(56301) = X(i)-Dao conjugate of X(j) for these {i, j}: {27, 86}, {3162, 34440}
X(56301) = X(i)-Ceva conjugate of X(j) for these {i, j}: {10, 4}, {56300, 56299}
X(56301) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(3151)}}, {{A, B, C, X(1172), X(7105)}}
X(56301) = barycentric product X(i)*X(j) for these (i, j): {2939, 92}, {3151, 4}, {18631, 281}
X(56301) = barycentric quotient X(i)/X(j) for these (i, j): {25, 34440}, {2939, 63}, {3151, 69}, {18631, 348}
X(56301) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1834, 1990, 8747}, {1834, 8747, 4}

X(56302) = KP2(X(5)) OF X(2) AND X(3)

Barycentrics    (-(b^2-c^2)^2+a^2*(b^2+c^2))*(a^8+b^2*c^2*(b^2-c^2)^2-3*a^6*(b^2+c^2)-a^2*(b^2-c^2)^2*(b^2+c^2)+a^4*(3*b^4+b^2*c^2+3*c^4)) : :

X(56302) lies on circumconic {{A, B, C, X(343), X(46106)}} and on these lines: {2, 216}, {3, 15912}, {5, 23607}, {20, 52}, {22, 9755}, {95, 31626}, {97, 648}, {343, 14570}, {401, 34545}, {418, 35360}, {467, 42459}, {925, 41271}, {1370, 41169}, {1972, 11794}, {1994, 8613}, {3060, 42329}, {3917, 44003}, {5422, 20477}, {5664, 20577}, {6360, 23958}, {8799, 50689}, {9308, 37068}, {10003, 11197}, {11140, 54547}, {14129, 34836}, {15108, 39352}, {19772, 51264}, {19773, 51271}, {20222, 45238}, {21734, 22257}, {23195, 47143}, {26842, 44354}, {30506, 32428}, {35061, 56266}, {35937, 41676}, {39284, 54105}, {41244, 52703}, {41480, 45794}, {41678, 56297}, {42441, 51888}

X(56302) = anticomplement of X(40684)
X(56302) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2148, 6662}
X(56302) = X(i)-Dao conjugate of X(j) for these {i, j}: {216, 6662}, {36412, 5}, {40684, 40684}
X(56302) = X(i)-Ceva conjugate of X(j) for these {i, j}: {95, 5}, {31626, 2}
X(56302) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {48, 2889}, {1173, 21270}, {20574, 21271}, {31626, 6327}, {33631, 5906}, {39180, 21294}
X(56302) = barycentric product X(i)*X(j) for these (i, j): {1614, 311}, {6663, 95}, {18831, 34979}, {46724, 5}
X(56302) = barycentric quotient X(i)/X(j) for these (i, j): {5, 6662}, {1614, 54}, {6663, 5}, {34979, 6368}, {46724, 95}
X(56302) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3164, 43988}, {216, 324, 2}, {418, 42453, 35360}, {1994, 8613, 43768}, {34836, 52945, 14129}

X(56303) = KP2(X(5)) OF X(3) AND X(4)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(-(b^2-c^2)^2+a^2*(b^2+c^2))*(a^8+b^2*c^2*(b^2-c^2)^2-3*a^6*(b^2+c^2)-a^2*(b^2+c^2)^3+a^4*(3*b^4+5*b^2*c^2+3*c^4)) : :

X(56303) lies on these lines: {3, 15912}, {4, 52}, {5, 35360}, {24, 9308}, {49, 35311}, {54, 648}, {74, 1105}, {107, 43598}, {143, 14978}, {216, 631}, {264, 3567}, {418, 41481}, {436, 56292}, {511, 44732}, {1093, 11459}, {1216, 46106}, {1941, 3520}, {1994, 37127}, {2052, 11412}, {2967, 37121}, {3090, 3168}, {3164, 26876}, {3541, 41169}, {4240, 18350}, {5462, 40684}, {5562, 13450}, {5907, 52661}, {6750, 41586}, {7509, 56296}, {7512, 41204}, {7999, 15466}, {8887, 14531}, {11455, 52578}, {14249, 15058}, {14920, 43839}, {15559, 44704}, {16080, 43866}, {31388, 51888}, {34334, 45959}, {35318, 37124}, {35921, 56298}, {37493, 52253}

X(56303) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2169, 45195}
X(56303) = X(i)-Dao conjugate of X(j) for these {i, j}: {14363, 45195}
X(56303) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1105, 5}
X(56303) = intersection, other than A, B, C, of circumconics {{A, B, C, X(68), X(18890)}}, {{A, B, C, X(5392), X(15318)}}
X(56303) = barycentric quotient X(i)/X(j) for these (i, j): {53, 45195}
X(56303) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 15912, 56302}, {52, 324, 4}, {143, 14978, 30506}

X(56304) = X(6)-CEVA CONJUGATE OF X(5)

Barycentrics    (-(b^2-c^2)^2+a^2*(b^2+c^2))*(-(b^2*c^2*(b^2-c^2)^2)+a^6*(b^2+c^2)-2*a^4*(b^4+b^2*c^2+c^4)+a^2*(b^6+c^6)) : :

X(56304) lies on these lines: {5, 45793}, {22, 9755}, {30, 52}, {216, 230}, {324, 427}, {378, 56303}, {523, 34986}, {925, 54034}, {6663, 41587}, {12161, 46200}, {31802, 41481}, {34751, 39910}, {41588, 42453}

X(56304) = X(i)-Dao conjugate of X(j) for these {i, j}: {311, 76}
X(56304) = X(i)-Ceva conjugate of X(j) for these {i, j}: {6, 5}
X(56304) = barycentric product X(i)*X(j) for these (i, j): {14570, 34964}, {23158, 324}
X(56304) = barycentric quotient X(i)/X(j) for these (i, j): {23158, 97}, {34964, 15412}

X(56305) = KP2(X(6)) OF X(1) AND X(4)

Barycentrics    a^2*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^3-a^2*b-a*b^2+b^3+c^3)*(a^3+b^3-a^2*c-a*c^2+c^3) : :

X(56305) lies on these lines: {3, 1398}, {4, 28776}, {24, 37547}, {25, 1260}, {28, 1792}, {55, 7337}, {212, 573}, {943, 7412}, {972, 52775}, {1061, 37533}, {1283, 1957}, {1802, 1973}, {2203, 26893}, {11436, 44085}, {14017, 40436}

X(56305) = isogonal conjugate of X(41004)
X(56305) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 41004}, {2, 26934}, {3, 17861}, {63, 3772}, {69, 3924}, {71, 16749}, {72, 17189}, {77, 1837}, {273, 53850}, {307, 40980}, {345, 36570}, {348, 40968}, {1444, 21935}, {4025, 53279}
X(56305) = X(i)-vertex conjugate of X(j) for these {i, j}: {63, 278}
X(56305) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 41004}, {3162, 3772}, {32664, 26934}, {36103, 17861}
X(56305) = X(i)-Ceva conjugate of X(j) for these {i, j}: {34406, 56003}
X(56305) = X(i)-cross conjugate of X(j) for these {i, j}: {3063, 1783}
X(56305) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1297)}}, {{A, B, C, X(3), X(55)}}, {{A, B, C, X(4), X(2299)}}, {{A, B, C, X(25), X(28)}}, {{A, B, C, X(31), X(3418)}}, {{A, B, C, X(33), X(1061)}}, {{A, B, C, X(42), X(41013)}}, {{A, B, C, X(57), X(251)}}, {{A, B, C, X(102), X(2328)}}, {{A, B, C, X(104), X(7169)}}, {{A, B, C, X(197), X(1486)}}, {{A, B, C, X(200), X(3345)}}, {{A, B, C, X(278), X(9085)}}, {{A, B, C, X(281), X(284)}}, {{A, B, C, X(945), X(2192)}}, {{A, B, C, X(951), X(51476)}}, {{A, B, C, X(1175), X(2258)}}, {{A, B, C, X(1436), X(9456)}}, {{A, B, C, X(2194), X(3417)}}, {{A, B, C, X(2335), X(2359)}}, {{A, B, C, X(7097), X(41890)}}, {{A, B, C, X(7412), X(8021)}}, {{A, B, C, X(10623), X(34429)}}, {{A, B, C, X(29206), X(56098)}}, {{A, B, C, X(37741), X(40419)}}
X(56305) = barycentric product X(i)*X(j) for these (i, j): {1, 55994}, {4, 56003}, {19, 40436}, {34399, 607}, {34406, 6}
X(56305) = barycentric quotient X(i)/X(j) for these (i, j): {6, 41004}, {19, 17861}, {25, 3772}, {28, 16749}, {31, 26934}, {607, 1837}, {1395, 36570}, {1474, 17189}, {1973, 3924}, {2204, 40980}, {2212, 40968}, {2333, 21935}, {34406, 76}, {40436, 304}, {52425, 53850}, {52775, 13149}, {55994, 75}, {56003, 69}

X(56306) = KP2(X(6)) OF X(2) AND X(3)

Barycentrics    a^2*(2*a^6-b^6-b^2*c^4+2*c^6+2*a^2*c^2*(b^2-c^2)-a^4*(b^2+2*c^2))*(2*a^6+2*b^6-b^4*c^2-c^6-a^4*(2*b^2+c^2)-2*a^2*(b^4-b^2*c^2)) : :

X(56306) lies on these lines: {20, 10002}, {22, 15905}, {69, 20587}, {154, 15394}, {253, 42671}, {1350, 7488}, {3522, 51347}, {6636, 40358}, {7492, 52513}, {8801, 11348}, {10565, 23608}

X(56306) = isogonal conjugate of X(1853)
X(56306) = trilinear pole of line {8673, 16040}
X(56306) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 1853}, {19, 20208}, {64, 20322}, {158, 53852}, {2184, 46829}
X(56306) = X(i)-vertex conjugate of X(j) for these {i, j}: {6, 253}
X(56306) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 1853}, {6, 20208}, {32, 53851}, {1147, 53852}
X(56306) = X(i)-cross conjugate of X(j) for these {i, j}: {39575, 2}, {52613, 110}
X(56306) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(22)}}, {{A, B, C, X(3), X(20)}}, {{A, B, C, X(4), X(1166)}}, {{A, B, C, X(5), X(38435)}}, {{A, B, C, X(6), X(253)}}, {{A, B, C, X(30), X(10298)}}, {{A, B, C, X(54), X(3346)}}, {{A, B, C, X(59), X(347)}}, {{A, B, C, X(60), X(280)}}, {{A, B, C, X(64), X(31361)}}, {{A, B, C, X(69), X(250)}}, {{A, B, C, X(74), X(16251)}}, {{A, B, C, X(95), X(34168)}}, {{A, B, C, X(160), X(1576)}}, {{A, B, C, X(186), X(50480)}}, {{A, B, C, X(206), X(21458)}}, {{A, B, C, X(237), X(15389)}}, {{A, B, C, X(264), X(43697)}}, {{A, B, C, X(376), X(2071)}}, {{A, B, C, X(393), X(1177)}}, {{A, B, C, X(842), X(34208)}}, {{A, B, C, X(1014), X(26703)}}, {{A, B, C, X(1217), X(40441)}}, {{A, B, C, X(1249), X(15384)}}, {{A, B, C, X(1294), X(3431)}}, {{A, B, C, X(1370), X(6636)}}, {{A, B, C, X(1383), X(2373)}}, {{A, B, C, X(1790), X(37741)}}, {{A, B, C, X(2165), X(3447)}}, {{A, B, C, X(2693), X(20421)}}, {{A, B, C, X(2697), X(45838)}}, {{A, B, C, X(2998), X(51862)}}, {{A, B, C, X(3091), X(9715)}}, {{A, B, C, X(3108), X(34427)}}, {{A, B, C, X(3146), X(38444)}}, {{A, B, C, X(3424), X(8882)}}, {{A, B, C, X(3425), X(52223)}}, {{A, B, C, X(3522), X(11413)}}, {{A, B, C, X(3529), X(38448)}}, {{A, B, C, X(3532), X(50710)}}, {{A, B, C, X(3563), X(51316)}}, {{A, B, C, X(3565), X(5649)}}, {{A, B, C, X(5059), X(38438)}}, {{A, B, C, X(6391), X(34570)}}, {{A, B, C, X(6759), X(10282)}}, {{A, B, C, X(10304), X(21312)}}, {{A, B, C, X(13472), X(15318)}}, {{A, B, C, X(13575), X(39955)}}, {{A, B, C, X(14910), X(34285)}}, {{A, B, C, X(15324), X(33629)}}, {{A, B, C, X(16774), X(29011)}}, {{A, B, C, X(17040), X(42484)}}, {{A, B, C, X(18355), X(33643)}}, {{A, B, C, X(18855), X(34225)}}, {{A, B, C, X(40801), X(41891)}}
X(56306) = barycentric product X(i)*X(j) for these (i, j): {15905, 34407}, {34412, 6}
X(56306) = barycentric quotient X(i)/X(j) for these (i, j): {3, 20208}, {6, 1853}, {154, 46829}, {206, 53851}, {577, 53852}, {610, 20322}, {34407, 52581}, {34412, 76}

X(56307) = KP2(X(6)) OF X(2) AND X(4)

Barycentrics    a^2*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^4-2*a^2*b^2+b^4+c^4)*(a^4+b^4-2*a^2*c^2+c^4) : :

X(56307) lies on these lines: {3, 6530}, {4, 16391}, {22, 232}, {24, 511}, {25, 317}, {26, 19189}, {95, 6641}, {157, 523}, {262, 36794}, {264, 3148}, {378, 14356}, {393, 37183}, {458, 3613}, {648, 9307}, {1176, 39575}, {1485, 1576}, {2374, 42297}, {2453, 48379}, {2967, 3425}, {3060, 8882}, {5413, 26875}, {6644, 35908}, {7509, 39604}, {8430, 21397}, {9530, 15078}, {10594, 14111}, {11337, 22341}, {14379, 17928}, {21213, 51862}, {21284, 52692}, {32112, 40914}, {36426, 52275}, {41768, 51776}, {44096, 50666}

X(56307) = isogonal conjugate of X(1899)
X(56307) = polar conjugate of X(41760)
X(56307) = trilinear pole of line {3569, 6753}
X(56307) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 1899}, {2, 2083}, {3, 17871}, {19, 6389}, {31, 41009}, {48, 41760}, {63, 3767}, {75, 40947}, {92, 39643}, {158, 426}, {293, 2450}, {304, 42295}, {326, 41762}, {656, 1632}, {1096, 44141}, {1820, 41770}, {2156, 28405}, {6751, 40440}
X(56307) = X(i)-vertex conjugate of X(j) for these {i, j}: {69, 393}, {9307, 9307}
X(56307) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 41009}, {3, 1899}, {6, 6389}, {132, 2450}, {206, 40947}, {427, 52532}, {1147, 426}, {1249, 41760}, {3162, 3767}, {6503, 44141}, {15259, 41762}, {22391, 39643}, {32664, 2083}, {36103, 17871}, {40596, 1632}
X(56307) = X(i)-Ceva conjugate of X(j) for these {i, j}: {34405, 56004}
X(56307) = X(i)-cross conjugate of X(j) for these {i, j}: {3049, 648}, {52584, 110}
X(56307) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(22)}}, {{A, B, C, X(3), X(95)}}, {{A, B, C, X(4), X(24)}}, {{A, B, C, X(5), X(26)}}, {{A, B, C, X(6), X(232)}}, {{A, B, C, X(20), X(17928)}}, {{A, B, C, X(21), X(11337)}}, {{A, B, C, X(23), X(1995)}}, {{A, B, C, X(25), X(1974)}}, {{A, B, C, X(54), X(1217)}}, {{A, B, C, X(64), X(18848)}}, {{A, B, C, X(66), X(14910)}}, {{A, B, C, X(68), X(34225)}}, {{A, B, C, X(69), X(1297)}}, {{A, B, C, X(74), X(18850)}}, {{A, B, C, X(96), X(34439)}}, {{A, B, C, X(98), X(34207)}}, {{A, B, C, X(111), X(10603)}}, {{A, B, C, X(157), X(1576)}}, {{A, B, C, X(184), X(3155)}}, {{A, B, C, X(186), X(378)}}, {{A, B, C, X(199), X(1011)}}, {{A, B, C, X(237), X(3148)}}, {{A, B, C, X(253), X(895)}}, {{A, B, C, X(276), X(39968)}}, {{A, B, C, X(305), X(34427)}}, {{A, B, C, X(324), X(3060)}}, {{A, B, C, X(381), X(2070)}}, {{A, B, C, X(382), X(45735)}}, {{A, B, C, X(393), X(3563)}}, {{A, B, C, X(405), X(2915)}}, {{A, B, C, X(427), X(21213)}}, {{A, B, C, X(648), X(9308)}}, {{A, B, C, X(687), X(805)}}, {{A, B, C, X(967), X(40414)}}, {{A, B, C, X(1093), X(34428)}}, {{A, B, C, X(1173), X(18355)}}, {{A, B, C, X(1177), X(2165)}}, {{A, B, C, X(1300), X(18532)}}, {{A, B, C, X(1494), X(6391)}}, {{A, B, C, X(1502), X(46239)}}, {{A, B, C, X(1593), X(3515)}}, {{A, B, C, X(1657), X(43809)}}, {{A, B, C, X(2351), X(15389)}}, {{A, B, C, X(2353), X(9468)}}, {{A, B, C, X(3049), X(40947)}}, {{A, B, C, X(3129), X(3130)}}, {{A, B, C, X(3131), X(3132)}}, {{A, B, C, X(3432), X(52518)}}, {{A, B, C, X(3516), X(15750)}}, {{A, B, C, X(3518), X(10594)}}, {{A, B, C, X(3520), X(32534)}}, {{A, B, C, X(3527), X(14860)}}, {{A, B, C, X(4185), X(20832)}}, {{A, B, C, X(5020), X(9909)}}, {{A, B, C, X(5094), X(21284)}}, {{A, B, C, X(5481), X(36948)}}, {{A, B, C, X(6330), X(40802)}}, {{A, B, C, X(6636), X(7485)}}, {{A, B, C, X(6660), X(11328)}}, {{A, B, C, X(6662), X(15317)}}, {{A, B, C, X(7488), X(7503)}}, {{A, B, C, X(8749), X(34208)}}, {{A, B, C, X(8797), X(41891)}}, {{A, B, C, X(9723), X(47390)}}, {{A, B, C, X(11413), X(22467)}}, {{A, B, C, X(13472), X(18853)}}, {{A, B, C, X(14489), X(40410)}}, {{A, B, C, X(15316), X(15318)}}, {{A, B, C, X(15319), X(38260)}}, {{A, B, C, X(15740), X(45301)}}, {{A, B, C, X(17974), X(18890)}}, {{A, B, C, X(17983), X(41489)}}, {{A, B, C, X(18124), X(44177)}}, {{A, B, C, X(18401), X(34801)}}, {{A, B, C, X(22261), X(34438)}}, {{A, B, C, X(23582), X(40416)}}, {{A, B, C, X(34436), X(45838)}}, {{A, B, C, X(34570), X(36889)}}, {{A, B, C, X(40144), X(47847)}}, {{A, B, C, X(42407), X(56004)}}, {{A, B, C, X(43725), X(45857)}}
X(56307) = barycentric product X(i)*X(j) for these (i, j): {4, 56004}, {25, 42407}, {2489, 42297}, {34405, 6}
X(56307) = barycentric quotient X(i)/X(j) for these (i, j): {2, 41009}, {3, 6389}, {4, 41760}, {6, 1899}, {19, 17871}, {22, 28405}, {24, 41770}, {25, 3767}, {31, 2083}, {32, 40947}, {112, 1632}, {184, 39643}, {217, 6751}, {232, 2450}, {394, 44141}, {577, 426}, {1974, 42295}, {2207, 41762}, {7592, 18953}, {8743, 41761}, {14576, 27362}, {34405, 76}, {40938, 52532}, {42297, 52608}, {42407, 305}, {56004, 69}
X(56307) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9308, 36176, 157}

X(56308) = X(5)-CEVA CONJUGATE OF X(6)

Barycentrics    a^2*(a^10-3*a^8*(b^2+c^2)-(b^2-c^2)^4*(b^2+c^2)+a^6*(4*b^4+5*b^2*c^2+4*c^4)-2*a^4*(2*b^6+b^4*c^2+b^2*c^4+2*c^6)+3*a^2*(b^8-b^6*c^2-b^2*c^6+c^8)) : :

X(56308) lies on these lines: {2, 14652}, {3, 161}, {5, 1601}, {6, 2351}, {22, 9756}, {24, 19172}, {25, 2934}, {26, 23709}, {50, 47328}, {51, 2965}, {97, 44668}, {154, 157}, {184, 566}, {456, 21394}, {512, 34985}, {577, 34751}, {925, 45793}, {973, 8883}, {1157, 7730}, {2070, 9222}, {3053, 3148}, {3155, 42265}, {3156, 42262}, {5172, 23383}, {10192, 54375}, {13409, 17847}, {15109, 23195}, {15139, 46832}, {15577, 37068}, {17809, 40947}, {17824, 42441}, {19468, 51255}, {30715, 36178}, {32379, 46025}, {41205, 56304}, {43653, 50669}

X(56308) = perspector of circumconic {{A, B, C, X(16039), X(32692)}}
X(56308) = X(i)-isoconjugate-of-X(j) for these {i, j}: {75, 3432}, {6798, 40440}, {14213, 40140}
X(56308) = X(i)-Dao conjugate of X(j) for these {i, j}: {54, 95}, {206, 3432}
X(56308) = X(i)-Ceva conjugate of X(j) for these {i, j}: {5, 6}, {2888, 45800}
X(56308) = X(i)-cross conjugate of X(j) for these {i, j}: {8565, 45800}
X(56308) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2888), X(6145)}}, {{A, B, C, X(3432), X(54034)}}, {{A, B, C, X(51477), X(52677)}}
X(56308) = barycentric product X(i)*X(j) for these (i, j): {4, 45800}, {216, 52677}, {264, 8565}, {2888, 6}
X(56308) = barycentric quotient X(i)/X(j) for these (i, j): {32, 3432}, {217, 6798}, {2888, 76}, {8565, 3}, {45800, 69}, {52677, 276}, {54034, 40140}
X(56308) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 1601, 3432}, {157, 6641, 154}

X(56309) = KP2(X(7)) OF X(2) AND X(9)

Barycentrics    (a+b-c)*(a-b+c)*(a^4+2*b*(b-c)^2*c-3*a^3*(b+c)-a*(b-c)^2*(b+c)+3*a^2*(b^2+c^2)) : :

X(56309) lies on these lines: {1, 1088}, {2, 3160}, {7, 9580}, {57, 14189}, {63, 35312}, {77, 4666}, {85, 10582}, {165, 658}, {200, 664}, {223, 36905}, {226, 2898}, {241, 24600}, {279, 10580}, {347, 3875}, {348, 4847}, {354, 42309}, {390, 479}, {516, 7056}, {934, 7411}, {1214, 45742}, {1323, 11019}, {1419, 10025}, {1996, 13405}, {2124, 3177}, {2951, 50561}, {3058, 30623}, {3668, 14548}, {3870, 25716}, {3886, 7182}, {4326, 23062}, {5932, 17270}, {6610, 24352}, {9446, 10389}, {9533, 9778}, {9812, 10004}, {10436, 33673}, {10980, 33765}, {17078, 31146}, {25006, 31600}, {30350, 52511}, {30353, 47374}, {36640, 51351}, {40443, 52769}

X(56309) = X(i)-isoconjugate-of-X(j) for these {i, j}: {663, 42301}, {3063, 42303}
X(56309) = X(i)-Dao conjugate of X(j) for these {i, j}: {10001, 42303}, {10481, 142}
X(56309) = X(i)-Ceva conjugate of X(j) for these {i, j}: {32008, 7}, {34019, 30625}
X(56309) = X(i)-cross conjugate of X(j) for these {i, j}: {11495, 30625}
X(56309) = intersection, other than A, B, C, of circumconics {{A, B, C, X(200), X(24011)}}, {{A, B, C, X(10390), X(19605)}}
X(56309) = barycentric product X(i)*X(j) for these (i, j): {1, 34019}, {11495, 85}, {30625, 7}
X(56309) = barycentric quotient X(i)/X(j) for these (i, j): {651, 42301}, {664, 42303}, {11495, 9}, {30625, 8}, {34019, 75}
X(56309) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1323, 11019, 17093}, {3160, 31527, 2}, {3160, 34059, 9312}, {14189, 31526, 57}

X(56310) = X(9)-CEVA CONJUGATE OF X(7)

Barycentrics    (a+b-c)*(a-b+c)*(-(b*(b-c)^4*c)+a^5*(b+c)+a*(b-c)^2*(b+c)^3-2*a^2*(b-c)^2*(2*b^2+3*b*c+2*c^2)-a^4*(4*b^2+b*c+4*c^2)+a^3*(6*b^3-2*b^2*c-2*b*c^2+6*c^3)) : :

X(56310) lies on cubic K977 and on these lines: {2, 42449}, {7, 354}, {9, 56309}, {144, 35312}, {279, 21346}, {347, 52160}, {480, 664}, {658, 11495}, {1212, 3160}, {1445, 2082}, {2346, 43750}, {3059, 31627}, {6172, 15913}, {8232, 17084}, {30628, 37780}

X(56310) = reflection of X(i) in X(j) for these {i,j}: {7, 50561}
X(56310) = X(i)-Dao conjugate of X(j) for these {i, j}: {1088, 85}
X(56310) = X(i)-Ceva conjugate of X(j) for these {i, j}: {9, 7}, {56309, 3160}
X(56310) = barycentric product X(i)*X(j) for these (i, j): {170, 85}
X(56310) = barycentric quotient X(i)/X(j) for these (i, j): {170, 9}
X(56310) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1088, 5572, 7}

X(56311) = KP2(X(8)) OF X(1) AND X(10)

Barycentrics    (a-b-c)*(a^3+a*b*c+a^2*(b+c)-b*c*(b+c)) : :

X(56311) lies on these lines: {1, 979}, {2, 988}, {3, 5205}, {4, 29641}, {8, 9}, {10, 846}, {12, 33116}, {21, 3701}, {29, 4518}, {31, 41261}, {35, 3992}, {37, 1220}, {45, 5793}, {55, 341}, {56, 18743}, {65, 190}, {78, 27538}, {86, 56083}, {92, 37318}, {99, 35991}, {100, 28029}, {145, 42360}, {192, 54418}, {210, 1043}, {213, 644}, {239, 16916}, {312, 958}, {321, 5260}, {333, 3714}, {344, 388}, {345, 2551}, {405, 3757}, {612, 4195}, {756, 54331}, {894, 1655}, {946, 17777}, {964, 5283}, {989, 4339}, {1001, 56085}, {1054, 8720}, {1089, 5251}, {1104, 32926}, {1222, 5919}, {1265, 3486}, {1329, 32851}, {1447, 18135}, {1621, 4696}, {1722, 3210}, {1793, 52409}, {1834, 33118}, {1885, 34337}, {1940, 6335}, {1975, 30758}, {1997, 7288}, {1999, 5247}, {2292, 17261}, {2329, 3985}, {2478, 3705}, {2646, 4009}, {2650, 32938}, {2975, 4358}, {3006, 5046}, {3091, 30741}, {3146, 39570}, {3219, 17751}, {3295, 4737}, {3333, 30947}, {3436, 17776}, {3485, 56084}, {3616, 8055}, {3617, 32929}, {3687, 18250}, {3699, 52352}, {3704, 42033}, {3712, 21031}, {3812, 32939}, {3831, 24627}, {3871, 4723}, {3876, 49492}, {3912, 12527}, {3913, 44720}, {3920, 11319}, {3923, 56080}, {3924, 32925}, {3932, 7270}, {3948, 37225}, {3952, 34772}, {3977, 24982}, {3995, 17016}, {3996, 4662}, {4066, 54335}, {4075, 30115}, {4217, 50286}, {4313, 5423}, {4387, 4673}, {4388, 12572}, {4391, 29070}, {4420, 46877}, {4425, 19879}, {4429, 50065}, {4432, 37588}, {4642, 32936}, {4676, 5710}, {4692, 5259}, {4720, 32635}, {4756, 34195}, {4936, 49495}, {4968, 5047}, {4975, 5288}, {5015, 11113}, {5016, 32862}, {5025, 30763}, {5080, 52364}, {5088, 33942}, {5089, 37087}, {5100, 15171}, {5234, 11679}, {5266, 13735}, {5297, 11115}, {5300, 11114}, {5433, 37758}, {5552, 10538}, {5835, 17340}, {5882, 47624}, {6284, 32850}, {6651, 17752}, {6763, 49999}, {6872, 10327}, {7172, 11106}, {7836, 30798}, {10371, 17233}, {10404, 17234}, {10448, 32931}, {10449, 41229}, {10459, 32930}, {10572, 16086}, {10915, 21290}, {11681, 33113}, {12513, 38475}, {12526, 25728}, {13741, 37592}, {16706, 25992}, {16826, 33816}, {16865, 26227}, {17260, 31339}, {17264, 34606}, {17350, 54421}, {17480, 28011}, {17526, 29634}, {17676, 29679}, {17685, 30179}, {17738, 27000}, {19842, 20989}, {19860, 56082}, {21077, 25650}, {21935, 33115}, {24068, 30117}, {24349, 54392}, {24440, 32934}, {24443, 25965}, {25079, 37617}, {25524, 30829}, {25531, 52541}, {25583, 32817}, {26139, 28018}, {27002, 46827}, {27383, 27411}, {27396, 27410}, {28058, 52346}, {28661, 38314}, {28808, 30478}, {30055, 48899}, {30740, 32831}, {37549, 49447}, {41575, 52354}, {50171, 50223}

X(56311) = anticomplement of X(24178)
X(56311) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1408, 43677}, {3669, 6010}
X(56311) = X(i)-Dao conjugate of X(j) for these {i, j}: {3687, 4357}, {16613, 514}, {24178, 24178}
X(56311) = X(i)-Ceva conjugate of X(j) for these {i, j}: {37, 7081}, {1220, 8}
X(56311) = intersection, other than A, B, C, of circumconics {{A, B, C, X(8), X(39694)}}, {{A, B, C, X(9), X(979)}}, {{A, B, C, X(5853), X(6002)}}
X(56311) = barycentric product X(i)*X(j) for these (i, j): {312, 5247}, {1999, 8}, {3699, 6002}
X(56311) = barycentric quotient X(i)/X(j) for these (i, j): {1999, 7}, {2321, 43677}, {3699, 54986}, {3939, 6010}, {5247, 57}, {6002, 3676}, {16613, 53540}, {39774, 3674}
X(56311) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 30568, 19582}, {3, 46937, 5205}, {10, 7283, 32932}, {21, 3701, 7081}, {45, 5793, 31359}, {321, 5260, 16824}, {405, 4385, 3757}, {950, 3717, 8}, {3699, 52352, 56176}, {3714, 5302, 333}, {4968, 5047, 16823}, {17738, 30030, 27000}

X(56312) = X(6)-CEVA CONJUGATE OF X(8)

Barycentrics    (a-b-c)*(a*b^2*c^2+a^2*(b-c)^2*(b+c)-b^2*c^2*(b+c)+a^3*(b^2+c^2)) : :

X(56312) lies on these lines: {1, 979}, {8, 23638}, {9, 2319}, {43, 56080}, {190, 1403}, {192, 39929}, {312, 21334}, {329, 2899}, {346, 20684}, {668, 20537}, {1397, 8707}, {2345, 52651}, {3161, 21838}, {3677, 24349}, {3794, 4903}, {3831, 27184}, {3952, 17127}, {4009, 20359}, {4388, 36926}, {5205, 20368}, {6685, 56078}, {8055, 17794}, {18906, 41318}, {19579, 41840}, {24514, 56079}, {35104, 44723}

X(56312) = X(i)-Dao conjugate of X(j) for these {i, j}: {3596, 76}
X(56312) = X(i)-Ceva conjugate of X(j) for these {i, j}: {6, 8}
X(56312) = intersection, other than A, B, C, of circumconics {{A, B, C, X(979), X(2319)}}, {{A, B, C, X(7155), X(39694)}}
X(56312) = barycentric product X(i)*X(j) for these (i, j): {1, 45242}, {23159, 7017}, {32468, 75}
X(56312) = barycentric quotient X(i)/X(j) for these (i, j): {23159, 222}, {32468, 1}, {45242, 75}
X(56312) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7155, 27538, 7081}, {19582, 56276, 56311}

X(56313) = KP2(X(8)) OF X(10) AND X(10)

Barycentrics    (a-b-c)*(a^3-b^3+a*b*c-c^3+2*a^2*(b+c)) : :

X(56313) lies on these lines: {1, 8258}, {2, 986}, {5, 17777}, {8, 21}, {9, 38408}, {10, 846}, {12, 190}, {35, 16086}, {40, 29641}, {45, 1213}, {65, 33116}, {71, 1761}, {78, 9398}, {100, 3145}, {191, 1330}, {192, 5230}, {256, 56276}, {312, 26066}, {341, 17611}, {344, 1284}, {346, 18231}, {498, 30358}, {631, 30285}, {644, 2295}, {758, 25650}, {896, 20077}, {956, 20849}, {960, 32851}, {962, 8229}, {1046, 3178}, {1125, 11533}, {1220, 44416}, {1222, 45081}, {1265, 5218}, {1281, 3501}, {1283, 8715}, {1385, 47624}, {1406, 28965}, {1654, 20653}, {1698, 4425}, {2276, 25082}, {2475, 4427}, {2895, 27558}, {2933, 37311}, {2975, 52273}, {3017, 4065}, {3085, 32937}, {3159, 17734}, {3596, 31496}, {3616, 6703}, {3617, 23937}, {3647, 36974}, {3649, 41878}, {3685, 6734}, {3687, 18249}, {3695, 37327}, {3701, 17787}, {3705, 5250}, {3710, 7081}, {3714, 42033}, {3868, 29839}, {3869, 33113}, {3904, 24099}, {3915, 29840}, {3932, 8424}, {3936, 11684}, {3977, 24987}, {3995, 54355}, {4201, 4414}, {4220, 26264}, {4300, 23691}, {4339, 35261}, {4388, 12514}, {4418, 21674}, {4438, 37598}, {4585, 8614}, {4640, 7270}, {4642, 33115}, {4646, 33118}, {4647, 25446}, {4918, 35466}, {5177, 24280}, {5205, 6684}, {5221, 17234}, {5253, 51583}, {5530, 27064}, {5552, 7105}, {5657, 9840}, {5687, 20834}, {7080, 27544}, {7206, 51285}, {8055, 19877}, {8245, 9588}, {8582, 25101}, {8731, 10453}, {9369, 31397}, {9534, 12567}, {9778, 48890}, {9959, 26446}, {10588, 56084}, {11043, 30947}, {11688, 17776}, {16824, 54357}, {17084, 53332}, {17491, 31888}, {17751, 32849}, {18743, 24914}, {18755, 21711}, {21035, 26115}, {21935, 32936}, {25459, 33135}, {25466, 32939}, {26109, 27577}, {26131, 52068}, {26139, 28096}, {27529, 28803}, {27554, 27704}, {28604, 56079}, {28653, 56083}, {28742, 52157}, {30055, 48917}, {32850, 37568}, {33121, 37548}, {33841, 41842}, {38057, 45705}, {39800, 49730}, {50247, 50252}

X(56313) = anticomplement of X(24161)
X(56313) = perspector of circumconic {{A, B, C, X(645), X(54986)}}
X(56313) = X(i)-isoconjugate-of-X(j) for these {i, j}: {56, 1247}, {604, 54119}, {1408, 36934}, {4017, 53633}
X(56313) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 1247}, {333, 86}, {3161, 54119}, {24161, 24161}, {34961, 53633}
X(56313) = X(i)-Ceva conjugate of X(j) for these {i, j}: {10, 8}, {56078, 3161}, {56311, 19582}
X(56313) = intersection, other than A, B, C, of circumconics {{A, B, C, X(21), X(1046)}}, {{A, B, C, X(333), X(7108)}}, {{A, B, C, X(958), X(7241)}}, {{A, B, C, X(2305), X(34435)}}
X(56313) = barycentric product X(i)*X(j) for these (i, j): {10, 40605}, {1046, 312}, {2305, 3596}, {2907, 306}, {3144, 345}, {3178, 333}, {17778, 8}, {36927, 3936}
X(56313) = barycentric quotient X(i)/X(j) for these (i, j): {8, 54119}, {9, 1247}, {1046, 57}, {2305, 56}, {2321, 36934}, {2907, 27}, {3144, 278}, {3178, 226}, {5546, 53633}, {17778, 7}, {36927, 24624}, {40605, 86}
X(56313) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 56078, 56311}, {10, 56311, 36926}, {10, 846, 26117}, {1043, 21677, 8}, {1046, 3178, 17778}, {3161, 9780, 2899}, {3704, 18253, 333}, {3712, 21677, 1043}, {4418, 21674, 26051}, {4427, 27690, 2475}, {9780, 9791, 5051}

X(56314) = KP2(X(9)) OF X(1) AND X(2)

Barycentrics    a*(2*a^2+2*b^2-b*c+c^2-a*(4*b+c))*(2*a^2+b^2-b*c+2*c^2-a*(b+4*c)) : :

X(56314) lies on these lines: {145, 344}, {192, 2402}, {1420, 1445}, {1743, 3870}, {3158, 19604}, {6600, 43760}, {8686, 56177}, {16948, 41610}, {17093, 32093}, {56155, 56176}

X(56314) = trilinear pole of line {3309, 4394}
X(56314) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 4859}, {56, 24392}, {58, 21949}
X(56314) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 24392}, {9, 4859}, {10, 21949}
X(56314) = X(i)-cross conjugate of X(j) for these {i, j}: {3669, 100}, {25082, 2}
X(56314) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(145)}}, {{A, B, C, X(2), X(2346)}}, {{A, B, C, X(6), X(1279)}}, {{A, B, C, X(7), X(765)}}, {{A, B, C, X(8), X(54125)}}, {{A, B, C, X(9), X(1280)}}, {{A, B, C, X(21), X(6553)}}, {{A, B, C, X(75), X(55920)}}, {{A, B, C, X(82), X(89)}}, {{A, B, C, X(105), X(39975)}}, {{A, B, C, X(192), X(42720)}}, {{A, B, C, X(346), X(34894)}}, {{A, B, C, X(519), X(14497)}}, {{A, B, C, X(749), X(26745)}}, {{A, B, C, X(943), X(1219)}}, {{A, B, C, X(983), X(1002)}}, {{A, B, C, X(1037), X(1252)}}, {{A, B, C, X(1156), X(36606)}}, {{A, B, C, X(1257), X(7160)}}, {{A, B, C, X(2191), X(40400)}}, {{A, B, C, X(2287), X(56088)}}, {{A, B, C, X(5558), X(55991)}}, {{A, B, C, X(7162), X(43533)}}, {{A, B, C, X(7320), X(40436)}}, {{A, B, C, X(8769), X(55935)}}, {{A, B, C, X(9282), X(41439)}}, {{A, B, C, X(14621), X(17127)}}, {{A, B, C, X(27789), X(40776)}}, {{A, B, C, X(30651), X(34445)}}, {{A, B, C, X(34860), X(56203)}}, {{A, B, C, X(34893), X(39956)}}, {{A, B, C, X(39697), X(55918)}}
X(56314) = barycentric product X(i)*X(j) for these (i, j): {1, 56081}
X(56314) = barycentric quotient X(i)/X(j) for these (i, j): {1, 4859}, {9, 24392}, {37, 21949}, {56081, 75}

X(56315) = X(3)-CEVA CONJUGATE OF X(9)

Barycentrics    a*(a-b-c)*(a^6*(b+c)-b*(b-c)^2*c*(b+c)^3+a^5*(b^2-3*b*c+c^2)-2*a^3*(b-c)^2*(b^2+b*c+c^2)+a*(b^2-c^2)^2*(b^2+b*c+c^2)+a^4*(-2*b^3+b^2*c+b*c^2-2*c^3)+a^2*(b^5-b^4*c-b*c^4+c^5)) : :
X(56315) = -3*X[3158]+2*X[3190]

X(56315) lies on these lines: {1, 856}, {9, 7003}, {40, 376}, {200, 44707}, {212, 56183}, {2900, 3169}, {3158, 3190}, {3185, 3900}, {7125, 13138}, {8270, 9451}, {15829, 44692}

X(56315) = X(i)-Dao conjugate of X(j) for these {i, j}: {318, 264}
X(56315) = X(i)-Ceva conjugate of X(j) for these {i, j}: {3, 9}
X(56315) = barycentric product X(i)*X(j) for these (i, j): {18751, 55}
X(56315) = barycentric quotient X(i)/X(j) for these (i, j): {18751, 6063}
X(56315) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7046, 40945, 9}

X(56316) = KP2(X(9)) OF X(4) AND X(10)

Barycentrics    a*(a-b-c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^3+b^3+c^3-a^2*(b+c)-a*(b^2+b*c+c^2)) : :

X(56316) lies on these lines: {1, 17917}, {4, 2900}, {10, 451}, {19, 3158}, {25, 6600}, {28, 56176}, {29, 4420}, {33, 200}, {92, 3935}, {108, 41539}, {210, 4183}, {278, 3870}, {518, 4219}, {1013, 3681}, {1172, 3694}, {1435, 3243}, {1783, 4849}, {1824, 56183}, {1848, 5853}, {1859, 3689}, {1861, 13405}, {1891, 12437}, {1897, 3896}, {2299, 3939}, {3873, 35994}, {3957, 17923}, {4123, 23600}, {5174, 34772}, {6197, 8715}, {6743, 46878}, {7076, 21805}, {11406, 52804}, {11471, 11523}, {15500, 18391}, {15627, 53013}, {17442, 19589}, {28609, 52840}

X(56316) = X(i)-isoconjugate-of-X(j) for these {i, j}: {222, 37887}, {1014, 43708}, {6598, 7053}
X(56316) = X(i)-Dao conjugate of X(j) for these {i, j}: {8286, 4025}, {23050, 6598}, {35193, 1444}
X(56316) = X(i)-Ceva conjugate of X(j) for these {i, j}: {40445, 9}
X(56316) = intersection, other than A, B, C, of circumconics {{A, B, C, X(33), X(41505)}}, {{A, B, C, X(200), X(56278)}}, {{A, B, C, X(2324), X(15627)}}
X(56316) = barycentric product X(i)*X(j) for these (i, j): {33, 33116}, {281, 34772}, {321, 41503}, {5174, 9}, {13739, 2321}, {15556, 2322}, {37583, 7101}
X(56316) = barycentric quotient X(i)/X(j) for these (i, j): {33, 37887}, {1334, 43708}, {5174, 85}, {7079, 6598}, {13739, 1434}, {33116, 7182}, {34772, 348}, {37583, 7177}, {41503, 81}, {53008, 43683}
X(56316) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {33, 200, 281}

X(56317) = KP2(X(9)) OF X(10) AND X(10)

Barycentrics    a*(a-b-c)*(a^4+a^2*b*c+a*b*c*(b+c)-(b^2-c^2)^2) : :

X(56317) lies on these lines: {1, 442}, {9, 33}, {10, 451}, {25, 16547}, {37, 56178}, {40, 7414}, {42, 17737}, {55, 4516}, {57, 2000}, {78, 4720}, {100, 16577}, {184, 16554}, {191, 1717}, {199, 16553}, {200, 4007}, {210, 52405}, {403, 5587}, {522, 4418}, {612, 1962}, {756, 3939}, {846, 53388}, {936, 37696}, {975, 17581}, {990, 3928}, {1062, 5705}, {1376, 34977}, {1421, 11680}, {1824, 5285}, {1897, 6358}, {2475, 18625}, {3100, 5745}, {3189, 30142}, {3193, 31938}, {3601, 37277}, {3683, 9629}, {3745, 15733}, {3811, 5496}, {3920, 5853}, {4123, 11679}, {4220, 44661}, {4939, 32942}, {5249, 37782}, {5273, 9539}, {5791, 8144}, {6555, 30729}, {6608, 23954}, {6734, 33178}, {7046, 54283}, {7191, 24386}, {9579, 54289}, {9640, 26066}, {9644, 31446}, {9817, 30827}, {16585, 35989}, {17059, 33123}, {18593, 35990}, {18685, 53011}, {21677, 38336}, {25431, 56176}, {28043, 28050}, {28125, 28135}, {40635, 40910}, {46488, 52381}

X(56317) = X(i)-isoconjugate-of-X(j) for these {i, j}: {7, 34435}, {56, 54454}, {269, 56280}
X(56317) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 54454}, {21, 86}, {6600, 56280}
X(56317) = X(i)-Ceva conjugate of X(j) for these {i, j}: {10, 9}, {2475, 1781}, {56316, 2900}
X(56317) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1172), X(7110)}}, {{A, B, C, X(2299), X(7073)}}, {{A, B, C, X(2475), X(4183)}}
X(56317) = barycentric product X(i)*X(j) for these (i, j): {10, 40582}, {37, 52360}, {210, 52361}, {229, 2321}, {281, 52362}, {1781, 8}, {2475, 9}, {18625, 200}, {28754, 33}
X(56317) = barycentric quotient X(i)/X(j) for these (i, j): {9, 54454}, {41, 34435}, {220, 56280}, {229, 1434}, {1781, 7}, {2475, 85}, {18625, 1088}, {28754, 7182}, {40582, 86}, {52360, 274}, {52362, 348}
X(56317) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1824, 5285, 16548}, {2328, 40967, 9}

X(56318) = KP2(X(10)) OF X(1) AND X(8)

Barycentrics    (b+c)*(a^3+b*c*(b+c)-a*(b^2-b*c+c^2)) : :
X(56318) = -3*X[2]+2*X[3670]

X(56318) lies on these lines: {1, 3159}, {2, 3670}, {3, 32933}, {4, 8}, {7, 20336}, {10, 3120}, {21, 190}, {29, 1257}, {34, 28997}, {35, 4427}, {37, 2275}, {65, 3701}, {69, 21594}, {73, 4552}, {75, 3876}, {78, 990}, {100, 53905}, {140, 51583}, {144, 54429}, {145, 2901}, {192, 19767}, {201, 52358}, {213, 22036}, {226, 3710}, {228, 36510}, {238, 17142}, {244, 25079}, {274, 33948}, {312, 3868}, {335, 27097}, {346, 5746}, {350, 17141}, {377, 1265}, {386, 17147}, {404, 32939}, {518, 3702}, {519, 17537}, {595, 20045}, {596, 49997}, {712, 4721}, {726, 1193}, {756, 19874}, {758, 1089}, {894, 25263}, {942, 4358}, {946, 22010}, {960, 4968}, {976, 3923}, {978, 17155}, {982, 25591}, {986, 26030}, {1018, 21067}, {1038, 28968}, {1046, 17763}, {1086, 17674}, {1125, 3989}, {1150, 3927}, {1203, 17150}, {1215, 2292}, {1222, 1320}, {1230, 10974}, {1330, 17484}, {1334, 21101}, {1468, 32935}, {1479, 36500}, {1757, 27368}, {1836, 5300}, {1897, 3194}, {1909, 53332}, {1930, 20347}, {2287, 19848}, {2321, 4101}, {2475, 16086}, {2478, 56084}, {2650, 3994}, {3006, 12047}, {3175, 3241}, {3191, 4511}, {3212, 42711}, {3214, 4090}, {3216, 17495}, {3294, 4115}, {3487, 17776}, {3648, 29301}, {3649, 3932}, {3671, 4082}, {3678, 4647}, {3685, 22012}, {3687, 9569}, {3695, 3936}, {3696, 4005}, {3705, 22000}, {3714, 3962}, {3721, 27040}, {3743, 29822}, {3751, 24077}, {3753, 52353}, {3754, 3992}, {3760, 20247}, {3782, 4202}, {3790, 22008}, {3811, 32929}, {3812, 4009}, {3822, 27690}, {3872, 22027}, {3874, 29824}, {3878, 4692}, {3881, 4975}, {3889, 49499}, {3891, 16466}, {3915, 32920}, {3931, 46897}, {3940, 50044}, {3944, 36568}, {3951, 11679}, {3953, 17154}, {3954, 17794}, {3963, 22076}, {3969, 41014}, {3977, 13411}, {3985, 21808}, {3993, 25295}, {3998, 27383}, {4011, 28082}, {4015, 4714}, {4024, 48304}, {4066, 4067}, {4075, 56191}, {4084, 4125}, {4126, 9710}, {4134, 17163}, {4187, 30566}, {4283, 26971}, {4295, 10327}, {4359, 5044}, {4363, 16454}, {4365, 25294}, {4415, 5051}, {4418, 5293}, {4420, 32932}, {4454, 6904}, {4568, 25244}, {4645, 14450}, {4671, 10449}, {4723, 5836}, {4742, 34791}, {4756, 5260}, {4861, 9369}, {4942, 12635}, {4996, 51255}, {5192, 37549}, {5222, 19791}, {5247, 32938}, {5255, 32927}, {5262, 27064}, {5294, 34937}, {5423, 43214}, {5904, 11330}, {5905, 54433}, {6147, 18139}, {7066, 34388}, {7081, 56288}, {7283, 34772}, {8258, 29683}, {9534, 28605}, {9780, 27538}, {11110, 33761}, {11115, 30115}, {11374, 33113}, {11523, 49687}, {12053, 22031}, {12514, 26227}, {12701, 49688}, {13740, 41242}, {14001, 30884}, {14839, 18101}, {16062, 33151}, {16393, 49721}, {16817, 27065}, {16863, 24594}, {17137, 33931}, {17146, 50190}, {17152, 33941}, {17262, 19765}, {17351, 37539}, {17489, 24514}, {17733, 32912}, {17753, 31130}, {17757, 30449}, {17760, 56024}, {17781, 50215}, {18055, 27109}, {19372, 28996}, {19847, 24167}, {20050, 22034}, {20244, 33937}, {20886, 31835}, {21214, 49532}, {21327, 23447}, {22037, 53343}, {23661, 51379}, {24080, 30114}, {24161, 33115}, {24165, 27627}, {24171, 25881}, {24282, 27801}, {24883, 37759}, {24983, 26611}, {25030, 37829}, {25248, 27020}, {25277, 49474}, {25650, 32849}, {25688, 27102}, {25734, 31424}, {25917, 49483}, {26801, 33888}, {27156, 31323}, {27255, 31063}, {29069, 50702}, {30149, 31023}, {30173, 31041}, {30568, 54392}, {30578, 37162}, {30905, 52012}, {30941, 33939}, {30947, 43220}, {32922, 40085}, {32936, 37573}, {32940, 37607}, {33146, 33833}, {33297, 33775}, {37462, 42697}, {38314, 51673}, {49274, 53336}

X(56318) = reflection of X(i) in X(j) for these {i,j}: {17751, 1089}, {8, 4696}
X(56318) = anticomplement of X(3670)
X(56318) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1408, 44040}
X(56318) = X(i)-Dao conjugate of X(j) for these {i, j}: {3670, 3670}, {4415, 3663}
X(56318) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1222, 10}, {1257, 8}, {40424, 306}
X(56318) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {3453, 1}, {40394, 69}
X(56318) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(4674)}}, {{A, B, C, X(10), X(38462)}}, {{A, B, C, X(92), X(4080)}}
X(56318) = barycentric product X(i)*X(j) for these (i, j): {4, 42705}, {10, 32939}, {37, 44139}, {321, 404}, {3952, 47796}, {4033, 48281}, {20293, 4552}, {21721, 99}, {27801, 44085}
X(56318) = barycentric quotient X(i)/X(j) for these (i, j): {404, 81}, {2321, 44040}, {3952, 56248}, {20293, 4560}, {21721, 523}, {23067, 40518}, {32939, 86}, {42705, 69}, {44085, 1333}, {44139, 274}, {44311, 17197}, {47796, 7192}, {48281, 1019}, {48387, 7252}
X(56318) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3159, 3995}, {65, 3967, 3701}, {756, 49598, 19874}, {758, 1089, 17751}, {982, 25591, 26094}, {986, 32931, 26030}, {1215, 2292, 26115}, {3678, 4647, 4651}, {3869, 4385, 8}, {3952, 17164, 10}, {4115, 22011, 3294}, {17165, 25253, 1}, {19582, 24349, 3616}, {19791, 41249, 5222}, {25248, 31052, 27020}

X(56319) = KP2(X(10)) OF X(4) AND X(9)

Barycentrics    (b+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^3+b*c*(b+c)-a*(b^2-b*c+c^2)) : :

X(56319) lies on these lines: {4, 2901}, {9, 22027}, {19, 17915}, {37, 158}, {71, 42456}, {92, 3995}, {190, 56014}, {225, 2321}, {273, 45744}, {278, 321}, {594, 860}, {1068, 2345}, {1172, 1897}, {1824, 15733}, {1826, 3950}, {1841, 38462}, {1865, 3943}, {1880, 56258}, {1953, 45131}, {3247, 54396}, {3694, 40149}, {4043, 46108}, {4552, 51574}, {5136, 16777}, {5257, 53008}, {5750, 23710}, {17917, 31993}, {17923, 31025}, {34064, 44734}

X(56319) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3737, 40518}
X(56319) = X(i)-Ceva conjugate of X(j) for these {i, j}: {40444, 10}
X(56319) = barycentric product X(i)*X(j) for these (i, j): {4, 56318}, {393, 42705}, {404, 41013}, {1824, 44139}, {1826, 32939}, {21721, 648}
X(56319) = barycentric quotient X(i)/X(j) for these (i, j): {404, 1444}, {4559, 40518}, {21721, 525}, {32939, 17206}, {42705, 3926}, {44085, 1437}, {44311, 17219}, {47796, 15419}, {48387, 23189}, {53008, 44040}, {56318, 69}
X(56319) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {37, 41013, 281}

X(56320) = KP2(X(11)) OF X(1) AND X(2)

Barycentrics    -((b-c)*(a^3-a^2*b+b^3-b*c^2-a*(b+c)^2)*(-a^3+a^2*c+a*(b+c)^2+c*(b^2-c^2))) : :

X(56320) lies on these lines: {448, 525}, {514, 652}, {522, 3465}, {523, 2074}, {647, 17925}, {650, 17924}, {655, 14543}, {666, 54952}, {879, 1175}, {885, 943}, {905, 24002}, {929, 15439}, {2394, 40395}, {2401, 2982}, {2432, 40573}, {3267, 15411}, {3309, 50343}, {4077, 14838}, {4391, 17494}, {14618, 17926}, {14977, 40412}, {26080, 52599}, {32641, 32651}, {37986, 51258}, {40435, 43991}, {52222, 52560}

X(56320) = reflection of X(i) in X(j) for these {i,j}: {17924, 650}, {4077, 14838}
X(56320) = trilinear pole of line {11, 125}
X(56320) = perspector of circumconic {{A, B, C, X(40395), X(40412)}}
X(56320) = X(i)-isoconjugate-of-X(j) for these {i, j}: {63, 53323}, {99, 40978}, {100, 2260}, {101, 942}, {109, 40937}, {110, 2294}, {162, 18591}, {163, 442}, {190, 40956}, {651, 14547}, {653, 23207}, {662, 40952}, {692, 5249}, {906, 1838}, {1020, 8021}, {1252, 50354}, {1331, 1841}, {1415, 6734}, {1783, 4303}, {1813, 1859}, {1865, 4575}, {1897, 14597}, {1983, 45926}, {4551, 46882}, {4559, 54356}, {4565, 40967}, {4574, 46883}, {7012, 52306}, {7045, 33525}, {8750, 18607}, {23067, 46884}
X(56320) = X(i)-Dao conjugate of X(j) for these {i, j}: {11, 40937}, {115, 442}, {125, 18591}, {136, 1865}, {244, 2294}, {661, 50354}, {1015, 942}, {1084, 40952}, {1086, 5249}, {1146, 6734}, {3162, 53323}, {4988, 23752}, {5190, 1838}, {5521, 1841}, {8054, 2260}, {8287, 16585}, {17115, 33525}, {26932, 18607}, {34467, 14597}, {36901, 1234}, {38986, 40978}, {38991, 14547}, {39006, 4303}, {40622, 55010}, {53167, 3824}, {55053, 40956}, {55064, 40967}, {55065, 21675}, {55067, 54356}
X(56320) = X(i)-Ceva conjugate of X(j) for these {i, j}: {54952, 943}
X(56320) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {163, 2894}, {943, 21294}, {1175, 150}, {1794, 13219}, {2259, 3448}, {15439, 2893}
X(56320) = X(i)-cross conjugate of X(j) for these {i, j}: {16732, 2}, {53524, 7}, {53560, 4}
X(56320) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(2752)}}, {{A, B, C, X(104), X(54235)}}, {{A, B, C, X(267), X(279)}}, {{A, B, C, X(277), X(1247)}}, {{A, B, C, X(278), X(3465)}}, {{A, B, C, X(348), X(7040)}}, {{A, B, C, X(513), X(17925)}}, {{A, B, C, X(514), X(522)}}, {{A, B, C, X(523), X(525)}}, {{A, B, C, X(650), X(652)}}, {{A, B, C, X(812), X(29051)}}, {{A, B, C, X(915), X(1814)}}, {{A, B, C, X(1019), X(18108)}}, {{A, B, C, X(1821), X(35145)}}, {{A, B, C, X(2395), X(4705)}}, {{A, B, C, X(2402), X(3309)}}, {{A, B, C, X(2982), X(40447)}}, {{A, B, C, X(3669), X(50344)}}, {{A, B, C, X(4608), X(7372)}}, {{A, B, C, X(6332), X(44426)}}, {{A, B, C, X(40437), X(46102)}}
X(56320) = barycentric product X(i)*X(j) for these (i, j): {11, 54952}, {693, 943}, {1175, 850}, {1794, 46107}, {2259, 3261}, {2982, 4391}, {3267, 40570}, {14775, 69}, {15439, 34387}, {23978, 32651}, {24026, 36048}, {40395, 525}, {40412, 523}, {40422, 513}, {40435, 514}, {40447, 905}, {40573, 6332}, {52560, 7253}
X(56320) = barycentric quotient X(i)/X(j) for these (i, j): {25, 53323}, {244, 50354}, {512, 40952}, {513, 942}, {514, 5249}, {522, 6734}, {523, 442}, {647, 18591}, {649, 2260}, {650, 40937}, {661, 2294}, {663, 14547}, {667, 40956}, {798, 40978}, {850, 1234}, {905, 18607}, {943, 100}, {1175, 110}, {1459, 4303}, {1794, 1331}, {1946, 23207}, {2259, 101}, {2501, 1865}, {2605, 500}, {2982, 651}, {3120, 23752}, {3737, 54356}, {4024, 21675}, {4041, 40967}, {4802, 3824}, {6003, 39772}, {6591, 1841}, {7117, 52306}, {7178, 55010}, {7252, 46882}, {7253, 51978}, {7649, 1838}, {14775, 4}, {14838, 16585}, {14936, 33525}, {15313, 14054}, {15439, 59}, {18344, 1859}, {21789, 8021}, {22383, 14597}, {28473, 41571}, {32651, 1262}, {35057, 31938}, {36048, 7045}, {40395, 648}, {40412, 99}, {40422, 668}, {40435, 190}, {40447, 6335}, {40570, 112}, {40573, 653}, {43925, 46890}, {52560, 4566}, {54244, 1844}, {54952, 4998}

X(56321) = KP2(X(11)) OF X(1) AND X(8)

Barycentrics    (b-c)*(a^2+b^2-b*c-2*c^2-a*(2*b+c))*(a^2-2*b^2-b*c+c^2-a*(b+2*c)) : :
X(56321) = -4*X[21186]+3*X[48242]

X(56321) lies on these lines: {415, 2501}, {522, 17950}, {523, 4833}, {850, 17161}, {3239, 4024}, {4036, 4397}, {4581, 6089}, {4620, 17136}, {17097, 43728}, {21186, 48242}, {23352, 28183}, {28132, 40500}, {36802, 39185}

X(56321) = isogonal conjugate of X(53324)
X(56321) = isotomic conjugate of X(17136)
X(56321) = trilinear pole of line {115, 124}
X(56321) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 53324}, {31, 17136}, {56, 53388}, {108, 22361}, {109, 2646}, {110, 2650}, {163, 17056}, {407, 4575}, {651, 21748}, {692, 3664}, {1331, 40985}, {1333, 22003}, {1415, 5745}, {1576, 18698}, {4565, 21811}, {36050, 37836}, {36059, 40950}
X(56321) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 53388}, {2, 17136}, {3, 53324}, {11, 2646}, {37, 22003}, {115, 17056}, {124, 37836}, {136, 407}, {244, 2650}, {1086, 3664}, {1146, 5745}, {2968, 6737}, {4858, 18698}, {4988, 23755}, {5521, 40985}, {6741, 21677}, {20620, 40950}, {38983, 22361}, {38991, 21748}, {55064, 21811}, {55065, 21674}
X(56321) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {17097, 3448}, {40430, 33650}
X(56321) = X(i)-cross conjugate of X(j) for these {i, j}: {21044, 2}
X(56321) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(17950)}}, {{A, B, C, X(4), X(2695)}}, {{A, B, C, X(158), X(55036)}}, {{A, B, C, X(476), X(523)}}, {{A, B, C, X(513), X(4777)}}, {{A, B, C, X(514), X(28161)}}, {{A, B, C, X(522), X(693)}}, {{A, B, C, X(900), X(28183)}}, {{A, B, C, X(2166), X(38955)}}, {{A, B, C, X(2399), X(4560)}}, {{A, B, C, X(4017), X(50520)}}, {{A, B, C, X(4802), X(28165)}}, {{A, B, C, X(4926), X(28205)}}, {{A, B, C, X(4977), X(28187)}}, {{A, B, C, X(7040), X(54457)}}, {{A, B, C, X(7192), X(7649)}}, {{A, B, C, X(28147), X(28169)}}, {{A, B, C, X(36917), X(44184)}}
X(56321) = barycentric product X(i)*X(j) for these (i, j): {1577, 40430}, {17097, 4391}, {40442, 46110}
X(56321) = barycentric quotient X(i)/X(j) for these (i, j): {2, 17136}, {6, 53324}, {9, 53388}, {10, 22003}, {514, 3664}, {522, 5745}, {523, 17056}, {650, 2646}, {652, 22361}, {661, 2650}, {663, 21748}, {1577, 18698}, {2501, 407}, {3064, 40950}, {3120, 23755}, {3239, 6737}, {3700, 21677}, {4024, 21674}, {4036, 42708}, {4041, 21811}, {6589, 37836}, {6591, 40985}, {17097, 651}, {40430, 662}, {40442, 1813}

X(56322) = KP2(X(11)) OF X(2) AND X(7)

Barycentrics    (b-c)*(a^2+b*(b-c)-a*(2*b+c))*(a^2+c*(-b+c)-a*(b+2*c)) : :

X(56322) lies on these lines: {7, 21127}, {514, 657}, {522, 3935}, {523, 885}, {650, 24002}, {665, 17096}, {666, 4552}, {918, 4560}, {929, 53243}, {1170, 2401}, {1654, 56157}, {3709, 42310}, {4130, 4391}, {4581, 47890}, {6605, 43991}, {17924, 47965}, {28132, 31618}

X(56322) = reflection of X(i) in X(j) for these {i,j}: {24002, 650}, {31605, 14282}, {7, 21127}
X(56322) = trilinear pole of line {11, 116}
X(56322) = perspector of circumconic {{A, B, C, X(21453), X(32008)}}
X(56322) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 35326}, {6, 35338}, {41, 35312}, {56, 35341}, {58, 35310}, {59, 21127}, {100, 1475}, {101, 354}, {109, 1212}, {110, 21808}, {142, 692}, {163, 3925}, {251, 35335}, {651, 2293}, {653, 22079}, {662, 52020}, {664, 20229}, {934, 8012}, {1110, 21104}, {1252, 48151}, {1262, 6608}, {1332, 40983}, {1414, 21795}, {1415, 4847}, {1418, 3939}, {1461, 3059}, {1783, 22053}, {1813, 1827}, {1855, 36059}, {2149, 6362}, {2488, 4564}, {4557, 18164}, {4559, 17194}, {4565, 21039}, {4626, 8551}, {6066, 23599}, {6614, 45791}, {7045, 10581}, {20880, 32739}, {32665, 51463}, {32666, 51384}, {32669, 51416}, {53241, 54325}
X(56322) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 35341}, {3, 35326}, {9, 35338}, {10, 35310}, {11, 1212}, {115, 3925}, {116, 40606}, {244, 21808}, {514, 21104}, {650, 6362}, {661, 48151}, {1015, 354}, {1084, 52020}, {1086, 142}, {1146, 4847}, {2968, 51972}, {3160, 35312}, {4988, 55282}, {6615, 21127}, {8054, 1475}, {14714, 8012}, {17115, 10581}, {20620, 1855}, {35092, 51463}, {35094, 51384}, {35508, 3059}, {38991, 2293}, {39006, 22053}, {39025, 20229}, {40585, 35335}, {40608, 21795}, {40615, 10481}, {40617, 1418}, {40619, 20880}, {40620, 17169}, {40622, 52023}, {40624, 1229}, {40625, 16713}, {55064, 21039}, {55067, 17194}, {55153, 51416}
X(56322) = X(i)-Ceva conjugate of X(j) for these {i, j}: {6606, 2346}
X(56322) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {101, 2890}, {1174, 150}, {2346, 21293}, {6606, 21280}, {10482, 33650}, {53243, 3434}, {55281, 17138}, {56255, 21294}
X(56322) = X(i)-cross conjugate of X(j) for these {i, j}: {1111, 2}, {2310, 7}, {23821, 86}, {24012, 43750}, {24225, 75}, {38347, 1}, {38358, 4}, {38375, 8}, {45743, 314}, {47970, 7192}
X(56322) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(765)}}, {{A, B, C, X(7), X(14189)}}, {{A, B, C, X(330), X(9295)}}, {{A, B, C, X(513), X(4724)}}, {{A, B, C, X(514), X(522)}}, {{A, B, C, X(523), X(918)}}, {{A, B, C, X(650), X(657)}}, {{A, B, C, X(651), X(3737)}}, {{A, B, C, X(665), X(3709)}}, {{A, B, C, X(693), X(2402)}}, {{A, B, C, X(1440), X(42483)}}, {{A, B, C, X(1654), X(54117)}}, {{A, B, C, X(2346), X(31618)}}, {{A, B, C, X(2400), X(4608)}}, {{A, B, C, X(3261), X(56321)}}, {{A, B, C, X(4580), X(14208)}}, {{A, B, C, X(4802), X(28898)}}, {{A, B, C, X(7012), X(9503)}}, {{A, B, C, X(7192), X(10566)}}, {{A, B, C, X(10405), X(36917)}}, {{A, B, C, X(17925), X(47947)}}, {{A, B, C, X(23836), X(25576)}}, {{A, B, C, X(36101), X(54235)}}, {{A, B, C, X(36796), X(43760)}}
X(56322) = barycentric product X(i)*X(j) for these (i, j): {11, 6606}, {1019, 56127}, {1170, 4391}, {1174, 3261}, {1803, 46110}, {2346, 693}, {3120, 55281}, {3676, 56118}, {3900, 42311}, {4998, 56284}, {10482, 52621}, {10509, 3239}, {21453, 522}, {24002, 6605}, {31618, 650}, {32008, 514}, {34387, 53243}, {40443, 44426}, {42310, 4762}, {46107, 47487}, {56157, 7192}, {56255, 7199}
X(56322) = barycentric quotient X(i)/X(j) for these (i, j): {1, 35338}, {6, 35326}, {7, 35312}, {9, 35341}, {11, 6362}, {37, 35310}, {38, 35335}, {244, 48151}, {512, 52020}, {513, 354}, {514, 142}, {522, 4847}, {523, 3925}, {649, 1475}, {650, 1212}, {657, 8012}, {661, 21808}, {663, 2293}, {693, 20880}, {900, 51463}, {918, 51384}, {1019, 18164}, {1086, 21104}, {1170, 651}, {1174, 101}, {1459, 22053}, {1803, 1813}, {1946, 22079}, {2170, 21127}, {2310, 6608}, {2346, 100}, {2804, 51416}, {2826, 41555}, {3022, 6607}, {3063, 20229}, {3064, 1855}, {3120, 55282}, {3239, 51972}, {3261, 1233}, {3271, 2488}, {3309, 15185}, {3669, 1418}, {3676, 10481}, {3709, 21795}, {3737, 17194}, {3900, 3059}, {4041, 21039}, {4130, 45791}, {4391, 1229}, {4444, 53239}, {4560, 16713}, {6362, 6067}, {6548, 53240}, {6586, 40606}, {6605, 644}, {6606, 4998}, {7178, 52023}, {7192, 17169}, {7199, 16708}, {10482, 3939}, {10509, 658}, {10566, 18087}, {14936, 10581}, {17925, 53238}, {18344, 1827}, {21453, 664}, {28292, 41570}, {28473, 41548}, {31618, 4554}, {32008, 190}, {40443, 6516}, {42310, 32041}, {42311, 4569}, {47487, 1331}, {47660, 17672}, {52619, 53236}, {53243, 59}, {53522, 51424}, {55281, 4600}, {56118, 3699}, {56127, 4033}, {56157, 3952}, {56255, 1018}, {56284, 11}
X(56322) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {514, 14282, 31605}

X(56323) = KP2(X(11)) OF X(4) AND X(8)

Barycentrics    (b-c)*(a^2+a*(-2*b+c)+b*(b+c))*(a^2+a*(b-2*c)+c*(b+c)) : :
X(56323) = -3*X[2]+2*X[6615], -4*X[8062]+3*X[27545], -2*X[24457]+3*X[48209], -4*X[44409]+3*X[53361]

X(56323) lies on these lines: {2, 6615}, {513, 4397}, {522, 4318}, {523, 1222}, {649, 3239}, {693, 43932}, {900, 3733}, {901, 3952}, {1476, 43728}, {2475, 39270}, {3120, 40451}, {3287, 23617}, {3572, 56258}, {3737, 11115}, {4374, 43930}, {4391, 30198}, {4418, 50346}, {4459, 40528}, {4579, 32735}, {6362, 56321}, {6613, 35157}, {8062, 27545}, {15150, 17926}, {24457, 48209}, {28217, 50344}, {32017, 43928}, {40446, 53152}, {43923, 44426}, {43931, 47694}, {44409, 53361}

X(56323) = anticomplement of X(6615)
X(56323) = isogonal conjugate of X(23845)
X(56323) = isotomic conjugate of X(21272)
X(56323) = polar conjugate of X(17906)
X(56323) = trilinear pole of line {1015, 1146}
X(56323) = perspector of circumconic {{A, B, C, X(1222), X(32017)}}
X(56323) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 23845}, {6, 21362}, {19, 23113}, {31, 21272}, {32, 21580}, {48, 17906}, {59, 6615}, {100, 1201}, {101, 3752}, {108, 22072}, {109, 3057}, {110, 4642}, {163, 4415}, {190, 20228}, {604, 25268}, {651, 2347}, {662, 21796}, {692, 3663}, {765, 6363}, {1122, 3939}, {1252, 48334}, {1293, 45219}, {1331, 1828}, {1415, 3452}, {1897, 22344}, {2149, 21120}, {4076, 42336}, {4559, 18163}, {4565, 21809}, {6516, 40982}, {24027, 42337}, {26563, 32739}, {32665, 51415}, {34080, 45204}
X(56323) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 21272}, {3, 23845}, {6, 23113}, {9, 21362}, {11, 3057}, {115, 4415}, {244, 4642}, {513, 6363}, {522, 42337}, {650, 21120}, {661, 48334}, {1015, 3752}, {1084, 21796}, {1086, 3663}, {1146, 3452}, {1249, 17906}, {2968, 6736}, {3161, 25268}, {3756, 12640}, {5521, 1828}, {6376, 21580}, {6615, 6615}, {6741, 21031}, {8054, 1201}, {34467, 22344}, {35092, 51415}, {38983, 22072}, {38991, 2347}, {40451, 5836}, {40615, 52563}, {40617, 1122}, {40619, 26563}, {40620, 18600}, {40621, 45204}, {40624, 20895}, {40625, 17183}, {55053, 20228}, {55064, 21809}, {55067, 18163}
X(56323) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1222, 40451}, {6613, 40420}, {8706, 1222}
X(56323) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {1222, 33650}, {1476, 149}, {3451, 4440}, {6613, 3434}, {8706, 3436}, {23617, 37781}, {40420, 150}, {51476, 39351}, {56173, 3448}
X(56323) = X(i)-cross conjugate of X(j) for these {i, j}: {2170, 2}, {4939, 8}, {40451, 1222}, {40528, 23617}
X(56323) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(5205)}}, {{A, B, C, X(4), X(1168)}}, {{A, B, C, X(7), X(82)}}, {{A, B, C, X(84), X(55036)}}, {{A, B, C, X(100), X(3737)}}, {{A, B, C, X(190), X(56322)}}, {{A, B, C, X(513), X(649)}}, {{A, B, C, X(514), X(2403)}}, {{A, B, C, X(522), X(693)}}, {{A, B, C, X(523), X(900)}}, {{A, B, C, X(885), X(46135)}}, {{A, B, C, X(2254), X(3287)}}, {{A, B, C, X(2370), X(36123)}}, {{A, B, C, X(2475), X(10266)}}, {{A, B, C, X(2739), X(8048)}}, {{A, B, C, X(2757), X(40437)}}, {{A, B, C, X(2995), X(3062)}}, {{A, B, C, X(3065), X(38955)}}, {{A, B, C, X(4373), X(7155)}}, {{A, B, C, X(4492), X(27807)}}, {{A, B, C, X(4777), X(4926)}}, {{A, B, C, X(4778), X(6006)}}, {{A, B, C, X(4962), X(28161)}}, {{A, B, C, X(4977), X(28217)}}, {{A, B, C, X(5553), X(54457)}}, {{A, B, C, X(6548), X(7649)}}, {{A, B, C, X(7219), X(10309)}}, {{A, B, C, X(9372), X(26703)}}, {{A, B, C, X(13577), X(34919)}}, {{A, B, C, X(28183), X(28221)}}, {{A, B, C, X(28209), X(39386)}}
X(56323) = barycentric product X(i)*X(j) for these (i, j): {190, 40451}, {1086, 8706}, {1146, 6613}, {1222, 514}, {1261, 24002}, {1476, 4391}, {3261, 51476}, {3451, 35519}, {3676, 52549}, {4560, 56173}, {23617, 693}, {32017, 513}, {40420, 522}, {40446, 6332}, {40528, 4554}, {56190, 7199}, {56258, 7192}
X(56323) = barycentric quotient X(i)/X(j) for these (i, j): {1, 21362}, {2, 21272}, {3, 23113}, {4, 17906}, {6, 23845}, {8, 25268}, {11, 21120}, {75, 21580}, {244, 48334}, {512, 21796}, {513, 3752}, {514, 3663}, {522, 3452}, {523, 4415}, {649, 1201}, {650, 3057}, {652, 22072}, {661, 4642}, {663, 2347}, {667, 20228}, {693, 26563}, {900, 51415}, {1015, 6363}, {1146, 42337}, {1222, 190}, {1261, 644}, {1476, 651}, {2170, 6615}, {3239, 6736}, {3451, 109}, {3667, 45204}, {3669, 1122}, {3676, 52563}, {3700, 21031}, {3737, 18163}, {4041, 21809}, {4391, 20895}, {4394, 45219}, {4459, 28006}, {4521, 12640}, {4534, 14284}, {4560, 17183}, {6591, 1828}, {6613, 1275}, {7192, 18600}, {8706, 1016}, {22383, 22344}, {23617, 100}, {32017, 668}, {40420, 664}, {40446, 653}, {40451, 514}, {40528, 650}, {43931, 27499}, {51476, 101}, {52549, 3699}, {56173, 4552}, {56190, 1018}, {56258, 3952}

X(56324) = X(6)-CEVA CONJUGATE OF X(11)

Barycentrics    (a-b-c)*(b-c)*(-(b*(b-c)^2*c*(b+c))+a^3*(b^2+c^2)-a*(b-c)^2*(b^2+b*c+c^2)) : :

X(56324) lies on these lines: {11, 47394}, {65, 514}, {522, 14310}, {523, 1459}, {650, 784}, {652, 4976}, {663, 56283}, {2530, 40166}, {17102, 21185}, {20358, 23877}, {46393, 48264}

X(56324) = reflection of X(i) in X(j) for these {i,j}: {11, 47394}, {663, 56283}
X(56324) = perspector of circumconic {{A, B, C, X(13478), X(24220)}}
X(56324) = X(i)-Dao conjugate of X(j) for these {i, j}: {34387, 76}
X(56324) = X(i)-Ceva conjugate of X(j) for these {i, j}: {6, 11}
X(56324) = barycentric product X(i)*X(j) for these (i, j): {3737, 40564}, {24220, 522}, {44411, 4560}
X(56324) = barycentric quotient X(i)/X(j) for these (i, j): {23161, 44717}, {24220, 664}, {44411, 4552}

X(56325) = KP2(X(12)) OF X(2) AND X(2)

Barycentrics    a*(a+b-c)*(a-b+c)*(b+c)^2*(a^3-b*c*(b+c)-a*(b^2-b*c+c^2)) : :
X(56325) = -3*X[2]+X[54121]

X(56325) lies on these lines: {2, 54121}, {9, 4559}, {10, 40590}, {12, 15281}, {37, 65}, {44, 21741}, {56, 34261}, {75, 4552}, {226, 40491}, {241, 4032}, {261, 6648}, {478, 958}, {517, 14749}, {570, 8609}, {572, 11998}, {594, 2197}, {674, 41381}, {1214, 6358}, {1415, 38871}, {1880, 56285}, {2092, 40663}, {2277, 24914}, {2321, 51574}, {3666, 3911}, {3950, 40599}, {5433, 17053}, {5750, 40937}, {16578, 21233}, {21061, 37558}, {21078, 22275}, {44671, 52024}

X(56325) = complement of X(54121)
X(56325) = center of circumconic {{A, B, C, X(655), X(4552)}}
X(56325) = X(i)-isoconjugate-of-X(j) for these {i, j}: {21, 53083}, {58, 46880}, {60, 2051}, {284, 20028}, {333, 52150}, {2150, 54121}, {2185, 34434}, {17185, 40453}
X(56325) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 46880}, {12, 2}, {1193, 17185}, {21796, 17183}, {34589, 4560}, {40590, 20028}, {40611, 53083}
X(56325) = X(i)-Ceva conjugate of X(j) for these {i, j}: {2, 12}, {31629, 2975}, {52357, 14973}, {52358, 52357}, {56173, 181}
X(56325) = X(i)-complementary conjugate of X(j) for these {i, j}: {31, 12}, {32, 37662}, {560, 21796}, {572, 141}, {2206, 1193}, {2975, 2887}, {11109, 21243}, {14829, 626}, {17074, 17046}, {20986, 10}, {21061, 21245}, {21173, 21252}, {22118, 18589}, {32739, 4391}, {52139, 3454}
X(56325) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(34278)}}, {{A, B, C, X(12), X(2292)}}, {{A, B, C, X(37), X(21061)}}, {{A, B, C, X(71), X(52139)}}, {{A, B, C, X(75), X(20718)}}, {{A, B, C, X(572), X(2245)}}
X(56325) = barycentric product X(i)*X(j) for these (i, j): {1, 52357}, {10, 37558}, {12, 2975}, {37, 52358}, {572, 6358}, {1441, 52139}, {3952, 51662}, {11109, 201}, {14829, 2171}, {14973, 7}, {17074, 594}, {17496, 21859}, {17751, 65}, {20617, 8}, {20986, 34388}, {21061, 226}
X(56325) = barycentric quotient X(i)/X(j) for these (i, j): {12, 54121}, {37, 46880}, {65, 20028}, {181, 34434}, {572, 2185}, {1400, 53083}, {1402, 52150}, {2171, 2051}, {2975, 261}, {11998, 26856}, {14829, 52379}, {14973, 8}, {17074, 1509}, {17751, 314}, {20617, 7}, {20986, 60}, {21061, 333}, {21859, 56188}, {31629, 31620}, {37558, 86}, {51662, 7192}, {52087, 17185}, {52139, 21}, {52357, 75}, {52358, 274}
X(56325) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {37, 2171, 20616}, {594, 2197, 21859}, {15281, 15282, 12}

X(56326) = X(7)-CEVA CONJUGATE OF X(12)

Barycentrics    (a+b-c)*(a-b+c)*(b+c)^2*(a^2-b*c+a*(b+c)) : :

X(56326) lies on these lines: {7, 31011}, {12, 6058}, {57, 4552}, {65, 2901}, {181, 3027}, {201, 4424}, {209, 22027}, {226, 306}, {389, 517}, {536, 553}, {1211, 22022}, {1708, 54359}, {1825, 49542}, {2051, 52212}, {2099, 48863}, {2245, 22002}, {3666, 3911}, {3982, 4059}, {4605, 6354}, {10473, 36862}, {16609, 20616}, {21853, 22001}, {22014, 53510}, {39579, 56285}, {52357, 52567}

X(56326) = X(i)-isoconjugate-of-X(j) for these {i, j}: {60, 39798}, {284, 39949}, {596, 2150}, {2185, 40148}, {2194, 39747}, {7054, 20615}, {7252, 34594}
X(56326) = X(i)-Dao conjugate of X(j) for these {i, j}: {594, 8}, {1214, 39747}, {40590, 39949}, {56325, 596}
X(56326) = X(i)-Ceva conjugate of X(j) for these {i, j}: {7, 12}
X(56326) = intersection, other than A, B, C, of circumconics {{A, B, C, X(306), X(3293)}}, {{A, B, C, X(2051), X(3936)}}
X(56326) = barycentric product X(i)*X(j) for these (i, j): {12, 4360}, {181, 40087}, {226, 3995}, {1441, 3293}, {4075, 7}, {4129, 4552}, {4605, 47793}, {18140, 2171}, {20949, 21859}, {27808, 51650}, {32911, 6358}, {34388, 595}, {40093, 7235}, {56249, 65}
X(56326) = barycentric quotient X(i)/X(j) for these (i, j): {12, 596}, {65, 39949}, {181, 40148}, {226, 39747}, {595, 60}, {1254, 20615}, {2171, 39798}, {2220, 2150}, {3293, 21}, {3871, 1098}, {3995, 333}, {4075, 8}, {4129, 4560}, {4132, 3737}, {4222, 270}, {4360, 261}, {4551, 34594}, {4552, 37205}, {6358, 40013}, {18140, 52379}, {32911, 2185}, {40087, 18021}, {51650, 3733}, {56249, 314}
X(56326) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2171, 6358, 226}

X(56327) = X(8)-CEVA CONJUGATE OF X(12)

Barycentrics    (a+b-c)*(a-b+c)*(b+c)^2*(a^6-a^5*(b+c)+b*c*(b^2-c^2)^2+a^2*(b^2+c^2)^2-a^4*(2*b^2+b*c+2*c^2)+2*a^3*(b^3+c^3)-a*(b^5-b^4*c-b*c^4+c^5)) : :

X(56327) lies on these lines: {10, 201}, {12, 7314}, {65, 22001}, {78, 4552}, {389, 517}, {516, 1825}, {1713, 40968}, {2171, 8804}, {4605, 7066}, {5750, 40937}, {6796, 23067}, {13411, 16577}, {30147, 48866}, {40965, 41538}

X(56327) = X(i)-Dao conjugate of X(j) for these {i, j}: {6354, 7}
X(56327) = X(i)-Ceva conjugate of X(j) for these {i, j}: {8, 12}
X(56327) = barycentric product X(i)*X(j) for these (i, j): {12, 54107}, {411, 6358}, {1089, 34035}, {1630, 34388}
X(56327) = barycentric quotient X(i)/X(j) for these (i, j): {411, 2185}, {1630, 60}, {34035, 757}, {44087, 2150}, {54107, 261}
X(56327) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {201, 56285, 10}, {15443, 51879, 56326}

X(56328) = KP3(X(1)) OF X(2) AND X(2)

Barycentrics    a*(a^2+2*a*b+b^2+c^2)*(a^2+b^2+2*a*c+c^2) : :

X(56328) lies on these lines: {1, 69}, {6, 63}, {7, 34}, {31, 54404}, {33, 7224}, {42, 52396}, {43, 39977}, {56, 77}, {58, 988}, {75, 1220}, {81, 1474}, {86, 614}, {87, 29821}, {106, 1310}, {141, 5287}, {189, 7129}, {193, 17011}, {269, 7056}, {286, 3673}, {292, 2277}, {320, 977}, {326, 1193}, {386, 56220}, {518, 2334}, {540, 17274}, {579, 2279}, {611, 42019}, {612, 5224}, {942, 969}, {975, 52782}, {979, 18906}, {996, 3875}, {998, 3663}, {1027, 4778}, {1100, 28022}, {1120, 17393}, {1126, 3751}, {1222, 4360}, {1411, 7190}, {1438, 1449}, {1469, 43070}, {2191, 3945}, {2297, 2999}, {2647, 4328}, {2983, 54369}, {2995, 17863}, {3226, 54982}, {3445, 38315}, {3619, 17022}, {3620, 17019}, {3664, 24162}, {3672, 17016}, {3920, 5232}, {3946, 24268}, {4666, 10013}, {5138, 26923}, {5227, 28606}, {5307, 19785}, {5738, 13577}, {6337, 39946}, {10436, 33945}, {16496, 41434}, {16973, 25426}, {17012, 51171}, {17013, 51170}, {17394, 28011}, {18194, 40763}, {18734, 39273}, {18816, 36123}, {27633, 54317}, {32691, 43363}, {34260, 45126}, {36099, 36101}, {36741, 54337}, {37129, 37215}, {37492, 51686}, {37549, 54344}

X(56328) = isogonal conjugate of X(612)
X(56328) = isotomic conjugate of X(4385)
X(56328) = trilinear pole of line {649, 905}
X(56328) = perspector of circumconic {{A, B, C, X(1310), X(37215)}}
X(56328) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 612}, {2, 54416}, {3, 7102}, {4, 7085}, {6, 2345}, {8, 1460}, {9, 2285}, {10, 44119}, {19, 5227}, {25, 54433}, {31, 4385}, {33, 1038}, {37, 2303}, {42, 1010}, {55, 388}, {56, 3974}, {72, 4206}, {99, 50494}, {100, 8678}, {101, 6590}, {110, 48395}, {190, 2484}, {200, 4320}, {210, 5323}, {220, 7365}, {281, 2286}, {480, 7197}, {663, 14594}, {668, 8646}, {692, 2517}, {941, 34261}, {1184, 30701}, {1260, 7103}, {1474, 3610}, {1783, 2522}, {1918, 44154}, {1973, 19799}, {2287, 8898}, {4557, 47844}, {5286, 7123}, {7070, 10375}, {8750, 23874}, {8816, 30706}, {10376, 56182}, {17742, 40184}, {51644, 56183}
X(56328) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 3974}, {2, 4385}, {3, 612}, {6, 5227}, {9, 2345}, {223, 388}, {244, 48395}, {478, 2285}, {1015, 6590}, {1086, 2517}, {6337, 19799}, {6505, 54433}, {6609, 4320}, {8054, 8678}, {15487, 5286}, {26932, 23874}, {32664, 54416}, {34021, 44154}, {36033, 7085}, {36103, 7102}, {38986, 50494}, {39006, 2522}, {40589, 2303}, {40592, 1010}, {51574, 3610}, {55053, 2484}
X(56328) = X(i)-cross conjugate of X(j) for these {i, j}: {1036, 2339}, {1245, 2221}, {1468, 57}, {3803, 100}, {17017, 1}, {37492, 39273}, {37592, 2}
X(56328) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(6)}}, {{A, B, C, X(2), X(1014)}}, {{A, B, C, X(7), X(63)}}, {{A, B, C, X(9), X(82)}}, {{A, B, C, X(19), X(256)}}, {{A, B, C, X(33), X(23868)}}, {{A, B, C, X(37), X(9348)}}, {{A, B, C, X(42), X(614)}}, {{A, B, C, X(43), X(29821)}}, {{A, B, C, X(57), X(75)}}, {{A, B, C, X(60), X(78)}}, {{A, B, C, X(65), X(988)}}, {{A, B, C, X(66), X(79)}}, {{A, B, C, X(80), X(43726)}}, {{A, B, C, X(84), X(2363)}}, {{A, B, C, X(89), X(4373)}}, {{A, B, C, X(105), X(941)}}, {{A, B, C, X(222), X(326)}}, {{A, B, C, X(264), X(7249)}}, {{A, B, C, X(284), X(56098)}}, {{A, B, C, X(309), X(9311)}}, {{A, B, C, X(350), X(1428)}}, {{A, B, C, X(513), X(2214)}}, {{A, B, C, X(518), X(1449)}}, {{A, B, C, X(524), X(15309)}}, {{A, B, C, X(674), X(29186)}}, {{A, B, C, X(749), X(39959)}}, {{A, B, C, X(765), X(9452)}}, {{A, B, C, X(893), X(1716)}}, {{A, B, C, X(903), X(39980)}}, {{A, B, C, X(904), X(1974)}}, {{A, B, C, X(1036), X(1039)}}, {{A, B, C, X(1088), X(8809)}}, {{A, B, C, X(1100), X(3751)}}, {{A, B, C, X(1106), X(1193)}}, {{A, B, C, X(1169), X(3415)}}, {{A, B, C, X(1245), X(1472)}}, {{A, B, C, X(1246), X(2481)}}, {{A, B, C, X(1258), X(40422)}}, {{A, B, C, X(1268), X(8056)}}, {{A, B, C, X(1390), X(39956)}}, {{A, B, C, X(1439), X(3673)}}, {{A, B, C, X(1509), X(40405)}}, {{A, B, C, X(2160), X(4492)}}, {{A, B, C, X(2298), X(9309)}}, {{A, B, C, X(2339), X(30479)}}, {{A, B, C, X(2991), X(25417)}}, {{A, B, C, X(2997), X(20028)}}, {{A, B, C, X(3062), X(56139)}}, {{A, B, C, X(3296), X(17040)}}, {{A, B, C, X(3422), X(34207)}}, {{A, B, C, X(3551), X(13610)}}, {{A, B, C, X(3737), X(56225)}}, {{A, B, C, X(4570), X(34183)}}, {{A, B, C, X(5486), X(5557)}}, {{A, B, C, X(5559), X(38005)}}, {{A, B, C, X(5561), X(15321)}}, {{A, B, C, X(6391), X(7100)}}, {{A, B, C, X(7121), X(9288)}}, {{A, B, C, X(7163), X(43725)}}, {{A, B, C, X(7167), X(43096)}}, {{A, B, C, X(7177), X(19611)}}, {{A, B, C, X(10435), X(14616)}}, {{A, B, C, X(19604), X(39704)}}, {{A, B, C, X(25430), X(39979)}}, {{A, B, C, X(28476), X(46010)}}, {{A, B, C, X(32085), X(52133)}}, {{A, B, C, X(36603), X(55955)}}, {{A, B, C, X(39717), X(39970)}}, {{A, B, C, X(41441), X(55927)}}, {{A, B, C, X(43664), X(47647)}}
X(56328) = barycentric product X(i)*X(j) for these (i, j): {304, 51686}, {1036, 85}, {1039, 348}, {1245, 274}, {1310, 514}, {1472, 76}, {2221, 75}, {2281, 310}, {2339, 7}, {10436, 34260}, {15413, 32691}, {30479, 57}, {36099, 4025}, {37215, 513}, {54982, 649}, {56219, 86}
X(56328) = barycentric quotient X(i)/X(j) for these (i, j): {1, 2345}, {2, 4385}, {3, 5227}, {6, 612}, {9, 3974}, {19, 7102}, {31, 54416}, {48, 7085}, {56, 2285}, {57, 388}, {58, 2303}, {63, 54433}, {69, 19799}, {72, 3610}, {81, 1010}, {222, 1038}, {269, 7365}, {274, 44154}, {513, 6590}, {514, 2517}, {603, 2286}, {604, 1460}, {614, 5286}, {649, 8678}, {651, 14594}, {661, 48395}, {667, 2484}, {738, 7197}, {798, 50494}, {905, 23874}, {1019, 47844}, {1036, 9}, {1039, 281}, {1042, 8898}, {1245, 37}, {1310, 190}, {1333, 44119}, {1407, 4320}, {1412, 5323}, {1435, 7103}, {1459, 2522}, {1468, 34261}, {1472, 6}, {1474, 4206}, {1919, 8646}, {2221, 1}, {2281, 42}, {2339, 8}, {3942, 26933}, {7289, 7386}, {30479, 312}, {32691, 1783}, {34260, 31359}, {36099, 1897}, {37215, 668}, {51686, 19}, {54982, 1978}, {56219, 10}
X(56328) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2221, 56219, 2339}

X(56329) = KP3(X(1)) OF X(6) AND X(6)

Barycentrics    a*(2*a*b^2*c+b^2*c^2+a^2*(b^2+c^2))*(2*a*b*c^2+b^2*c^2+a^2*(b^2+c^2)) : :

X(56329) lies on these lines: {1, 1197}, {2, 1740}, {31, 1258}, {57, 50661}, {81, 18194}, {274, 18169}, {330, 21352}, {614, 40738}, {3009, 39738}, {10458, 56066}, {11328, 39970}, {18192, 39950}, {21001, 45223}, {26102, 32020}, {30701, 40790}

X(56329) = trilinear pole of line {23572, 513}
X(56329) = X(i)-cross conjugate of X(j) for these {i, j}: {31997, 87}
X(56329) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(25), X(40763)}}, {{A, B, C, X(31), X(87)}}, {{A, B, C, X(43), X(3112)}}, {{A, B, C, X(85), X(9285)}}, {{A, B, C, X(86), X(1613)}}, {{A, B, C, X(238), X(56046)}}, {{A, B, C, X(256), X(54128)}}, {{A, B, C, X(614), X(40790)}}, {{A, B, C, X(694), X(56328)}}, {{A, B, C, X(727), X(43531)}}, {{A, B, C, X(741), X(1472)}}, {{A, B, C, X(743), X(7166)}}, {{A, B, C, X(870), X(893)}}, {{A, B, C, X(1621), X(18192)}}, {{A, B, C, X(2258), X(2665)}}, {{A, B, C, X(3009), X(26102)}}, {{A, B, C, X(3226), X(39967)}}, {{A, B, C, X(5560), X(30505)}}, {{A, B, C, X(5561), X(55028)}}, {{A, B, C, X(7303), X(40746)}}, {{A, B, C, X(9315), X(40737)}}, {{A, B, C, X(30650), X(38275)}}, {{A, B, C, X(36614), X(55919)}}
X(56329) = barycentric product X(i)*X(j) for these (i, j): {56211, 81}, {56240, 86}
X(56329) = barycentric quotient X(i)/X(j) for these (i, j): {56211, 321}, {56240, 10}

X(56330) = KP3(X(1)) OF X(7) AND X(7)

Barycentrics    a*(a^4-2*a^3*(2*b+c)+(b-c)^2*(b^2+c^2)+2*a^2*(3*b^2+b*c+c^2)-2*a*(2*b^3-b^2*c-2*b*c^2+c^3))*(a^4-2*a^3*(b+2*c)+(b-c)^2*(b^2+c^2)+2*a^2*(b^2+b*c+3*c^2)-2*a*(b^3-2*b^2*c-b*c^2+2*c^3)) : :

X(56330) lies on these lines: {1, 17093}, {33, 10578}, {55, 1445}, {200, 344}, {220, 3870}, {2328, 41610}, {2332, 4233}, {4319, 21453}, {4666, 17044}, {7675, 52013}

X(56330) = trilinear pole of line {657, 3309}
X(56330) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(33)}}, {{A, B, C, X(2), X(2346)}}, {{A, B, C, X(7), X(6605)}}, {{A, B, C, X(9), X(1088)}}, {{A, B, C, X(78), X(10578)}}, {{A, B, C, X(241), X(10389)}}, {{A, B, C, X(1280), X(7320)}}, {{A, B, C, X(3477), X(56328)}}, {{A, B, C, X(7162), X(43672)}}, {{A, B, C, X(17097), X(56088)}}, {{A, B, C, X(31359), X(39959)}}

X(56331) = KP3(X(1)) OF X(7) AND X(9)

Barycentrics    (a+b-c)*(a-b+c)*(3*a^2+3*b^2-2*b*c-c^2-2*a*(3*b+c))*(3*a^2-b^2-2*b*c+3*c^2-2*a*(b+3*c)) : :

X(56331) lies on these lines: {1, 36620}, {2, 5543}, {7, 165}, {226, 55937}, {479, 37703}, {673, 5226}, {1088, 3160}, {3475, 3599}, {3616, 56074}, {4323, 7249}, {4373, 40719}, {5435, 27475}, {5936, 7190}, {9436, 30712}, {11019, 38254}, {31527, 31721}, {55082, 56026}

X(56331) = X(i)-isoconjugate-of-X(j) for these {i, j}: {55, 10980}
X(56331) = X(i)-Dao conjugate of X(j) for these {i, j}: {223, 10980}
X(56331) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(165)}}, {{A, B, C, X(2), X(7)}}, {{A, B, C, X(8), X(13405)}}, {{A, B, C, X(200), X(2346)}}, {{A, B, C, X(1458), X(39967)}}, {{A, B, C, X(3616), X(7091)}}, {{A, B, C, X(5556), X(43672)}}, {{A, B, C, X(6605), X(55920)}}, {{A, B, C, X(7045), X(25417)}}, {{A, B, C, X(7056), X(52351)}}, {{A, B, C, X(7320), X(14942)}}, {{A, B, C, X(17097), X(39959)}}, {{A, B, C, X(25430), X(43736)}}, {{A, B, C, X(39391), X(40141)}}
X(56331) = barycentric quotient X(i)/X(j) for these (i, j): {57, 10980}

X(56332) = KP3(X(2)) OF X(1) AND X(1)

Barycentrics    (2*a*b^2*c+b^2*c^2+a^2*(b^2+c^2))*(2*a*b*c^2+b^2*c^2+a^2*(b^2+c^2)) : :

X(56332) lies on these lines: {2, 1740}, {6, 40418}, {7, 1424}, {8, 39745}, {10, 56247}, {75, 194}, {310, 16738}, {384, 20992}, {1268, 26042}, {1575, 56212}, {2296, 17379}, {3741, 53147}, {6384, 21264}, {16571, 16819}, {17157, 27494}, {17178, 39734}, {17277, 32011}, {17349, 56166}, {17792, 20139}, {19591, 39741}, {20028, 26802}, {25528, 26959}, {27145, 31002}, {27164, 56052}, {27188, 31241}

X(56332) = trilinear pole of line {50510, 50516}
X(56332) = X(i)-cross conjugate of X(j) for these {i, j}: {17030, 2}, {56240, 56329}
X(56332) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(7)}}, {{A, B, C, X(6), X(330)}}, {{A, B, C, X(87), X(194)}}, {{A, B, C, X(192), X(308)}}, {{A, B, C, X(256), X(2998)}}, {{A, B, C, X(513), X(1218)}}, {{A, B, C, X(751), X(38262)}}, {{A, B, C, X(941), X(39925)}}, {{A, B, C, X(1221), X(3551)}}, {{A, B, C, X(1964), X(30651)}}, {{A, B, C, X(2221), X(37128)}}, {{A, B, C, X(3227), X(39972)}}, {{A, B, C, X(6063), X(9229)}}, {{A, B, C, X(7123), X(20992)}}, {{A, B, C, X(7241), X(39968)}}, {{A, B, C, X(9309), X(54117)}}, {{A, B, C, X(14377), X(40409)}}, {{A, B, C, X(34248), X(51974)}}, {{A, B, C, X(36598), X(36871)}}, {{A, B, C, X(38247), X(40433)}}, {{A, B, C, X(39694), X(39971)}}
X(56332) = barycentric product X(i)*X(j) for these (i, j): {274, 56240}, {56211, 86}, {56329, 75}
X(56332) = barycentric quotient X(i)/X(j) for these (i, j): {56211, 10}, {56240, 37}, {56329, 1}

X(56333) = KP3(X(2)) OF X(1) AND X(6)

Barycentrics    (a^2*b^3*c+a*b^3*c^2+b^3*c^3+a^3*(b^3+c^3))*(a^2*b*c^3+a*b^2*c^3+b^3*c^3+a^3*(b^3+c^3)) : :

X(56333) lies on these lines: {2, 40935}, {75, 16584}, {310, 2275}, {675, 773}, {2296, 18278}, {6384, 26959}, {8049, 26973}, {17030, 56052}, {17750, 40418}, {26974, 56166}, {27158, 31002}

X(56333) = X(i)-isoconjugate-of-X(j) for these {i, j}: {692, 772}
X(56333) = X(i)-Dao conjugate of X(j) for these {i, j}: {1086, 772}
X(56333) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(7)}}, {{A, B, C, X(274), X(2162)}}, {{A, B, C, X(308), X(3223)}}, {{A, B, C, X(2275), X(16584)}}, {{A, B, C, X(32020), X(39967)}}
X(56333) = barycentric product X(i)*X(j) for these (i, j): {3261, 773}
X(56333) = barycentric quotient X(i)/X(j) for these (i, j): {514, 772}, {773, 101}, {3261, 35554}

X(56334) = KP3(X(2)) OF X(4) AND X(4)

Barycentrics    (a^4+5*b^4-2*b^2*c^2+c^4-2*a^2*(b^2-c^2))*(a^4+b^4-2*b^2*c^2+5*c^4+2*a^2*(b^2-c^2)) : :

X(56334) lies on these lines: {69, 5254}, {95, 32990}, {253, 5025}, {264, 32972}, {393, 40413}, {1799, 37667}, {6340, 7778}, {8797, 32988}, {9229, 33180}, {11382, 37174}, {32971, 41762}, {33040, 40412}, {33200, 35510}

X(56334) = trilinear pole of line {12075, 525}
X(56334) = isotomic conjugate of X(32973)
X(56334) = X(i)-cross conjugate of X(j) for these {i, j}: {14064, 2}
X(56334) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(69)}}, {{A, B, C, X(76), X(6392)}}, {{A, B, C, X(193), X(42407)}}, {{A, B, C, X(230), X(40429)}}, {{A, B, C, X(393), X(1502)}}, {{A, B, C, X(1916), X(52223)}}, {{A, B, C, X(2987), X(22263)}}, {{A, B, C, X(5395), X(8801)}}, {{A, B, C, X(6339), X(9307)}}, {{A, B, C, X(8781), X(17040)}}, {{A, B, C, X(17983), X(43681)}}, {{A, B, C, X(32085), X(38259)}}, {{A, B, C, X(51316), X(54122)}}, {{A, B, C, X(52395), X(53101)}}
X(56334) = barycentric quotient X(i)/X(j) for these (i, j): {2, 32973}

X(56335) = KP3(X(2)) OF X(7) AND X(7)

Barycentrics    (a^2-2*a*b+5*b^2+2*a*c-2*b*c+c^2)*(a^2+b^2+2*a*(b-c)-2*b*c+5*c^2) : :

X(56335) lies on these lines: {2, 52528}, {8, 3663}, {144, 17743}, {279, 40420}, {312, 26563}, {333, 18600}, {1220, 7195}, {1311, 6571}, {3008, 56201}, {3662, 10405}, {6557, 17284}, {9965, 40394}, {12541, 56088}, {21454, 56046}, {27184, 56086}, {31359, 43037}, {41824, 51351}

X(56335) = trilinear pole of line {23813, 522}
X(56335) = X(i)-isoconjugate-of-X(j) for these {i, j}: {41, 4308}, {692, 43061}, {1415, 8710}
X(56335) = X(i)-Dao conjugate of X(j) for these {i, j}: {1086, 43061}, {1146, 8710}, {3160, 4308}
X(56335) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(8)}}, {{A, B, C, X(76), X(279)}}, {{A, B, C, X(145), X(30701)}}, {{A, B, C, X(277), X(43533)}}, {{A, B, C, X(514), X(1219)}}, {{A, B, C, X(1434), X(36606)}}, {{A, B, C, X(2996), X(55937)}}, {{A, B, C, X(5485), X(14377)}}, {{A, B, C, X(6553), X(9311)}}, {{A, B, C, X(6650), X(43681)}}
X(56335) = barycentric product X(i)*X(j) for these (i, j): {35519, 6571}, {56199, 85}
X(56335) = barycentric quotient X(i)/X(j) for these (i, j): {7, 4308}, {514, 43061}, {522, 8710}, {6571, 109}, {56199, 9}

X(56336) = KP3(X(3)) OF X(1) AND X(3)

Barycentrics    a^2*(a^2-b^2-c^2)*(2*a^3+2*b^3-b^2*c-2*b*c^2+c^3-a^2*(2*b+c)-2*a*(b^2+c^2))*(2*a^3+b^3-2*b^2*c-b*c^2+2*c^3-a^2*(b+2*c)-2*a*(b^2+c^2)) : :

X(56336) lies on these lines: {1, 6875}, {29, 5705}, {165, 56148}, {255, 40442}, {945, 11012}, {1037, 36152}, {1057, 26357}, {1059, 37579}, {1069, 45231}, {1807, 26921}, {3422, 14794}, {3679, 10570}, {3731, 56225}, {5010, 52185}, {7100, 54320}

X(56336) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 31266}
X(56336) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 31266}
X(56336) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3)}}, {{A, B, C, X(80), X(34259)}}, {{A, B, C, X(90), X(7092)}}, {{A, B, C, X(271), X(15910)}}, {{A, B, C, X(1437), X(2163)}}, {{A, B, C, X(1444), X(15446)}}, {{A, B, C, X(1790), X(39980)}}, {{A, B, C, X(1792), X(15175)}}, {{A, B, C, X(5561), X(34800)}}
X(56336) = barycentric product X(i)*X(j) for these (i, j): {3, 56062}, {56027, 63}
X(56336) = barycentric quotient X(i)/X(j) for these (i, j): {3, 31266}, {56027, 92}, {56062, 264}

X(56337) = KP3(X(3)) OF X(2) AND X(2)

Barycentrics    a^2*(a^2-b^2-c^2)*(a^8-2*a^6*(2*b^2+c^2)+(b^2-c^2)^2*(b^4+c^4)+2*a^4*(3*b^4+b^2*c^2+c^4)-2*a^2*(2*b^6-b^4*c^2-2*b^2*c^4+c^6))*(a^8-2*a^6*(b^2+2*c^2)+(b^2-c^2)^2*(b^4+c^4)+2*a^4*(b^4+b^2*c^2+3*c^4)-2*a^2*(b^6-2*b^4*c^2-b^2*c^4+2*c^6)) : :

X(56337) lies on these lines: {3, 317}, {69, 16391}, {95, 426}, {264, 40448}, {418, 56307}, {577, 1993}, {1092, 9723}, {1105, 46724}, {6394, 44149}, {34385, 41009}, {36748, 51776}

X(56337) = trilinear pole of line {32320, 52584}
X(56337) = X(i)-isoconjugate-of-X(j) for these {i, j}: {158, 6641}, {2181, 19179}
X(56337) = X(i)-Dao conjugate of X(j) for these {i, j}: {1147, 6641}
X(56337) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(95)}}, {{A, B, C, X(69), X(97)}}, {{A, B, C, X(264), X(394)}}, {{A, B, C, X(511), X(34817)}}, {{A, B, C, X(1073), X(40410)}}, {{A, B, C, X(3425), X(14533)}}, {{A, B, C, X(8797), X(14919)}}, {{A, B, C, X(31626), X(36948)}}, {{A, B, C, X(36609), X(55958)}}, {{A, B, C, X(43725), X(51444)}}
X(56337) = barycentric quotient X(i)/X(j) for these (i, j): {97, 19179}, {577, 6641}

X(56338) = KP3(X(3)) OF X(2) AND X(3)

Barycentrics    a^2*(a^2-b^2-c^2)*(2*a^4+2*b^4-3*b^2*c^2+c^4-a^2*(4*b^2+3*c^2))*(2*a^4+b^4-3*b^2*c^2+2*c^4-a^2*(3*b^2+4*c^2)) : :

X(56338) lies on these lines: {2, 10985}, {3, 1199}, {4, 14938}, {22, 14489}, {276, 51350}, {394, 44180}, {577, 31626}, {631, 22268}, {1214, 23958}, {1217, 3522}, {3346, 21734}, {3523, 22270}, {5422, 36748}, {6636, 40801}, {14941, 26874}, {15692, 46412}, {18317, 19708}, {22352, 54032}, {34287, 56302}, {37872, 43768}, {43988, 54114}, {46832, 56266}

X(56338) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 1656}, {92, 15004}, {158, 10979}, {1953, 4994}
X(56338) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 1656}, {1147, 10979}, {22391, 15004}
X(56338) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(3)}}, {{A, B, C, X(4), X(1199)}}, {{A, B, C, X(69), X(1994)}}, {{A, B, C, X(74), X(8796)}}, {{A, B, C, X(184), X(1383)}}, {{A, B, C, X(248), X(39955)}}, {{A, B, C, X(275), X(3431)}}, {{A, B, C, X(287), X(56072)}}, {{A, B, C, X(459), X(20421)}}, {{A, B, C, X(577), X(22052)}}, {{A, B, C, X(1795), X(25417)}}, {{A, B, C, X(1993), X(2996)}}, {{A, B, C, X(2052), X(11270)}}, {{A, B, C, X(2987), X(34817)}}, {{A, B, C, X(4846), X(11538)}}, {{A, B, C, X(6504), X(55999)}}, {{A, B, C, X(9289), X(11140)}}, {{A, B, C, X(13452), X(39284)}}, {{A, B, C, X(13582), X(42021)}}, {{A, B, C, X(34386), X(40393)}}, {{A, B, C, X(41895), X(55978)}}, {{A, B, C, X(51336), X(51477)}}
X(56338) = barycentric product X(i)*X(j) for these (i, j): {13472, 69}
X(56338) = barycentric quotient X(i)/X(j) for these (i, j): {3, 1656}, {54, 4994}, {184, 15004}, {577, 10979}, {13472, 4}

X(56339) = KP3(X(3)) OF X(2) AND X(6)

Barycentrics    (a^2-b^2-c^2)*(a^4-6*a^2*b^2+b^4-c^4)*(a^4-b^4-6*a^2*c^2+c^4) : :

X(56339) lies on these lines: {2, 22401}, {3, 193}, {4, 14489}, {20, 40801}, {185, 54032}, {394, 6337}, {439, 577}, {1073, 37188}, {1217, 43981}, {1297, 3522}, {1368, 2996}, {1578, 6462}, {1579, 6463}, {3164, 3346}, {3538, 31859}, {5013, 11433}, {5481, 15717}, {6225, 54961}, {6527, 54114}, {7404, 14938}, {17974, 43652}, {26206, 32973}, {32982, 35142}

X(56339) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 5020}, {31, 43981}
X(56339) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 43981}, {6, 5020}
X(56339) = X(i)-cross conjugate of X(j) for these {i, j}: {40680, 2}
X(56339) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(3)}}, {{A, B, C, X(4), X(14912)}}, {{A, B, C, X(68), X(38259)}}, {{A, B, C, X(69), X(193)}}, {{A, B, C, X(78), X(54123)}}, {{A, B, C, X(248), X(52223)}}, {{A, B, C, X(253), X(9290)}}, {{A, B, C, X(287), X(5395)}}, {{A, B, C, X(441), X(3522)}}, {{A, B, C, X(525), X(34380)}}, {{A, B, C, X(3053), X(40323)}}, {{A, B, C, X(4846), X(18845)}}, {{A, B, C, X(5013), X(36748)}}, {{A, B, C, X(6390), X(52898)}}, {{A, B, C, X(11270), X(52583)}}, {{A, B, C, X(14642), X(43718)}}, {{A, B, C, X(15077), X(41895)}}, {{A, B, C, X(31371), X(53101)}}, {{A, B, C, X(34403), X(42313)}}, {{A, B, C, X(40319), X(51336)}}
X(56339) = barycentric product X(i)*X(j) for these (i, j): {17040, 69}
X(56339) = barycentric quotient X(i)/X(j) for these (i, j): {2, 43981}, {3, 5020}, {17040, 4}

X(56340) = KP3(X(4)) OF X(2) AND X(2)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^8+5*b^8-4*a^6*c^2-8*b^6*c^2+2*b^4*c^4+c^8+2*a^4*(b^4+3*c^4)-4*a^2*(2*b^6-3*b^4*c^2+c^6))*(a^8-4*a^6*b^2+b^8+2*b^4*c^4-8*b^2*c^6+5*c^8+2*a^4*(3*b^4+c^4)-4*a^2*(b^6-3*b^2*c^4+2*c^6)) : :

X(56340) lies on these lines: {4, 6527}, {69, 1105}, {264, 6619}, {317, 18848}, {393, 13567}, {1093, 44131}, {1217, 32000}, {6389, 40402}, {6618, 40680}, {8884, 18909}, {18850, 32001}, {34208, 52249}

X(56340) = X(i)-isoconjugate-of-X(j) for these {i, j}: {255, 6618}
X(56340) = X(i)-Dao conjugate of X(j) for these {i, j}: {6523, 6618}
X(56340) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(93)}}, {{A, B, C, X(69), X(459)}}, {{A, B, C, X(95), X(38253)}}, {{A, B, C, X(253), X(2052)}}, {{A, B, C, X(1249), X(44556)}}, {{A, B, C, X(8795), X(36889)}}, {{A, B, C, X(22263), X(43717)}}
X(56340) = barycentric quotient X(i)/X(j) for these (i, j): {393, 6618}

X(56341) = KP3(X(4)) OF X(4) AND X(6)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(2*b^2*c^2*(b^2-c^2)^2+a^6*(2*b^2+c^2)-2*a^4*(2*b^4+b^2*c^2+c^4)+a^2*(2*b^6-b^4*c^2-2*b^2*c^4+c^6))*(2*b^2*c^2*(b^2-c^2)^2+a^6*(b^2+2*c^2)-2*a^4*(b^4+b^2*c^2+2*c^4)+a^2*(b^6-2*b^4*c^2-b^2*c^4+2*c^6)) : :

X(56341) lies on the Jerabek hyperbola and on these lines: {3, 14767}, {4, 15649}, {6, 42400}, {25, 50446}, {53, 43718}, {54, 19212}, {1176, 52253}, {1853, 8612}, {3527, 8887}, {9969, 38449}, {13472, 41204}

X(56341) = isogonal conjugate of X(26874)
X(56341) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(4)}}, {{A, B, C, X(51), X(42487)}}, {{A, B, C, X(53), X(264)}}, {{A, B, C, X(275), X(45838)}}, {{A, B, C, X(2052), X(3613)}}, {{A, B, C, X(2980), X(40402)}}, {{A, B, C, X(8796), X(8801)}}, {{A, B, C, X(43530), X(53864)}}
X(56341) = barycentric quotient X(i)/X(j) for these (i, j): {6, 26874}

X(56342) = KP3(X(6)) OF X(1) AND X(2)

Barycentrics    a^2*(a^3+a^2*b+a*b^2+b^3+c^3)*(a^3+b^3+a^2*c+a*c^2+c^3) : :

X(56342) lies on these lines: {6, 977}, {31, 579}, {81, 3662}, {604, 2172}, {608, 8743}, {739, 833}, {1333, 2275}, {2214, 4645}, {2221, 3218}, {2298, 17750}, {2300, 56003}, {5749, 40401}, {32911, 40406}

X(56342) = isogonal conjugate of X(32777)
X(56342) = trilinear pole of line {667, 43060}
X(56342) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 32777}, {2, 976}, {63, 5090}, {75, 2273}, {100, 48300}, {190, 832}, {306, 17520}, {1978, 8636}, {7033, 22398}
X(56342) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 32777}, {206, 2273}, {3162, 5090}, {8054, 48300}, {32664, 976}, {55053, 832}
X(56342) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(1474)}}, {{A, B, C, X(6), X(31)}}, {{A, B, C, X(7), X(58)}}, {{A, B, C, X(9), X(40188)}}, {{A, B, C, X(19), X(251)}}, {{A, B, C, X(56), X(1257)}}, {{A, B, C, X(57), X(1169)}}, {{A, B, C, X(69), X(9309)}}, {{A, B, C, X(75), X(3415)}}, {{A, B, C, X(88), X(46010)}}, {{A, B, C, X(513), X(9021)}}, {{A, B, C, X(593), X(2215)}}, {{A, B, C, X(937), X(1041)}}, {{A, B, C, X(941), X(1438)}}, {{A, B, C, X(1172), X(8743)}}, {{A, B, C, X(1244), X(2997)}}, {{A, B, C, X(1400), X(2275)}}, {{A, B, C, X(1412), X(2983)}}, {{A, B, C, X(1798), X(3450)}}, {{A, B, C, X(2189), X(39943)}}, {{A, B, C, X(2259), X(30650)}}, {{A, B, C, X(2285), X(3218)}}, {{A, B, C, X(6186), X(45988)}}, {{A, B, C, X(8752), X(39955)}}, {{A, B, C, X(9372), X(36058)}}, {{A, B, C, X(37741), X(38813)}}
X(56342) = barycentric product X(i)*X(j) for these (i, j): {1, 977}, {513, 833}
X(56342) = barycentric quotient X(i)/X(j) for these (i, j): {6, 32777}, {25, 5090}, {31, 976}, {32, 2273}, {649, 48300}, {667, 832}, {833, 668}, {977, 75}, {1980, 8636}, {2203, 17520}

X(56343) = KP3(X(6)) OF X(1) AND X(6)

Barycentrics    a^2*(2*a+2*b+c)*(2*a+b+2*c) : :

X(56343) lies on these lines: {1, 2308}, {6, 35}, {10, 30590}, {31, 1126}, {34, 3339}, {43, 39748}, {56, 1203}, {57, 52372}, {58, 5313}, {60, 55088}, {86, 3624}, {87, 3216}, {106, 1468}, {238, 10013}, {255, 13404}, {292, 7296}, {595, 41434}, {849, 52558}, {870, 32092}, {939, 54301}, {978, 39949}, {979, 3293}, {996, 3632}, {1027, 48074}, {1171, 17104}, {1193, 2163}, {1220, 3679}, {1222, 3633}, {1411, 3340}, {1698, 5278}, {2191, 16469}, {2334, 3295}, {3017, 18514}, {3226, 32042}, {3445, 16466}, {3585, 48870}, {3894, 16478}, {4324, 48857}, {5315, 7373}, {5331, 52680}, {6763, 16475}, {7150, 11072}, {10591, 37666}, {15338, 48861}, {16473, 42019}, {16477, 37522}, {19872, 37604}, {30652, 50587}, {37129, 37211}, {37595, 41872}, {51093, 56145}

X(56343) = isogonal conjugate of X(1698)
X(56343) = isotomic conjugate of X(30596)
X(56343) = trilinear pole of line {649, 2605}
X(56343) = perspector of circumconic {{A, B, C, X(8652), X(37211)}}
X(56343) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 1698}, {2, 16777}, {4, 3927}, {6, 28605}, {7, 3715}, {8, 5221}, {9, 4654}, {10, 4658}, {31, 30596}, {37, 5333}, {45, 30589}, {57, 4007}, {58, 4066}, {72, 31902}, {80, 4880}, {88, 4727}, {99, 48005}, {100, 4802}, {101, 4823}, {190, 4813}, {226, 4877}, {291, 4716}, {513, 4756}, {651, 4820}, {660, 4810}, {662, 4838}, {668, 4834}, {799, 4826}, {897, 4938}, {943, 3824}, {1018, 4960}, {1100, 43260}, {3257, 4958}, {3296, 51572}, {3952, 4840}, {4391, 36074}, {4866, 5586}, {4898, 8056}, {4942, 9309}, {4949, 27834}, {5380, 30595}, {37211, 53585}
X(56343) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 30596}, {3, 1698}, {9, 28605}, {10, 4066}, {478, 4654}, {1015, 4823}, {1084, 4838}, {5452, 4007}, {6593, 4938}, {8054, 4802}, {32664, 16777}, {36033, 3927}, {38986, 48005}, {38991, 4820}, {38996, 4826}, {39026, 4756}, {39029, 4716}, {40589, 5333}, {55053, 4813}, {55055, 4958}
X(56343) = X(i)-Ceva conjugate of X(j) for these {i, j}: {30598, 56070}
X(56343) = X(i)-cross conjugate of X(j) for these {i, j}: {386, 1}, {28625, 25417}, {48340, 109}
X(56343) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(6)}}, {{A, B, C, X(3), X(3062)}}, {{A, B, C, X(4), X(28159)}}, {{A, B, C, X(9), X(60)}}, {{A, B, C, X(10), X(751)}}, {{A, B, C, X(19), X(3467)}}, {{A, B, C, X(21), X(2364)}}, {{A, B, C, X(28), X(15175)}}, {{A, B, C, X(31), X(849)}}, {{A, B, C, X(35), X(57)}}, {{A, B, C, X(36), X(17098)}}, {{A, B, C, X(43), X(3216)}}, {{A, B, C, X(54), X(84)}}, {{A, B, C, X(59), X(7091)}}, {{A, B, C, X(65), X(5561)}}, {{A, B, C, X(69), X(45132)}}, {{A, B, C, X(79), X(9309)}}, {{A, B, C, X(80), X(959)}}, {{A, B, C, X(81), X(37685)}}, {{A, B, C, X(102), X(3527)}}, {{A, B, C, X(103), X(14528)}}, {{A, B, C, X(104), X(13472)}}, {{A, B, C, X(105), X(39955)}}, {{A, B, C, X(213), X(7121)}}, {{A, B, C, X(222), X(1794)}}, {{A, B, C, X(251), X(39954)}}, {{A, B, C, X(274), X(39952)}}, {{A, B, C, X(291), X(15315)}}, {{A, B, C, X(511), X(29116)}}, {{A, B, C, X(514), X(9047)}}, {{A, B, C, X(593), X(39948)}}, {{A, B, C, X(596), X(749)}}, {{A, B, C, X(603), X(35200)}}, {{A, B, C, X(731), X(10014)}}, {{A, B, C, X(757), X(55991)}}, {{A, B, C, X(943), X(1014)}}, {{A, B, C, X(947), X(43908)}}, {{A, B, C, X(957), X(5559)}}, {{A, B, C, X(961), X(15446)}}, {{A, B, C, X(967), X(8056)}}, {{A, B, C, X(978), X(3293)}}, {{A, B, C, X(985), X(17127)}}, {{A, B, C, X(994), X(5560)}}, {{A, B, C, X(1002), X(5557)}}, {{A, B, C, X(1036), X(2316)}}, {{A, B, C, X(1168), X(32899)}}, {{A, B, C, X(1173), X(3417)}}, {{A, B, C, X(1193), X(1405)}}, {{A, B, C, X(1224), X(39956)}}, {{A, B, C, X(1245), X(4674)}}, {{A, B, C, X(1247), X(3453)}}, {{A, B, C, X(1389), X(44759)}}, {{A, B, C, X(1404), X(1468)}}, {{A, B, C, X(1408), X(28615)}}, {{A, B, C, X(1475), X(28873)}}, {{A, B, C, X(1791), X(43697)}}, {{A, B, C, X(1929), X(2258)}}, {{A, B, C, X(2078), X(3338)}}, {{A, B, C, X(2218), X(52375)}}, {{A, B, C, X(2221), X(39980)}}, {{A, B, C, X(2350), X(28499)}}, {{A, B, C, X(3108), X(3415)}}, {{A, B, C, X(3295), X(3361)}}, {{A, B, C, X(3422), X(38271)}}, {{A, B, C, X(3423), X(7163)}}, {{A, B, C, X(3431), X(10308)}}, {{A, B, C, X(3437), X(39394)}}, {{A, B, C, X(3449), X(7284)}}, {{A, B, C, X(3451), X(52185)}}, {{A, B, C, X(3500), X(39950)}}, {{A, B, C, X(7285), X(37741)}}, {{A, B, C, X(7290), X(17745)}}, {{A, B, C, X(7316), X(56342)}}, {{A, B, C, X(7373), X(13462)}}, {{A, B, C, X(8696), X(30650)}}, {{A, B, C, X(9282), X(15383)}}, {{A, B, C, X(9499), X(15378)}}, {{A, B, C, X(14491), X(16615)}}, {{A, B, C, X(14621), X(40408)}}, {{A, B, C, X(15173), X(36125)}}, {{A, B, C, X(15381), X(29374)}}, {{A, B, C, X(15803), X(37541)}}, {{A, B, C, X(15910), X(39943)}}, {{A, B, C, X(18772), X(56152)}}, {{A, B, C, X(22334), X(28163)}}, {{A, B, C, X(22453), X(38831)}}, {{A, B, C, X(28189), X(46851)}}, {{A, B, C, X(28193), X(44731)}}, {{A, B, C, X(28476), X(39951)}}, {{A, B, C, X(28625), X(56221)}}, {{A, B, C, X(30571), X(39961)}}, {{A, B, C, X(36871), X(40432)}}, {{A, B, C, X(39273), X(52123)}}, {{A, B, C, X(42290), X(42326)}}
X(56343) = barycentric product X(i)*X(j) for these (i, j): {1, 25417}, {4, 56070}, {57, 56203}, {100, 48074}, {514, 8652}, {2163, 30590}, {16777, 30597}, {28625, 86}, {30598, 6}, {32042, 649}, {34819, 75}, {37211, 513}, {42030, 56}, {56221, 81}
X(56343) = barycentric quotient X(i)/X(j) for these (i, j): {1, 28605}, {2, 30596}, {6, 1698}, {31, 16777}, {37, 4066}, {41, 3715}, {48, 3927}, {55, 4007}, {56, 4654}, {58, 5333}, {101, 4756}, {187, 4938}, {512, 4838}, {513, 4823}, {604, 5221}, {649, 4802}, {663, 4820}, {667, 4813}, {669, 4826}, {798, 48005}, {902, 4727}, {1126, 43260}, {1333, 4658}, {1474, 31902}, {1914, 4716}, {1919, 4834}, {1960, 4958}, {2163, 30589}, {2194, 4877}, {2260, 3824}, {2605, 23883}, {3052, 4898}, {3733, 4960}, {4367, 4842}, {4834, 53585}, {7113, 4880}, {8632, 4810}, {8643, 4949}, {8652, 190}, {9310, 4942}, {25417, 75}, {28625, 10}, {30598, 76}, {32042, 1978}, {34819, 1}, {37211, 668}, {42030, 3596}, {48074, 693}, {56070, 69}, {56203, 312}, {56221, 321}
X(56343) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 34819, 28625}, {25417, 56203, 56221}, {25417, 56221, 1}

X(56344) = KP3(X(6)) OF X(2) AND X(2)

Barycentrics    a^2*(a^4+2*a^2*b^2+b^4+c^4)*(a^4+b^4+2*a^2*c^2+c^4) : :

X(56344) lies on these lines: {6, 315}, {22, 32}, {83, 42295}, {213, 4463}, {1918, 4456}, {1974, 8743}, {2207, 52448}, {2422, 3800}, {3051, 56004}, {5422, 10014}, {7754, 9045}, {7760, 40405}, {7894, 41909}, {11610, 11641}, {13357, 40799}, {20065, 34482}, {20960, 46319}, {46288, 52580}

X(56344) = isogonal conjugate of X(7795)
X(56344) = trilinear pole of line {669, 2485}
X(56344) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 7795}, {662, 50552}
X(56344) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 7795}, {1084, 50552}
X(56344) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(38826)}}, {{A, B, C, X(4), X(22)}}, {{A, B, C, X(6), X(32)}}, {{A, B, C, X(25), X(76)}}, {{A, B, C, X(111), X(18840)}}, {{A, B, C, X(511), X(3527)}}, {{A, B, C, X(598), X(14248)}}, {{A, B, C, X(695), X(2353)}}, {{A, B, C, X(1383), X(2996)}}, {{A, B, C, X(3051), X(42295)}}, {{A, B, C, X(3108), X(18841)}}, {{A, B, C, X(3456), X(30495)}}, {{A, B, C, X(5007), X(5017)}}, {{A, B, C, X(5395), X(8753)}}, {{A, B, C, X(8751), X(56342)}}, {{A, B, C, X(8770), X(10159)}}, {{A, B, C, X(9307), X(51245)}}, {{A, B, C, X(10302), X(36616)}}, {{A, B, C, X(10630), X(53107)}}, {{A, B, C, X(14370), X(14906)}}, {{A, B, C, X(17042), X(46286)}}, {{A, B, C, X(18842), X(34572)}}, {{A, B, C, X(21399), X(27375)}}, {{A, B, C, X(22263), X(35140)}}, {{A, B, C, X(37892), X(40421)}}, {{A, B, C, X(39951), X(43527)}}, {{A, B, C, X(43717), X(52223)}}
X(56344) = barycentric quotient X(i)/X(j) for these (i, j): {6, 7795}, {512, 50552}

X(56345) = KP3(X(6)) OF X(3) AND X(3)

Barycentrics    a^2*(a^8+5*b^8-4*a^6*c^2-8*b^6*c^2+2*b^4*c^4+c^8+2*a^4*(b^4+3*c^4)-4*a^2*(2*b^6-3*b^4*c^2+c^6))*(a^8-4*a^6*b^2+b^8+2*b^4*c^4-8*b^2*c^6+5*c^8+2*a^4*(3*b^4+c^4)-4*a^2*(b^6-3*b^2*c^4+2*c^6)) : :

X(56345) lies on these lines: {6, 6509}, {25, 185}, {393, 13567}, {394, 41890}, {426, 11425}, {1880, 8807}, {1993, 41894}, {2165, 26958}, {3343, 41489}, {8882, 19180}, {10601, 41891}, {11427, 52224}, {11433, 52223}, {23292, 46952}, {37643, 51316}

X(56345) = X(i)-isoconjugate-of-X(j) for these {i, j}: {63, 6618}
X(56345) = X(i)-Dao conjugate of X(j) for these {i, j}: {3162, 6618}
X(56345) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}}, {{A, B, C, X(3), X(459)}}, {{A, B, C, X(4), X(1032)}}, {{A, B, C, X(54), X(38253)}}, {{A, B, C, X(64), X(185)}}, {{A, B, C, X(97), X(3532)}}, {{A, B, C, X(222), X(36121)}}, {{A, B, C, X(275), X(26883)}}, {{A, B, C, X(389), X(11425)}}, {{A, B, C, X(1039), X(41081)}}, {{A, B, C, X(1993), X(26958)}}, {{A, B, C, X(2184), X(15629)}}, {{A, B, C, X(3426), X(36609)}}, {{A, B, C, X(6330), X(22263)}}, {{A, B, C, X(6504), X(22466)}}, {{A, B, C, X(8796), X(14919)}}, {{A, B, C, X(10601), X(23292)}}, {{A, B, C, X(14457), X(17811)}}, {{A, B, C, X(14490), X(39284)}}, {{A, B, C, X(14528), X(16080)}}, {{A, B, C, X(34403), X(43690)}}
X(56345) = barycentric product X(i)*X(j) for these (i, j): {3, 56340}
X(56345) = barycentric quotient X(i)/X(j) for these (i, j): {25, 6618}, {56340, 264}

X(56346) = KP3(X(6)) OF X(3) AND X(4)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(3*a^4+3*b^4-2*b^2*c^2-c^4-2*a^2*(3*b^2+c^2))*(3*a^4-b^4-2*b^2*c^2+3*c^4-2*a^2*(b^2+3*c^2)) : :

X(56346) lies on the Kiepert hyperbola and on these lines: {2, 15905}, {3, 31363}, {4, 154}, {6, 459}, {10, 34231}, {25, 14484}, {27, 45100}, {76, 37669}, {83, 52283}, {98, 8889}, {226, 17917}, {262, 6353}, {275, 33629}, {297, 5395}, {321, 26668}, {393, 54867}, {427, 3424}, {428, 54520}, {458, 2996}, {461, 43672}, {468, 53099}, {470, 22237}, {471, 22235}, {472, 43540}, {473, 43541}, {485, 3536}, {486, 3535}, {631, 13599}, {801, 36794}, {1073, 11348}, {1131, 1586}, {1132, 1585}, {1249, 2052}, {1593, 40053}, {2051, 7490}, {3079, 5480}, {3090, 40448}, {3524, 54763}, {3543, 54923}, {3618, 37874}, {3839, 54552}, {5064, 54519}, {5071, 54660}, {5094, 43537}, {5392, 37645}, {5702, 14361}, {6504, 6819}, {6515, 42410}, {6622, 45300}, {6748, 54531}, {6820, 14389}, {6995, 43951}, {7394, 54705}, {7408, 54706}, {7608, 52290}, {7612, 52299}, {7714, 14492}, {9290, 37188}, {11001, 54838}, {11109, 43533}, {11433, 15291}, {11547, 39284}, {12233, 15005}, {13567, 38253}, {14033, 54828}, {14494, 38282}, {15682, 54585}, {16041, 54551}, {17809, 41374}, {17811, 18840}, {17907, 54629}, {18845, 37174}, {18890, 46831}, {30456, 40149}, {33190, 54682}, {41099, 54512}, {41106, 54667}, {41895, 52281}, {45867, 53108}, {47586, 52284}, {52282, 53101}, {52293, 53859}

X(56346) = polar conjugate of X(3091)
X(56346) = complement of X(41914)
X(56346) = trilinear pole of line {37931, 42658}
X(56346) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 3091}, {63, 17810}, {92, 26880}, {304, 33578}, {18596, 33579}
X(56346) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 3091}, {3162, 17810}, {22391, 26880}
X(56346) = X(i)-cross conjugate of X(j) for these {i, j}: {3087, 4}, {19467, 69}
X(56346) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(11425)}}, {{A, B, C, X(6), X(154)}}, {{A, B, C, X(54), X(394)}}, {{A, B, C, X(57), X(40396)}}, {{A, B, C, X(63), X(52663)}}, {{A, B, C, X(69), X(23292)}}, {{A, B, C, X(97), X(3431)}}, {{A, B, C, X(278), X(36123)}}, {{A, B, C, X(287), X(17040)}}, {{A, B, C, X(458), X(6353)}}, {{A, B, C, X(1032), X(14376)}}, {{A, B, C, X(1172), X(2297)}}, {{A, B, C, X(1585), X(3536)}}, {{A, B, C, X(1586), X(3535)}}, {{A, B, C, X(1988), X(43718)}}, {{A, B, C, X(2982), X(41081)}}, {{A, B, C, X(3618), X(17811)}}, {{A, B, C, X(6330), X(8801)}}, {{A, B, C, X(6340), X(54124)}}, {{A, B, C, X(7003), X(40435)}}, {{A, B, C, X(8795), X(36948)}}, {{A, B, C, X(10570), X(41514)}}, {{A, B, C, X(10603), X(46104)}}, {{A, B, C, X(11270), X(31626)}}, {{A, B, C, X(13452), X(55982)}}, {{A, B, C, X(13472), X(14919)}}, {{A, B, C, X(14542), X(34403)}}, {{A, B, C, X(16774), X(42313)}}, {{A, B, C, X(23964), X(39955)}}, {{A, B, C, X(25430), X(36121)}}, {{A, B, C, X(36609), X(43908)}}, {{A, B, C, X(36952), X(38442)}}, {{A, B, C, X(39944), X(39956)}}, {{A, B, C, X(39951), X(43717)}}, {{A, B, C, X(40402), X(46952)}}
X(56346) = barycentric product X(i)*X(j) for these (i, j): {14528, 264}, {31504, 8795}
X(56346) = barycentric quotient X(i)/X(j) for these (i, j): {4, 3091}, {25, 17810}, {184, 26880}, {275, 19188}, {1593, 33537}, {1974, 33578}, {8884, 19169}, {14528, 3}, {31504, 5562}, {34207, 33579}, {46092, 19210}
X(56346) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 43841, 8888}, {43841, 45062, 4}

X(56347) = KP3(X(6)) OF X(4) AND X(4)

Barycentrics    a^2*(a^8-2*a^6*(2*b^2+c^2)+(b^2-c^2)^2*(b^4+c^4)+2*a^4*(3*b^4+b^2*c^2+c^4)-2*a^2*(2*b^6-b^4*c^2-2*b^2*c^4+c^6))*(a^8-2*a^6*(b^2+2*c^2)+(b^2-c^2)^2*(b^4+c^4)+2*a^4*(b^4+b^2*c^2+3*c^4)-2*a^2*(b^6-2*b^4*c^2-b^2*c^4+2*c^6)) : :

X(56347) lies on these lines: {6, 11547}, {24, 184}, {275, 39643}, {394, 7763}, {577, 1993}, {2052, 40402}, {2430, 45681}, {3990, 42700}, {5422, 18883}, {14533, 19170}, {52032, 56004}

X(56347) = trilinear pole of line {39201, 924}
X(56347) = X(i)-isoconjugate-of-X(j) for these {i, j}: {92, 6641}, {1953, 19179}
X(56347) = X(i)-Dao conjugate of X(j) for these {i, j}: {22391, 6641}
X(56347) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(24)}}, {{A, B, C, X(3), X(389)}}, {{A, B, C, X(4), X(97)}}, {{A, B, C, X(6), X(184)}}, {{A, B, C, X(64), X(39284)}}, {{A, B, C, X(74), X(8796)}}, {{A, B, C, X(232), X(11402)}}, {{A, B, C, X(249), X(37874)}}, {{A, B, C, X(288), X(1073)}}, {{A, B, C, X(459), X(3431)}}, {{A, B, C, X(1994), X(15066)}}, {{A, B, C, X(2987), X(17040)}}, {{A, B, C, X(5392), X(30541)}}, {{A, B, C, X(5408), X(55020)}}, {{A, B, C, X(5409), X(55021)}}, {{A, B, C, X(10601), X(37672)}}, {{A, B, C, X(13472), X(14919)}}, {{A, B, C, X(13579), X(21399)}}, {{A, B, C, X(14528), X(16080)}}, {{A, B, C, X(20806), X(42287)}}, {{A, B, C, X(38253), X(55982)}}, {{A, B, C, X(40384), X(44731)}}, {{A, B, C, X(42313), X(43725)}}
X(56347) = barycentric product X(i)*X(j) for these (i, j): {4, 56337}
X(56347) = barycentric quotient X(i)/X(j) for these (i, j): {54, 19179}, {184, 6641}, {56337, 69}

X(56348) = KP3(X(7)) OF X(2) AND X(7)

Barycentrics    (a+b-c)*(a-b+c)*(a^2+3*b^2-4*b*c+c^2-2*a*(2*b+c))*(a^2+b^2-4*b*c+3*c^2-2*a*(b+2*c)) : :

X(56348) lies on these lines: {2, 10481}, {7, 9580}, {57, 42318}, {75, 51351}, {86, 34821}, {144, 1223}, {145, 42361}, {279, 21453}, {673, 21454}, {2400, 48268}, {3598, 55967}, {4373, 36845}, {4666, 7271}, {5936, 9436}, {10136, 52511}, {10578, 21314}, {11019, 20121}, {17014, 55941}, {28626, 40719}, {32093, 39695}, {37780, 56074}

X(56348) = X(i)-isoconjugate-of-X(j) for these {i, j}: {41, 18230}, {55, 10389}
X(56348) = X(i)-Dao conjugate of X(j) for these {i, j}: {223, 10389}, {3160, 18230}
X(56348) = X(i)-cross conjugate of X(j) for these {i, j}: {3731, 27818}, {10390, 56054}, {10580, 2}
X(56348) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(7)}}, {{A, B, C, X(4), X(56088)}}, {{A, B, C, X(200), X(55922)}}, {{A, B, C, X(279), X(10481)}}, {{A, B, C, X(354), X(40779)}}, {{A, B, C, X(1280), X(7091)}}, {{A, B, C, X(1458), X(39965)}}, {{A, B, C, X(3062), X(6605)}}, {{A, B, C, X(3296), X(43672)}}, {{A, B, C, X(5556), X(14942)}}, {{A, B, C, X(9436), X(21454)}}, {{A, B, C, X(25417), X(43736)}}, {{A, B, C, X(31507), X(41798)}}
X(56348) = barycentric product X(i)*X(j) for these (i, j): {10390, 85}, {34821, 76}, {56054, 7}
X(56348) = barycentric quotient X(i)/X(j) for these (i, j): {7, 18230}, {57, 10389}, {10390, 9}, {34821, 6}, {56054, 8}

X(56349) = KP3(X(8)) OF X(2) AND X(2)

Barycentrics    (a-b-c)*(a^2-2*a*b+5*b^2+2*a*c-2*b*c+c^2)*(a^2+b^2+2*a*(b-c)-2*b*c+5*c^2) : :

X(56349) lies on these lines: {7, 1222}, {8, 3663}, {341, 20895}, {346, 3452}, {1043, 9785}, {1219, 31995}, {2370, 6571}, {3616, 56202}, {4901, 6556}, {29627, 31325}

X(56349) = trilinear pole of line {3239, 21120}
X(56349) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 4308}, {1415, 43061}
X(56349) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 4308}, {1146, 43061}, {2968, 8710}
X(56349) = X(i)-cross conjugate of X(j) for these {i, j}: {56199, 56335}
X(56349) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(2051)}}, {{A, B, C, X(8), X(75)}}, {{A, B, C, X(86), X(38255)}}, {{A, B, C, X(312), X(4373)}}, {{A, B, C, X(536), X(23880)}}, {{A, B, C, X(969), X(1392)}}, {{A, B, C, X(3668), X(3701)}}, {{A, B, C, X(5853), X(28161)}}, {{A, B, C, X(30479), X(55022)}}
X(56349) = barycentric product X(i)*X(j) for these (i, j): {52622, 6571}, {56199, 75}, {56335, 8}
X(56349) = barycentric quotient X(i)/X(j) for these (i, j): {2, 4308}, {522, 43061}, {3239, 8710}, {6571, 1461}, {56199, 1}, {56335, 7}

X(56350) = KP3(X(9)) OF X(2) AND X(9)

Barycentrics    a*(a-b-c)*(2*a^2-4*a*b+2*b^2-3*a*c-3*b*c+c^2)*(2*a^2-3*a*b+b^2-4*a*c-3*b*c+2*c^2) : :

X(56350) lies on these lines: {2, 32007}, {9, 3957}, {200, 56244}, {3219, 21446}, {3715, 28071}, {4820, 28132}, {20015, 36916}, {28605, 36796}, {31618, 51352}, {43989, 56265}

X(56350) = X(i)-isoconjugate-of-X(j) for these {i, j}: {56, 20195}, {354, 39669}
X(56350) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 20195}
X(56350) = X(i)-Ceva conjugate of X(j) for these {i, j}: {56060, 56028}
X(56350) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(9)}}, {{A, B, C, X(21), X(56088)}}, {{A, B, C, X(55), X(89)}}, {{A, B, C, X(210), X(4080)}}, {{A, B, C, X(294), X(25417)}}, {{A, B, C, X(1280), X(4866)}}, {{A, B, C, X(2195), X(39955)}}, {{A, B, C, X(3693), X(28605)}}, {{A, B, C, X(3870), X(4373)}}, {{A, B, C, X(7073), X(27789)}}, {{A, B, C, X(8025), X(37658)}}, {{A, B, C, X(14942), X(56203)}}, {{A, B, C, X(21453), X(55920)}}, {{A, B, C, X(32635), X(56098)}}
X(56350) = barycentric product X(i)*X(j) for these (i, j): {56028, 8}, {56060, 9}
X(56350) = barycentric quotient X(i)/X(j) for these (i, j): {9, 20195}, {1174, 39669}, {56028, 7}, {56060, 85}

X(56351) = KP3(X(10)) OF X(2) AND X(2)

Barycentrics    (b+c)*(a^2+2*b^2+2*b*c+c^2+2*a*(b+c))*(a^2+b^2+2*b*c+2*c^2+2*a*(b+c)) : :

X(56351) lies on these lines: {10, 4360}, {80, 32101}, {86, 1224}, {313, 40087}, {594, 3995}, {1089, 56249}, {1220, 32025}, {1268, 15523}, {4802, 35352}, {8013, 18082}

X(56351) = trilinear pole of line {4024, 4129}
X(56351) = X(i)-isoconjugate-of-X(j) for these {i, j}: {163, 50522}, {1333, 17398}, {2194, 52783}
X(56351) = X(i)-Dao conjugate of X(j) for these {i, j}: {37, 17398}, {115, 50522}, {1214, 52783}
X(56351) = X(i)-cross conjugate of X(j) for these {i, j}: {23282, 190}
X(56351) = intersection, other than A, B, C, of circumconics {{A, B, C, X(10), X(12)}}, {{A, B, C, X(75), X(4360)}}, {{A, B, C, X(86), X(321)}}, {{A, B, C, X(257), X(28613)}}, {{A, B, C, X(740), X(4802)}}, {{A, B, C, X(1441), X(55955)}}
X(56351) = barycentric product X(i)*X(j) for these (i, j): {56213, 75}
X(56351) = barycentric quotient X(i)/X(j) for these (i, j): {10, 17398}, {226, 52783}, {523, 50522}, {56213, 1}

X(56352) = KP4(X(1)) OF X(2) AND X(4)

Barycentrics    a*(a^4+2*a*b^2*c+(b^2-c^2)^2-2*a^2*(b^2+c^2))*(a^4+2*a*b*c^2+(b^2-c^2)^2-2*a^2*(b^2+c^2)) : :

X(56352) lies on these lines: {1, 5422}, {28, 37533}, {37, 56041}, {57, 7130}, {278, 31053}, {279, 17483}, {1224, 19861}, {2006, 30852}, {3083, 3300}, {3084, 3302}, {17011, 56218}, {25930, 42326}, {26639, 30701}, {31164, 52374}, {34772, 40836}

X(56352) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 499}, {19, 24467}, {57, 7082}, {2164, 10052}
X(56352) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 24467}, {9, 499}, {5452, 7082}
X(56352) = X(i)-cross conjugate of X(j) for these {i, j}: {46389, 100}
X(56352) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(8), X(6504)}}, {{A, B, C, X(33), X(1252)}}, {{A, B, C, X(59), X(56002)}}, {{A, B, C, X(63), X(18359)}}, {{A, B, C, X(77), X(31626)}}, {{A, B, C, X(78), X(97)}}, {{A, B, C, X(80), X(13579)}}, {{A, B, C, X(84), X(55027)}}, {{A, B, C, X(92), X(4564)}}, {{A, B, C, X(189), X(1392)}}, {{A, B, C, X(275), X(1016)}}, {{A, B, C, X(312), X(2167)}}, {{A, B, C, X(335), X(5392)}}, {{A, B, C, X(394), X(1807)}}, {{A, B, C, X(1029), X(3577)}}, {{A, B, C, X(1041), X(8796)}}, {{A, B, C, X(1063), X(2052)}}, {{A, B, C, X(1096), X(30651)}}, {{A, B, C, X(1320), X(2994)}}, {{A, B, C, X(1897), X(4619)}}, {{A, B, C, X(2987), X(56179)}}, {{A, B, C, X(5561), X(11538)}}, {{A, B, C, X(7073), X(7123)}}, {{A, B, C, X(7131), X(30690)}}, {{A, B, C, X(17743), X(40393)}}, {{A, B, C, X(30535), X(56328)}}, {{A, B, C, X(56003), X(56225)}}
X(56352) = barycentric product X(i)*X(j) for these (i, j): {312, 7130}, {52186, 75}
X(56352) = barycentric quotient X(i)/X(j) for these (i, j): {1, 499}, {3, 24467}, {46, 10052}, {55, 7082}, {7130, 57}, {52186, 1}

X(56353) = KP4(X(1)) OF X(2) AND X(6)

Barycentrics    (a^2-3*a*b+b^2)*(a^2-3*a*c+c^2) : :

X(56353) lies on these lines: {145, 238}, {239, 16969}, {1222, 17339}, {1429, 5435}, {2295, 56042}, {2403, 25237}, {3208, 7153}, {4513, 27496}, {7754, 10027}, {9311, 17261}, {17244, 31227}, {17277, 24759}, {17389, 41629}

X(56353) = isotomic conjugate of X(48627)
X(56353) = trilinear pole of line {659, 13252}
X(56353) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 23524}, {6, 17063}, {31, 48627}, {56, 4051}, {58, 21951}, {81, 22172}, {101, 23765}, {513, 25577}, {649, 4499}, {692, 48415}, {893, 7240}, {1333, 48643}, {2162, 4941}
X(56353) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 4051}, {2, 48627}, {9, 17063}, {10, 21951}, {37, 48643}, {1015, 23765}, {1086, 48415}, {5375, 4499}, {32664, 23524}, {39026, 25577}, {40586, 22172}, {40597, 7240}
X(56353) = X(i)-cross conjugate of X(j) for these {i, j}: {20980, 100}, {25101, 2}, {31286, 190}
X(56353) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(83)}}, {{A, B, C, X(2), X(145)}}, {{A, B, C, X(6), X(16969)}}, {{A, B, C, X(7), X(18845)}}, {{A, B, C, X(8), X(335)}}, {{A, B, C, X(56), X(56011)}}, {{A, B, C, X(76), X(5559)}}, {{A, B, C, X(79), X(53107)}}, {{A, B, C, X(80), X(53105)}}, {{A, B, C, X(81), X(37679)}}, {{A, B, C, X(85), X(6630)}}, {{A, B, C, X(192), X(56180)}}, {{A, B, C, X(257), X(1000)}}, {{A, B, C, X(330), X(1120)}}, {{A, B, C, X(333), X(39703)}}, {{A, B, C, X(519), X(17758)}}, {{A, B, C, X(598), X(5557)}}, {{A, B, C, X(673), X(38247)}}, {{A, B, C, X(996), X(32009)}}, {{A, B, C, X(1255), X(56046)}}, {{A, B, C, X(1258), X(2334)}}, {{A, B, C, X(1911), X(2176)}}, {{A, B, C, X(2329), X(17752)}}, {{A, B, C, X(2985), X(25430)}}, {{A, B, C, X(3445), X(20332)}}, {{A, B, C, X(4998), X(9312)}}, {{A, B, C, X(5395), X(5558)}}, {{A, B, C, X(7121), X(9265)}}, {{A, B, C, X(27475), X(54120)}}, {{A, B, C, X(34914), X(43527)}}, {{A, B, C, X(37128), X(39969)}}, {{A, B, C, X(39694), X(40435)}}, {{A, B, C, X(41909), X(56179)}}
X(56353) = barycentric product X(i)*X(j) for these (i, j): {190, 25576}
X(56353) = barycentric quotient X(i)/X(j) for these (i, j): {1, 17063}, {2, 48627}, {9, 4051}, {10, 48643}, {31, 23524}, {37, 21951}, {42, 22172}, {43, 4941}, {100, 4499}, {101, 25577}, {171, 7240}, {513, 23765}, {514, 48415}, {25576, 514}

X(56354) = KP4(X(1)) OF X(2) AND X(8)

Barycentrics    a*(a^4+4*a*b^2*c+(b^2-c^2)^2-2*a^2*(b^2+c^2))*(a^4+4*a*b*c^2+(b^2-c^2)^2-2*a^2*(b^2+c^2)) : :

X(56354) lies on these lines: {1, 10601}, {28, 1819}, {57, 53995}, {63, 34051}, {78, 15500}, {81, 3553}, {223, 26611}, {274, 24556}, {277, 25930}, {278, 908}, {279, 5905}, {312, 16082}, {394, 1422}, {837, 20928}, {1123, 3083}, {1224, 8583}, {1336, 3084}, {2006, 30827}, {2401, 6332}, {5256, 56218}, {25243, 39747}, {26639, 54123}, {26669, 40399}, {28609, 52374}, {34056, 34526}

X(56354) = isogonal conjugate of X(3554)
X(56354) = isotomic conjugate of X(54284)
X(56354) = trilinear pole of line {13528, 513}
X(56354) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 3554}, {6, 3086}, {25, 26871}, {31, 54284}, {56, 53994}, {57, 30223}, {58, 24005}, {278, 19354}, {836, 8747}, {909, 1519}, {1333, 17869}, {1413, 38015}, {2189, 26955}, {8602, 49171}
X(56354) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 53994}, {2, 54284}, {3, 3554}, {9, 3086}, {10, 24005}, {37, 17869}, {5452, 30223}, {6505, 26871}, {23980, 1519}
X(56354) = X(i)-Ceva conjugate of X(j) for these {i, j}: {34401, 56287}
X(56354) = X(i)-cross conjugate of X(j) for these {i, j}: {4091, 190}, {14298, 100}, {42019, 56287}
X(56354) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(8), X(55987)}}, {{A, B, C, X(9), X(5905)}}, {{A, B, C, X(33), X(7123)}}, {{A, B, C, X(63), X(312)}}, {{A, B, C, X(77), X(40424)}}, {{A, B, C, X(78), X(394)}}, {{A, B, C, X(80), X(6504)}}, {{A, B, C, X(86), X(10601)}}, {{A, B, C, X(92), X(7131)}}, {{A, B, C, X(189), X(1320)}}, {{A, B, C, X(200), X(1252)}}, {{A, B, C, X(223), X(1262)}}, {{A, B, C, X(275), X(1039)}}, {{A, B, C, X(282), X(56003)}}, {{A, B, C, X(292), X(1096)}}, {{A, B, C, X(335), X(1041)}}, {{A, B, C, X(346), X(2324)}}, {{A, B, C, X(459), X(1063)}}, {{A, B, C, X(801), X(1016)}}, {{A, B, C, X(837), X(42019)}}, {{A, B, C, X(1032), X(1265)}}, {{A, B, C, X(1073), X(1807)}}, {{A, B, C, X(1797), X(40436)}}, {{A, B, C, X(2167), X(2339)}}, {{A, B, C, X(2184), X(18359)}}, {{A, B, C, X(2983), X(56225)}}, {{A, B, C, X(2994), X(3680)}}, {{A, B, C, X(3062), X(55027)}}, {{A, B, C, X(5560), X(13579)}}, {{A, B, C, X(7361), X(36796)}}, {{A, B, C, X(14554), X(42467)}}, {{A, B, C, X(34546), X(56089)}}, {{A, B, C, X(40802), X(56179)}}, {{A, B, C, X(42361), X(43736)}}
X(56354) = barycentric product X(i)*X(j) for these (i, j): {312, 53995}, {3998, 837}, {34401, 9}, {34413, 40}, {42019, 75}, {56287, 8}
X(56354) = barycentric quotient X(i)/X(j) for these (i, j): {1, 3086}, {2, 54284}, {6, 3554}, {9, 53994}, {10, 17869}, {37, 24005}, {55, 30223}, {63, 26871}, {201, 26955}, {212, 19354}, {517, 1519}, {1124, 38003}, {2324, 38015}, {3083, 40650}, {3990, 836}, {10310, 49171}, {34401, 85}, {34413, 309}, {42019, 1}, {53995, 57}, {55104, 18909}, {56287, 7}

X(56355) = KP4(X(1)) OF X(2) AND X(9)

Barycentrics    a*(2*a^3+2*a*(3*b-c)*c+(b-c)^2*(b+2*c)-a^2*(3*b+2*c))*(2*a^3-2*a*b*(b-3*c)+(b-c)^2*(2*b+c)-a^2*(2*b+3*c)) : :

X(56355) lies on these lines: {88, 25934}, {105, 2098}, {220, 34056}, {279, 6603}, {330, 25243}, {1002, 20323}, {1255, 17825}, {2006, 5328}, {2401, 25242}, {4105, 35348}, {4671, 16082}, {8056, 25930}, {17014, 56218}, {20007, 40836}

X(56355) = trilinear pole of line {15599, 513}
X(56355) = X(i)-isoconjugate-of-X(j) for these {i, j}: {909, 1538}
X(56355) = X(i)-Dao conjugate of X(j) for these {i, j}: {23980, 1538}
X(56355) = X(i)-cross conjugate of X(j) for these {i, j}: {26669, 2}
X(56355) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(8), X(4564)}}, {{A, B, C, X(85), X(1392)}}, {{A, B, C, X(145), X(2991)}}, {{A, B, C, X(220), X(1252)}}, {{A, B, C, X(1262), X(42019)}}, {{A, B, C, X(1320), X(7131)}}, {{A, B, C, X(1476), X(55937)}}, {{A, B, C, X(2125), X(41798)}}, {{A, B, C, X(2320), X(32008)}}, {{A, B, C, X(2338), X(56003)}}, {{A, B, C, X(2989), X(17743)}}, {{A, B, C, X(3497), X(41446)}}, {{A, B, C, X(3680), X(36101)}}, {{A, B, C, X(4373), X(43736)}}, {{A, B, C, X(7077), X(9310)}}, {{A, B, C, X(8025), X(17825)}}, {{A, B, C, X(10429), X(55027)}}, {{A, B, C, X(14497), X(17758)}}
X(56355) = barycentric quotient X(i)/X(j) for these (i, j): {517, 1538}

X(56356) = KP4(X(1)) OF X(4) AND X(7)

Barycentrics    a*(a+b-c)*(a-b+c)*(a^4-2*a^2*b^2+b^4+2*a*b*c^2-c^4)*(a^4-b^4+2*a*b^2*c-2*a^2*c^2+c^4) : :

X(56356) lies on these lines: {1, 50434}, {7, 1063}, {35, 77}, {63, 15066}, {69, 1443}, {81, 41502}, {269, 52392}, {1439, 18532}, {1442, 7056}, {1444, 35193}, {1814, 17092}

X(56356) = trilinear pole of line {905, 9404}
X(56356) = X(i)-isoconjugate-of-X(j) for these {i, j}: {33, 1062}, {42, 17584}, {55, 1479}, {210, 5358}, {2332, 18588}, {4183, 54360}, {4354, 7073}
X(56356) = X(i)-Dao conjugate of X(j) for these {i, j}: {223, 1479}, {40592, 17584}
X(56356) = X(i)-cross conjugate of X(j) for these {i, j}: {7163, 55985}, {15313, 651}
X(56356) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(35)}}, {{A, B, C, X(7), X(63)}}, {{A, B, C, X(8), X(35512)}}, {{A, B, C, X(59), X(1041)}}, {{A, B, C, X(86), X(15066)}}, {{A, B, C, X(269), X(1443)}}, {{A, B, C, X(273), X(7045)}}, {{A, B, C, X(277), X(43736)}}, {{A, B, C, X(1037), X(34207)}}, {{A, B, C, X(1039), X(15339)}}, {{A, B, C, X(1063), X(7163)}}, {{A, B, C, X(2346), X(56139)}}, {{A, B, C, X(7100), X(34801)}}, {{A, B, C, X(8809), X(18815)}}, {{A, B, C, X(40118), X(55017)}}
X(56356) = barycentric product X(i)*X(j) for these (i, j): {1063, 348}, {7163, 85}, {55985, 7}
X(56356) = barycentric quotient X(i)/X(j) for these (i, j): {57, 1479}, {81, 17584}, {222, 1062}, {1063, 281}, {1412, 5358}, {1439, 18588}, {2003, 4354}, {7163, 9}, {52373, 54360}, {55985, 8}

X(56357) = KP4(X(1)) OF X(6) AND X(6)

Barycentrics    a*(-2*a*b^2*c+b^2*c^2+a^2*(b^2+c^2))*(-2*a*b*c^2+b^2*c^2+a^2*(b^2+c^2)) : :

X(56357) lies on these lines: {2, 56247}, {37, 56329}, {43, 32020}, {330, 3009}, {612, 40738}, {1613, 51864}, {2663, 39948}, {3247, 9401}, {3550, 8640}, {21352, 39738}

X(56357) = isogonal conjugate of X(18194)
X(56357) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 18194}, {2, 23538}, {27, 22439}, {57, 39250}, {58, 21257}, {81, 21345}, {86, 23652}, {87, 14823}, {1333, 21435}
X(56357) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 18194}, {10, 21257}, {37, 21435}, {5452, 39250}, {32664, 23538}, {40586, 21345}, {40600, 23652}
X(56357) = X(i)-cross conjugate of X(j) for these {i, j}: {23572, 190}, {25142, 100}
X(56357) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(31), X(43)}}, {{A, B, C, X(87), X(3112)}}, {{A, B, C, X(92), X(30663)}}, {{A, B, C, X(100), X(3550)}}, {{A, B, C, X(292), X(3223)}}, {{A, B, C, X(312), X(9285)}}, {{A, B, C, X(612), X(40790)}}, {{A, B, C, X(694), X(56179)}}, {{A, B, C, X(978), X(1472)}}, {{A, B, C, X(983), X(41531)}}, {{A, B, C, X(1613), X(2176)}}, {{A, B, C, X(2162), X(32011)}}, {{A, B, C, X(2663), X(3247)}}, {{A, B, C, X(3226), X(39966)}}, {{A, B, C, X(5560), X(55028)}}, {{A, B, C, X(5561), X(30505)}}, {{A, B, C, X(9315), X(9361)}}, {{A, B, C, X(16468), X(32911)}}, {{A, B, C, X(18098), X(56256)}}, {{A, B, C, X(30651), X(38275)}}, {{A, B, C, X(39951), X(40763)}}
X(56357) = barycentric product X(i)*X(j) for these (i, j): {1, 56247}
X(56357) = barycentric quotient X(i)/X(j) for these (i, j): {6, 18194}, {10, 21435}, {31, 23538}, {37, 21257}, {42, 21345}, {55, 39250}, {213, 23652}, {228, 22439}, {2176, 14823}, {56247, 75}

X(56358) = KP4(X(1)) OF X(6) AND X(7)

Barycentrics    (a^2-a*b+b^2)*(a+b-c)*(a-b+c)*(a^2-a*c+c^2) : :

X(56358) lies on the K1031 and on these lines: {1, 5999}, {2, 1429}, {7, 171}, {31, 51935}, {56, 6384}, {57, 335}, {75, 183}, {85, 40038}, {86, 7179}, {226, 3407}, {272, 38813}, {273, 7009}, {310, 13588}, {385, 1423}, {604, 39746}, {673, 3772}, {675, 8685}, {871, 1402}, {1088, 7176}, {1284, 3113}, {1434, 24801}, {1469, 56154}, {2162, 6180}, {3212, 3905}, {3598, 4373}, {4308, 36620}, {4621, 36807}, {5226, 39716}, {5435, 39749}, {5936, 56196}, {5989, 30545}, {6649, 7248}, {7175, 53677}, {7225, 39745}, {7247, 56065}, {10404, 40164}, {17084, 29838}, {18613, 23865}, {20284, 37137}, {26228, 39732}, {27475, 37674}, {37543, 45965}, {40418, 55082}

X(56358) = isogonal conjugate of X(3056)
X(56358) = isotomic conjugate of X(3705)
X(56358) = trilinear pole of line {3287, 20980}
X(56358) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 3056}, {2, 20665}, {4, 20753}, {6, 3061}, {8, 7032}, {9, 2275}, {21, 3778}, {31, 3705}, {33, 3784}, {41, 3662}, {42, 3794}, {55, 982}, {56, 4073}, {60, 7237}, {81, 20684}, {86, 4531}, {200, 7248}, {220, 41777}, {284, 3721}, {314, 40935}, {333, 16584}, {513, 40499}, {663, 3888}, {692, 3810}, {983, 12836}, {1172, 20727}, {1253, 7185}, {1333, 4136}, {2053, 41886}, {2150, 16886}, {2175, 33930}, {2194, 2887}, {2311, 18904}, {2319, 20284}, {2320, 4787}, {2329, 3863}, {2330, 3865}, {2344, 3094}, {3063, 33946}, {3116, 52133}, {3117, 52652}, {3699, 50514}, {3777, 3939}, {7073, 7186}, {7239, 7252}, {8022, 40072}, {21751, 28660}, {21815, 52379}, {22364, 44130}, {31917, 52370}, {33891, 51858}
X(56358) = X(i)-vertex conjugate of X(j) for these {i, j}: {56, 52133}
X(56358) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 4073}, {2, 3705}, {3, 3056}, {9, 3061}, {37, 4136}, {223, 982}, {478, 2275}, {1086, 3810}, {1214, 2887}, {3160, 3662}, {6609, 7248}, {10001, 33946}, {17113, 7185}, {32664, 20665}, {36033, 20753}, {39026, 40499}, {40586, 20684}, {40590, 3721}, {40592, 3794}, {40593, 33930}, {40600, 4531}, {40611, 3778}, {40615, 3776}, {40617, 3777}, {40622, 3801}, {56325, 16886}
X(56358) = X(i)-cross conjugate of X(j) for these {i, j}: {667, 651}, {983, 17743}, {17072, 653}, {18758, 6}, {19522, 37128}, {24533, 37137}, {24793, 13149}, {28470, 190}, {31286, 658}, {47837, 38340}
X(56358) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(98)}}, {{A, B, C, X(2), X(7)}}, {{A, B, C, X(4), X(4518)}}, {{A, B, C, X(8), X(3424)}}, {{A, B, C, X(25), X(1037)}}, {{A, B, C, X(43), X(238)}}, {{A, B, C, X(55), X(21010)}}, {{A, B, C, X(56), X(1403)}}, {{A, B, C, X(57), X(552)}}, {{A, B, C, X(59), X(251)}}, {{A, B, C, X(60), X(5481)}}, {{A, B, C, X(77), X(1799)}}, {{A, B, C, X(79), X(262)}}, {{A, B, C, X(80), X(14458)}}, {{A, B, C, X(81), X(183)}}, {{A, B, C, X(92), X(7224)}}, {{A, B, C, X(95), X(56328)}}, {{A, B, C, X(105), X(1376)}}, {{A, B, C, X(111), X(41431)}}, {{A, B, C, X(257), X(54122)}}, {{A, B, C, X(278), X(8817)}}, {{A, B, C, X(305), X(52392)}}, {{A, B, C, X(312), X(7261)}}, {{A, B, C, X(333), X(41527)}}, {{A, B, C, X(385), X(52136)}}, {{A, B, C, X(614), X(5205)}}, {{A, B, C, X(904), X(47643)}}, {{A, B, C, X(951), X(28476)}}, {{A, B, C, X(983), X(56180)}}, {{A, B, C, X(1284), X(1469)}}, {{A, B, C, X(1390), X(9103)}}, {{A, B, C, X(2006), X(6063)}}, {{A, B, C, X(2113), X(9258)}}, {{A, B, C, X(2186), X(55037)}}, {{A, B, C, X(2481), X(13478)}}, {{A, B, C, X(2770), X(55017)}}, {{A, B, C, X(2862), X(40413)}}, {{A, B, C, X(3112), X(56046)}}, {{A, B, C, X(3296), X(7612)}}, {{A, B, C, X(3407), X(7033)}}, {{A, B, C, X(3415), X(52150)}}, {{A, B, C, X(3425), X(7163)}}, {{A, B, C, X(3596), X(15314)}}, {{A, B, C, X(5556), X(14484)}}, {{A, B, C, X(5557), X(7607)}}, {{A, B, C, X(5558), X(43537)}}, {{A, B, C, X(5559), X(53100)}}, {{A, B, C, X(5561), X(14492)}}, {{A, B, C, X(5970), X(55018)}}, {{A, B, C, X(7045), X(9073)}}, {{A, B, C, X(7091), X(9108)}}, {{A, B, C, X(7320), X(47586)}}, {{A, B, C, X(7357), X(18359)}}, {{A, B, C, X(9315), X(14665)}}, {{A, B, C, X(14486), X(42019)}}, {{A, B, C, X(29352), X(51476)}}, {{A, B, C, X(32085), X(56179)}}, {{A, B, C, X(34234), X(54128)}}, {{A, B, C, X(34429), X(37741)}}, {{A, B, C, X(34893), X(45819)}}
X(56358) = barycentric product X(i)*X(j) for these (i, j): {57, 7033}, {85, 983}, {181, 7307}, {226, 40415}, {279, 56180}, {349, 38813}, {604, 7034}, {1284, 40834}, {1434, 56196}, {1469, 3114}, {3113, 7146}, {3261, 8685}, {3407, 7179}, {3676, 4621}, {4552, 7255}, {6358, 7305}, {7132, 75}, {17743, 7}, {38810, 65}, {43265, 552}
X(56358) = barycentric quotient X(i)/X(j) for these (i, j): {1, 3061}, {2, 3705}, {6, 3056}, {7, 3662}, {9, 4073}, {10, 4136}, {12, 16886}, {31, 20665}, {42, 20684}, {48, 20753}, {56, 2275}, {57, 982}, {65, 3721}, {73, 20727}, {81, 3794}, {85, 33930}, {101, 40499}, {213, 4531}, {222, 3784}, {226, 2887}, {269, 41777}, {279, 7185}, {514, 3810}, {604, 7032}, {651, 3888}, {664, 33946}, {983, 9}, {1284, 18904}, {1400, 3778}, {1402, 16584}, {1403, 20284}, {1405, 4787}, {1407, 7248}, {1423, 41886}, {1431, 3863}, {1432, 3865}, {1434, 33947}, {1441, 20234}, {1447, 33891}, {1469, 3094}, {2003, 7186}, {2171, 7237}, {2275, 12836}, {3113, 52652}, {3212, 33890}, {3407, 52133}, {3668, 16888}, {3669, 3777}, {3676, 3776}, {4551, 7239}, {4621, 3699}, {7033, 312}, {7034, 28659}, {7132, 1}, {7146, 51836}, {7175, 7184}, {7176, 7187}, {7178, 3801}, {7179, 3314}, {7255, 4560}, {7296, 10877}, {7305, 2185}, {7307, 18021}, {8685, 101}, {17743, 8}, {18097, 16889}, {30725, 53533}, {38810, 314}, {38813, 284}, {40415, 333}, {43265, 6057}, {56180, 346}, {56196, 2321}

X(56359) = KP4(X(1)) OF X(7) AND X(7)

Barycentrics    a*(a+b-c)^2*(a-b+c)^2*(a^2-2*a*b+b^2+c^2)*(a^2+b^2-2*a*c+c^2) : :

X(56359) lies on these lines: {1, 7056}, {7, 33}, {34, 54128}, {55, 77}, {57, 1814}, {63, 220}, {69, 200}, {81, 2332}, {222, 39273}, {279, 17784}, {479, 4318}, {614, 658}, {1043, 4320}, {1088, 2263}, {1439, 56328}, {1443, 52429}, {1444, 2328}, {1448, 56146}, {1458, 56098}, {1619, 7177}, {2293, 56330}, {3676, 34036}, {3920, 10004}, {3938, 41355}, {4334, 7281}, {4911, 34398}, {5018, 7220}, {7073, 7190}, {7084, 10482}, {7191, 9533}, {8816, 29616}, {14935, 52001}, {52371, 52392}

X(56359) = isogonal conjugate of X(4319)
X(56359) = trilinear pole of line {657, 905}
X(56359) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 4319}, {2, 30706}, {3, 1863}, {6, 6554}, {8, 7083}, {9, 2082}, {21, 40965}, {33, 1040}, {55, 497}, {56, 4012}, {57, 28070}, {78, 40987}, {100, 17115}, {200, 614}, {210, 5324}, {220, 4000}, {281, 7124}, {346, 16502}, {480, 7195}, {607, 27509}, {657, 3732}, {728, 28017}, {1043, 40934}, {1253, 3673}, {1260, 1851}, {1473, 7046}, {1633, 3900}, {1763, 40176}, {2287, 16583}, {2322, 23620}, {2327, 52577}, {2328, 3914}, {2332, 18589}, {2999, 40175}, {4183, 17441}, {5089, 23601}, {7058, 21813}, {7071, 17170}, {7079, 7289}, {7256, 50490}, {40961, 56182}
X(56359) = X(i)-vertex conjugate of X(j) for these {i, j}: {56, 56098}
X(56359) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 4012}, {3, 4319}, {9, 6554}, {223, 497}, {478, 2082}, {5452, 28070}, {6609, 614}, {8054, 17115}, {17113, 3673}, {32664, 30706}, {36103, 1863}, {36908, 3914}, {40611, 40965}
X(56359) = X(i)-Ceva conjugate of X(j) for these {i, j}: {30705, 7131}
X(56359) = X(i)-cross conjugate of X(j) for these {i, j}: {1, 56179}, {649, 658}, {1037, 7131}, {3309, 651}, {9316, 57}, {17613, 88}
X(56359) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(33)}}, {{A, B, C, X(2), X(43736)}}, {{A, B, C, X(7), X(63)}}, {{A, B, C, X(31), X(1458)}}, {{A, B, C, X(57), X(241)}}, {{A, B, C, X(75), X(8809)}}, {{A, B, C, X(79), X(14457)}}, {{A, B, C, X(84), X(775)}}, {{A, B, C, X(86), X(17811)}}, {{A, B, C, X(269), X(1407)}}, {{A, B, C, X(273), X(56287)}}, {{A, B, C, X(278), X(15728)}}, {{A, B, C, X(614), X(649)}}, {{A, B, C, X(1037), X(1041)}}, {{A, B, C, X(1252), X(3870)}}, {{A, B, C, X(1476), X(26703)}}, {{A, B, C, X(2162), X(2191)}}, {{A, B, C, X(2249), X(40439)}}, {{A, B, C, X(2363), X(7091)}}, {{A, B, C, X(2862), X(40413)}}, {{A, B, C, X(4334), X(5018)}}, {{A, B, C, X(5665), X(56153)}}, {{A, B, C, X(7012), X(56262)}}, {{A, B, C, X(7131), X(8817)}}, {{A, B, C, X(38254), X(39962)}}, {{A, B, C, X(40399), X(42361)}}
X(56359) = barycentric product X(i)*X(j) for these (i, j): {1, 30705}, {7, 7131}, {57, 8817}, {269, 30701}, {279, 56179}, {479, 56243}, {514, 8269}, {1037, 85}, {1041, 348}, {1088, 7123}, {1439, 40411}, {3668, 40403}, {48070, 934}, {56328, 8816}
X(56359) = barycentric quotient X(i)/X(j) for these (i, j): {1, 6554}, {6, 4319}, {9, 4012}, {19, 1863}, {31, 30706}, {55, 28070}, {56, 2082}, {57, 497}, {77, 27509}, {222, 1040}, {269, 4000}, {279, 3673}, {603, 7124}, {604, 7083}, {608, 40987}, {649, 17115}, {738, 7195}, {934, 3732}, {1037, 9}, {1041, 281}, {1042, 16583}, {1106, 16502}, {1400, 40965}, {1407, 614}, {1410, 23620}, {1412, 5324}, {1426, 52577}, {1427, 3914}, {1435, 1851}, {1439, 18589}, {1461, 1633}, {3668, 53510}, {4320, 5286}, {4350, 41785}, {7023, 28017}, {7050, 40175}, {7053, 7289}, {7084, 220}, {7099, 1473}, {7123, 200}, {7131, 8}, {7169, 40176}, {7177, 17170}, {7216, 48403}, {8269, 190}, {8816, 4385}, {8817, 312}, {14935, 3119}, {30701, 341}, {30705, 75}, {34855, 51400}, {36057, 23601}, {37755, 21015}, {40403, 1043}, {43932, 48398}, {48070, 4397}, {52373, 17441}, {52778, 6558}, {56179, 346}, {56243, 5423}, {56260, 4082}

X(56360) = KP4(X(2)) OF X(4) AND X(4)

Barycentrics    (5*a^4+5*b^4-2*b^2*c^2+c^4-2*a^2*(3*b^2+c^2))*(5*a^4+b^4-2*b^2*c^2+5*c^4-2*a^2*(b^2+3*c^2)) : :

X(56360) lies on these lines: {3, 56334}, {69, 32989}, {230, 6340}, {253, 16925}, {264, 32973}, {305, 37667}, {3523, 9229}, {8797, 32971}, {32987, 40410}, {35927, 41762}

X(56360) = isotomic conjugate of X(32972)
X(56360) = X(i)-vertex conjugate of X(j) for these {i, j}: {6339, 52439}
X(56360) = X(i)-cross conjugate of X(j) for these {i, j}: {32970, 2}
X(56360) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(69)}}, {{A, B, C, X(66), X(36953)}}, {{A, B, C, X(98), X(6339)}}, {{A, B, C, X(193), X(230)}}, {{A, B, C, X(384), X(3523)}}, {{A, B, C, X(1031), X(53099)}}, {{A, B, C, X(2996), X(34285)}}, {{A, B, C, X(2998), X(43537)}}, {{A, B, C, X(3407), X(52224)}}, {{A, B, C, X(5395), X(40416)}}, {{A, B, C, X(7612), X(40405)}}, {{A, B, C, X(8781), X(16774)}}, {{A, B, C, X(8882), X(55999)}}
X(56360) = barycentric quotient X(i)/X(j) for these (i, j): {2, 32972}

X(56361) = KP4(X(3)) OF X(2) AND X(4)

Barycentrics    a^2*(a^8-(b^2-c^2)^3*(b^2+c^2)-2*a^6*(b^2+2*c^2)+2*a^4*c^2*(b^2+3*c^2)+2*a^2*(b^6-2*b^4*c^2+b^2*c^4-2*c^6))*(a^8+(b^2-c^2)^3*(b^2+c^2)-2*a^6*(2*b^2+c^2)+2*a^4*b^2*(3*b^2+c^2)+2*a^2*(-2*b^6+b^4*c^2-2*b^2*c^4+c^6)) : :

X(56361) lies on these lines: {3, 44405}, {24, 16172}, {394, 8553}, {1217, 22467}, {3580, 52350}, {3926, 35296}, {7395, 22268}, {7503, 22270}, {14376, 52275}, {17974, 44208}, {34897, 35302}

X(56361) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 3548}, {75, 44527}
X(56361) = X(i)-vertex conjugate of X(j) for these {i, j}: {6504, 6524}
X(56361) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 3548}, {206, 44527}, {577, 44752}
X(56361) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(3)}}, {{A, B, C, X(4), X(56002)}}, {{A, B, C, X(6), X(8553)}}, {{A, B, C, X(25), X(23357)}}, {{A, B, C, X(64), X(13579)}}, {{A, B, C, X(74), X(6504)}}, {{A, B, C, X(94), X(34438)}}, {{A, B, C, X(249), X(1993)}}, {{A, B, C, X(288), X(598)}}, {{A, B, C, X(297), X(44208)}}, {{A, B, C, X(323), X(26958)}}, {{A, B, C, X(393), X(1609)}}, {{A, B, C, X(459), X(43756)}}, {{A, B, C, X(2987), X(34207)}}, {{A, B, C, X(3527), X(11538)}}, {{A, B, C, X(5392), X(34439)}}, {{A, B, C, X(8796), X(55999)}}, {{A, B, C, X(11140), X(34436)}}, {{A, B, C, X(13575), X(43705)}}, {{A, B, C, X(13582), X(43719)}}, {{A, B, C, X(30535), X(43725)}}, {{A, B, C, X(40799), X(51477)}}
X(56361) = barycentric product X(i)*X(j) for these (i, j): {264, 44405}
X(56361) = barycentric quotient X(i)/X(j) for these (i, j): {3, 3548}, {32, 44527}, {1147, 44752}, {44405, 3}

X(56362) = KP4(X(3)) OF X(2) AND X(6)

Barycentrics    a^2*(2*a^4-b^4+b^2*c^2+2*c^4+a^2*(b^2-4*c^2))*(2*a^4+2*b^4+b^2*c^2-c^4+a^2*(-4*b^2+c^2)) : :

X(56362) lies on these lines: {187, 439}, {394, 5023}, {1073, 52275}, {1204, 17974}, {1214, 21508}, {3053, 5866}, {5206, 28724}, {6803, 14938}, {7487, 32132}, {13219, 16925}, {14376, 32973}, {14489, 17928}, {22467, 40801}, {32985, 34897}, {35302, 36609}

X(56362) = isogonal conjugate of X(44518)
X(56362) = trilinear pole of line {6132, 520}
X(56362) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 44518}, {19, 30771}, {75, 34481}
X(56362) = X(i)-vertex conjugate of X(j) for these {i, j}: {2207, 2996}
X(56362) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 44518}, {6, 30771}, {206, 34481}
X(56362) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(3)}}, {{A, B, C, X(4), X(249)}}, {{A, B, C, X(6), X(5023)}}, {{A, B, C, X(25), X(3053)}}, {{A, B, C, X(32), X(187)}}, {{A, B, C, X(39), X(5206)}}, {{A, B, C, X(54), X(5395)}}, {{A, B, C, X(64), X(2987)}}, {{A, B, C, X(74), X(2996)}}, {{A, B, C, X(76), X(11270)}}, {{A, B, C, X(83), X(3431)}}, {{A, B, C, X(111), X(40322)}}, {{A, B, C, X(193), X(40318)}}, {{A, B, C, X(237), X(3552)}}, {{A, B, C, X(248), X(41894)}}, {{A, B, C, X(253), X(43705)}}, {{A, B, C, X(574), X(15513)}}, {{A, B, C, X(598), X(13472)}}, {{A, B, C, X(671), X(13452)}}, {{A, B, C, X(1173), X(53101)}}, {{A, B, C, X(1204), X(36212)}}, {{A, B, C, X(1968), X(52144)}}, {{A, B, C, X(1993), X(8796)}}, {{A, B, C, X(3532), X(40802)}}, {{A, B, C, X(5013), X(5210)}}, {{A, B, C, X(5866), X(6337)}}, {{A, B, C, X(6339), X(34207)}}, {{A, B, C, X(7163), X(54123)}}, {{A, B, C, X(8588), X(37512)}}, {{A, B, C, X(9217), X(9292)}}, {{A, B, C, X(9605), X(15655)}}, {{A, B, C, X(11738), X(53105)}}, {{A, B, C, X(11741), X(16835)}}, {{A, B, C, X(14491), X(53107)}}, {{A, B, C, X(14528), X(30535)}}, {{A, B, C, X(18840), X(20421)}}, {{A, B, C, X(20251), X(53102)}}, {{A, B, C, X(29011), X(40824)}}
X(56362) = barycentric quotient X(i)/X(j) for these (i, j): {3, 30771}, {6, 44518}, {32, 34481}

X(56363) = KP4(X(6)) OF X(3) AND X(4)

Barycentrics    a^2*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(2*a^6-b^6-b^2*c^4+2*c^6+2*a^2*c^2*(b^2-c^2)-a^4*(b^2+2*c^2))*(2*a^6+2*b^6-b^4*c^2-c^6-a^4*(2*b^2+c^2)-2*a^2*(b^4-b^2*c^2)) : :

X(56363) lies on these lines: {22, 15905}, {112, 53852}, {154, 8743}, {315, 34412}, {459, 34407}, {1073, 3172}, {1249, 8779}, {1297, 17409}, {1301, 20232}, {11605, 41370}

X(56363) = isogonal conjugate of X(20208)
X(56363) = trilinear pole of line {2485, 42658}
X(56363) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 20208}, {63, 1853}, {92, 53852}, {1073, 20322}, {19611, 46829}
X(56363) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 20208}, {3162, 1853}, {22391, 53852}
X(56363) = X(i)-cross conjugate of X(j) for these {i, j}: {520, 112}
X(56363) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(23964)}}, {{A, B, C, X(4), X(22)}}, {{A, B, C, X(6), X(154)}}, {{A, B, C, X(25), X(459)}}, {{A, B, C, X(54), X(15324)}}, {{A, B, C, X(111), X(38253)}}, {{A, B, C, X(184), X(8779)}}, {{A, B, C, X(196), X(7115)}}, {{A, B, C, X(275), X(39955)}}, {{A, B, C, X(801), X(41894)}}, {{A, B, C, X(1383), X(2052)}}, {{A, B, C, X(1988), X(43706)}}, {{A, B, C, X(2189), X(7003)}}, {{A, B, C, X(3431), X(15388)}}, {{A, B, C, X(13472), X(14371)}}, {{A, B, C, X(32230), X(43697)}}
X(56363) = barycentric product X(i)*X(j) for these (i, j): {4, 56306}, {25, 34412}, {154, 34407}
X(56363) = barycentric quotient X(i)/X(j) for these (i, j): {6, 20208}, {25, 1853}, {184, 53852}, {204, 20322}, {3172, 46829}, {17409, 53851}, {34407, 41530}, {34412, 305}, {56306, 69}

X(56364) = KP4(X(6)) OF X(4) AND X(4)

Barycentrics    a^2*(a^4-2*a^2*b^2+b^4+c^4)*(a^4+b^4-2*a^2*c^2+c^4)*(a^4-(b^2-c^2)^2)^2 : :

X(56364) lies on these lines: {6, 52448}, {22, 232}, {25, 11610}, {107, 42295}, {184, 8743}, {217, 56347}, {287, 2052}, {297, 315}, {393, 41757}, {1501, 51334}, {1993, 36426}, {3425, 17409}, {3990, 4463}, {4055, 4456}, {6524, 41363}, {6747, 11605}, {8744, 51831}, {8746, 14533}, {10002, 34945}, {27373, 56344}, {39643, 42294}, {41372, 44415}

X(56364) = isogonal conjugate of X(6389)
X(56364) = polar conjugate of X(41009)
X(56364) = trilinear pole of line {2485, 17994}
X(56364) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 6389}, {19, 44141}, {48, 41009}, {63, 1899}, {69, 2083}, {75, 39643}, {92, 426}, {255, 41760}, {304, 40947}, {326, 3767}, {394, 17871}, {1102, 41762}, {1632, 24018}
X(56364) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 6389}, {6, 44141}, {206, 39643}, {1249, 41009}, {3162, 1899}, {6523, 41760}, {15259, 3767}, {22391, 426}
X(56364) = X(i)-cross conjugate of X(j) for these {i, j}: {6, 56004}, {669, 107}, {684, 32687}, {924, 112}
X(56364) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(43717)}}, {{A, B, C, X(4), X(22)}}, {{A, B, C, X(6), X(184)}}, {{A, B, C, X(25), X(232)}}, {{A, B, C, X(111), X(459)}}, {{A, B, C, X(248), X(32319)}}, {{A, B, C, X(393), X(8745)}}, {{A, B, C, X(669), X(42295)}}, {{A, B, C, X(1383), X(8796)}}, {{A, B, C, X(1629), X(33971)}}, {{A, B, C, X(1987), X(2351)}}, {{A, B, C, X(1993), X(23357)}}, {{A, B, C, X(2763), X(15384)}}, {{A, B, C, X(6531), X(39109)}}, {{A, B, C, X(8770), X(16080)}}, {{A, B, C, X(15388), X(18532)}}, {{A, B, C, X(34405), X(56307)}}, {{A, B, C, X(34427), X(35140)}}, {{A, B, C, X(39951), X(43530)}}
X(56364) = barycentric product X(i)*X(j) for these (i, j): {4, 56307}, {25, 34405}, {393, 56004}, {2207, 42407}
X(56364) = barycentric quotient X(i)/X(j) for these (i, j): {3, 44141}, {4, 41009}, {6, 6389}, {25, 1899}, {32, 39643}, {184, 426}, {393, 41760}, {1096, 17871}, {1973, 2083}, {1974, 40947}, {2207, 3767}, {8743, 28405}, {8745, 41770}, {27373, 52532}, {32713, 1632}, {34405, 305}, {34854, 2450}, {36417, 42295}, {40981, 6751}, {52439, 41762}, {56004, 3926}, {56307, 69}

X(56365) = KP4(X(11)) OF X(7) AND X(8)

Barycentrics    (a^3+2*b^3-2*b^2*c-b*c^2+c^3-a^2*(b+c)-a*(2*b^2-4*b*c+c^2))*(a^3+b^3-b^2*c-2*b*c^2+2*c^3-a^2*(b+c)-a*(b^2-4*b*c+2*c^2)) : :

X(56365) lies on these lines: {2, 31611}, {11, 4998}, {666, 46101}, {693, 10006}, {3816, 40419}, {3912, 6631}, {4887, 9436}, {8817, 10589}, {10584, 13577}, {14061, 28758}, {18771, 30941}, {18821, 45310}

X(56365) = isogonal conjugate of X(20958)
X(56365) = isotomic conjugate of X(3035)
X(56365) = trilinear pole of line {4440, 37781}
X(56365) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 20958}, {6, 17439}, {19, 22055}, {31, 3035}, {32, 20881}, {109, 11124}, {213, 18645}, {649, 14589}, {692, 21105}, {1110, 43909}, {1333, 21013}, {2149, 46101}, {6139, 35340}, {35328, 46393}
X(56365) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 3035}, {3, 20958}, {6, 22055}, {9, 17439}, {11, 11124}, {37, 21013}, {514, 43909}, {650, 46101}, {1086, 21105}, {5375, 14589}, {6376, 20881}, {6626, 18645}
X(56365) = X(i)-Ceva conjugate of X(j) for these {i, j}: {31619, 31628}
X(56365) = X(i)-cross conjugate of X(j) for these {i, j}: {2, 31619}, {11, 31611}, {883, 2481}, {6667, 2}, {52305, 666}
X(56365) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(7608)}}, {{A, B, C, X(2), X(693)}}, {{A, B, C, X(86), X(40410)}}, {{A, B, C, X(650), X(14947)}}, {{A, B, C, X(2481), X(4997)}}, {{A, B, C, X(3262), X(8797)}}, {{A, B, C, X(4555), X(6631)}}, {{A, B, C, X(8781), X(32020)}}, {{A, B, C, X(10159), X(18299)}}, {{A, B, C, X(17983), X(37129)}}, {{A, B, C, X(30786), X(31637)}}, {{A, B, C, X(35147), X(40429)}}
X(56365) = barycentric product X(i)*X(j) for these (i, j): {11, 31619}, {18771, 76}, {31611, 4998}, {31628, 693}, {34387, 38809}
X(56365) = barycentric quotient X(i)/X(j) for these (i, j): {1, 17439}, {2, 3035}, {3, 22055}, {6, 20958}, {10, 21013}, {11, 46101}, {75, 20881}, {86, 18645}, {100, 14589}, {514, 21105}, {650, 11124}, {666, 35313}, {1086, 43909}, {2720, 35328}, {18771, 6}, {31611, 11}, {31619, 4998}, {31628, 100}, {37139, 35340}, {38809, 59}, {40166, 42547}
X(56365) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 31611, 31628}

X(56366) = X(2)X(7)∩X(10)X(34)

Barycentrics    1 + 2*Cos[A] - Cos[2*A] - Cos[2*B] - Cos[2*C] : :

X(56366) lies on these lines: {2, 7}, {3, 31832}, {4, 5285}, {5, 37581}, {6, 26942}, {10, 34}, {11, 54326}, {12, 1460}, {33, 12618}, {40, 3088}, {47, 171}, {56, 17698}, {65, 19784}, {69, 2003}, {84, 7400}, {92, 54283}, {109, 26034}, {141, 222}, {198, 7536}, {219, 23292}, {278, 2345}, {306, 45126}, {343, 55400}, {344, 28754}, {388, 37037}, {406, 12572}, {427, 7085}, {440, 54322}, {478, 1211}, {499, 982}, {631, 26929}, {651, 32782}, {966, 37799}, {1214, 14376}, {1352, 3955}, {1370, 5314}, {1397, 12588}, {1407, 3763}, {1442, 32858}, {1458, 24943}, {1473, 7499}, {1478, 5329}, {1726, 24316}, {1766, 1848}, {1788, 35650}, {1899, 26890}, {1943, 3661}, {1947, 17907}, {2323, 11427}, {3085, 5269}, {3086, 3677}, {3220, 7494}, {3361, 19881}, {3454, 26364}, {3476, 48803}, {3541, 55104}, {3547, 7330}, {3589, 52424}, {3618, 52423}, {3745, 5808}, {4318, 29667}, {4417, 19795}, {5044, 34120}, {5094, 21015}, {5125, 40573}, {5230, 52357}, {5278, 40999}, {5709, 7404}, {5782, 34032}, {5824, 17602}, {5831, 31993}, {6354, 17369}, {6357, 17293}, {6389, 53819}, {6515, 54444}, {6676, 24320}, {7182, 17095}, {7484, 26933}, {8889, 26939}, {9316, 32781}, {9364, 33174}, {10056, 17716}, {10072, 17598}, {10198, 43531}, {12587, 20986}, {13567, 55432}, {14786, 37532}, {15149, 26036}, {16435, 51414}, {16549, 41342}, {16577, 17776}, {17073, 25091}, {17074, 33172}, {17080, 32779}, {17289, 21582}, {18623, 29611}, {18652, 53996}, {19822, 37800}, {19854, 32780}, {25760, 34029}, {26878, 37119}, {26892, 43653}, {26932, 55406}, {28420, 56078}, {28738, 33116}, {28793, 33066}, {28813, 37655}, {29647, 42289}, {36493, 41346}, {37176, 37583}, {37557, 45132}, {37638, 55438}, {37649, 55399}, {38047, 41539}, {45206, 53816}

X(56366) = isotomic conjugate of the polar conjugate of X(11392)
X(56366) = barycentric product X(i)*X(j) for these {i,j}: {69, 11392}, {349, 4280}, {4554, 46380}
X(56366) = barycentric quotient X(i)/X(j) for these {i,j}: {4280, 284}, {11392, 4}, {46380, 650}
X(56366) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3218, 55900}, {2, 28739, 226}, {2, 55910, 9}, {2, 55912, 27509}, {278, 2345, 6358}, {307, 5294, 1708}, {427, 7085, 50861}, {3306, 55903, 2}, {5094, 26867, 21015}, {11427, 26872, 2323}, {27509, 55912, 3929}

X(56367) = X(2)X(7)∩X(10)X(1448)

Barycentrics    1 - 4*Cos[A] + Cos[2*A] + Cos[2*B] + Cos[2*C] : :

X(55967) lies on these lines: {2, 7}, {3, 26929}, {4, 37581}, {8, 1943}, {10, 1448}, {12, 37153}, {20, 5285}, {48, 7364}, {55, 36706}, {56, 37176}, {69, 222}, {75, 278}, {77, 306}, {84, 52404}, {85, 19808}, {141, 1407}, {145, 52362}, {171, 255}, {193, 2003}, {196, 11683}, {219, 37669}, {220, 53415}, {223, 3687}, {241, 32777}, {268, 45200}, {281, 18750}, {304, 345}, {320, 19795}, {333, 1396}, {343, 22129}, {347, 18632}, {388, 1010}, {393, 1947}, {394, 26872}, {441, 7011}, {497, 54326}, {499, 18193}, {651, 5739}, {948, 20235}, {958, 24570}, {982, 3086}, {1038, 54433}, {1211, 6180}, {1259, 37180}, {1368, 26939}, {1395, 1935}, {1441, 19822}, {1456, 3966}, {1458, 33171}, {1473, 7494}, {1654, 27328}, {1751, 26961}, {1766, 21621}, {1812, 3173}, {2345, 7365}, {2975, 24538}, {3088, 5709}, {3089, 7330}, {3101, 36850}, {3210, 17086}, {3220, 10565}, {3339, 19784}, {3361, 19836}, {3436, 24537}, {3546, 26921}, {3547, 24467}, {3618, 52424}, {3677, 14986}, {3704, 15832}, {3784, 10519}, {3927, 34120}, {3937, 43653}, {3955, 6776}, {3974, 14594}, {4200, 6734}, {4293, 5329}, {4315, 48803}, {4331, 4418}, {4334, 32783}, {4359, 37800}, {4363, 6354}, {5018, 32778}, {6350, 18607}, {6353, 24320}, {6357, 42696}, {6358, 21406}, {6604, 37543}, {7085, 7386}, {7146, 45220}, {7169, 41735}, {7318, 39700}, {7321, 19794}, {7383, 26877}, {7396, 50861}, {7404, 37532}, {7499, 26866}, {9316, 26034}, {10319, 17170}, {10996, 26927}, {11064, 55466}, {11427, 55399}, {11433, 55400}, {11679, 34050}, {13567, 55406}, {14555, 34048}, {14826, 26884}, {16028, 55882}, {16051, 21015}, {16197, 26928}, {17076, 52421}, {17080, 17740}, {17598, 18477}, {18624, 32087}, {18625, 19825}, {18629, 19835}, {18656, 24310}, {18928, 55432}, {19645, 21279}, {19786, 39126}, {19843, 49598}, {19855, 32780}, {23292, 55405}, {24586, 45984}, {26867, 30739}, {28420, 28754}, {28439, 52373}, {28605, 37798}, {28753, 33116}, {28795, 37655}, {28807, 33066}, {30679, 52351}, {30680, 52381}, {34030, 52357}, {37648, 55438}, {37649, 55437}, {40680, 53819}, {41883, 54113}, {43216, 46017}, {51171, 52423}, {52283, 55110}

X(56367) = isotomic conjugate of the isogonal conjugate of X(2286)
X(56367) = isotomic conjugate of the polar conjugate of X(388)
X(56367) = X(i)-isoconjugate of X(j) for these (i,j): {6, 1039}, {9, 51686}, {19, 1036}, {25, 2339}, {29, 2281}, {33, 2221}, {281, 1472}, {607, 56328}, {650, 32691}, {663, 36099}, {1172, 1245}, {1973, 30479}, {2299, 56219}
X(56367) = X(i)-Dao conjugate of X(j) for these (i,j): {6, 1036}, {9, 1039}, {226, 56219}, {478, 51686}, {5515, 3064}, {6337, 30479}, {6505, 2339}, {17421, 650}, {40179, 497}, {40181, 33}, {55046, 18344}
X(56367) = cevapoint of X(i) and X(j) for these (i,j): {1038, 5227}, {2285, 8900}, {2522, 26933}
X(56367) = trilinear pole of line {23874, 51644}
X(56367) = barycentric product X(i)*X(j) for these {i,j}: {7, 54433}, {57, 19799}, {69, 388}, {73, 44154}, {75, 1038}, {76, 2286}, {77, 4385}, {85, 5227}, {304, 2285}, {305, 1460}, {307, 1010}, {345, 7365}, {348, 2345}, {612, 7182}, {664, 23874}, {668, 51644}, {1231, 2303}, {1264, 7103}, {1265, 7197}, {1434, 3610}, {2517, 6516}, {2522, 4554}, {3718, 4320}, {3974, 7056}, {4025, 14594}, {4998, 26933}, {5323, 20336}, {6063, 7085}, {7055, 7102}, {7386, 8817}, {8816, 27509}
X(56367) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1039}, {3, 1036}, {56, 51686}, {63, 2339}, {69, 30479}, {73, 1245}, {77, 56328}, {109, 32691}, {222, 2221}, {388, 4}, {603, 1472}, {612, 33}, {651, 36099}, {1010, 29}, {1038, 1}, {1214, 56219}, {1409, 2281}, {1460, 25}, {2285, 19}, {2286, 6}, {2303, 1172}, {2345, 281}, {2517, 44426}, {2522, 650}, {3610, 2321}, {3974, 7046}, {4320, 34}, {4385, 318}, {5227, 9}, {5323, 28}, {6516, 1310}, {6590, 3064}, {7085, 55}, {7102, 1857}, {7103, 1118}, {7197, 1119}, {7365, 278}, {7386, 497}, {8678, 18344}, {8898, 1880}, {8900, 36103}, {10376, 1426}, {14594, 1897}, {19459, 7083}, {19799, 312}, {23874, 522}, {26933, 11}, {44119, 2299}, {44154, 44130}, {51644, 513}, {54416, 607}, {54433, 8}
X(56367) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 63, 27509}, {2, 144, 27540}, {2, 329, 27539}, {2, 3218, 55905}, {2, 55912, 9}, {8, 18623, 1943}, {9, 20266, 2}, {222, 26942, 69}, {343, 22129, 26871}, {345, 348, 1214}, {3306, 55902, 2}, {5435, 28780, 2}, {7085, 26933, 7386}, {17077, 28776, 2}, {28774, 52358, 2}

X(56368) = X(2)X(3)∩X(99)X(10098)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(2*a^8 - 6*a^6*b^2 - a^4*b^4 + 6*a^2*b^6 - b^8 - 6*a^6*c^2 + 20*a^4*b^2*c^2 - 10*a^2*b^4*c^2 - a^4*c^4 - 10*a^2*b^2*c^4 + 2*b^4*c^4 + 6*a^2*c^6 - c^8) : :

X(56368) lies on the cubic K088 and these lines: {2, 3}, {99, 10098}, {112, 2696}, {648, 691}, {935, 1296}, {1289, 53961}, {1304, 30256}, {1499, 32729}, {10423, 20187}, {14654, 51258}, {39382, 53895}, {41676, 47291}, {47293, 53350}, {47545, 52474}

X(56368) = X(i)-isoconjugate of X(j) for these (i,j): {63, 10103}, {656, 10102}
X(56368) = X(i)-Dao conjugate of X(j) for these (i,j): {3162, 10103}, {40596, 10102}
X(56368) = barycentric product X(4235)*X(52232)
X(56368) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 10103}, {112, 10102}, {52232, 14977}
X(56368) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4235, 7473, 46619}, {4235, 7482, 7473}, {5000, 5001, 36168}, {7468, 7482, 46592}, {7472, 7473, 4235}, {7472, 7482, 46619}, {40894, 40895, 36166}

X(56369) = X(2)X(3)∩X(74)X(11564)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(5*a^6 - 8*a^4*b^2 + a^2*b^4 + 2*b^6 - 8*a^4*c^2 + 9*a^2*b^2*c^2 - 2*b^4*c^2 + a^2*c^4 - 2*b^2*c^4 + 2*c^6) : :
X(56369) = 3 X[2] - 4 X[47335], 3 X[3] - 2 X[18572], 6 X[3] - 5 X[30745], 2 X[4] - 3 X[186], 5 X[4] - 6 X[403], 3 X[4] - 4 X[468], 11 X[4] - 12 X[10151], 13 X[4] - 12 X[13473], X[4] - 3 X[13619], 5 X[4] - 9 X[35489], 7 X[4] - 12 X[37931], 5 X[4] - 8 X[37934], 17 X[4] - 24 X[37935], 19 X[4] - 24 X[37942], 7 X[4] - 9 X[37943], and many others

X(56369) lies on the cubic K330 and these lines: {2, 3}, {74, 11564}, {112, 41358}, {187, 44972}, {323, 12121}, {340, 35520}, {511, 7722}, {516, 31948}, {935, 14388}, {1204, 40242}, {1495, 10721}, {1503, 12244}, {1531, 15035}, {1990, 18365}, {2777, 12112}, {3043, 10294}, {3098, 41470}, {5095, 19924}, {5702, 16303}, {6103, 6781}, {6242, 14641}, {6325, 10098}, {6403, 48896}, {6776, 47280}, {7728, 35265}, {7967, 47469}, {8550, 47466}, {8588, 50718}, {8705, 48905}, {10722, 47326}, {10733, 32110}, {10990, 18400}, {11468, 34786}, {11522, 51701}, {11645, 13169}, {11738, 47445}, {13148, 13391}, {13449, 38704}, {13568, 43818}, {14712, 56016}, {14853, 47458}, {14912, 47464}, {14989, 16080}, {15463, 43576}, {15826, 43273}, {17702, 41724}, {17854, 44668}, {19651, 38808}, {20417, 25739}, {21445, 47000}, {29012, 32250}, {30247, 53938}, {31670, 52238}, {32210, 52863}, {32217, 48910}, {32710, 53693}, {33638, 40118}, {34627, 47492}, {34631, 47489}, {36990, 47448}, {38295, 47271}, {38723, 51391}, {40138, 47322}, {41869, 51693}, {46982, 47241}, {47003, 47247}, {47549, 54132}, {47581, 51538}

X(56369) = midpoint of X(17800) and X(37924)
X(56369) = reflection of X(i) in X(j) for these {i,j}: {4, 10295}, {186, 13619}, {323, 12121}, {382, 7575}, {858, 47308}, {3146, 11799}, {3153, 44246}, {3543, 44265}, {5073, 44267}, {7464, 20}, {7574, 550}, {10296, 3}, {10721, 1495}, {10722, 47326}, {10733, 32110}, {10989, 3534}, {14989, 47327}, {15682, 7426}, {15684, 44266}, {18323, 47335}, {35480, 37969}, {41869, 51693}, {44972, 187}, {46450, 16386}, {48910, 32217}
X(56369) = isogonal conjugate of X(43720)
X(56369) = anticomplement of X(18323)
X(56369) = circumcircle-inverse of X(35473)
X(56369) = polar-circle-inverse of X(3845)
X(56369) = orthoptic-circle-of-the-Steiner-inellipse inverse of X(52293)
X(56369) = X(1)-isoconjugate of X(43720)
X(56369) = X(3)-Dao conjugate of X(43720)
X(56369) = crossdifference of every pair of points on line {647, 15860}
X(56369) = barycentric quotient X(6)/X(43720)
X(56369) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 18572, 30745}, {4, 10295, 186}, {4, 13619, 10295}, {4, 35473, 5094}, {4, 35486, 16868}, {4, 35491, 35478}, {4, 35503, 35486}, {4, 37458, 34484}, {4, 37943, 37984}, {20, 7492, 3534}, {20, 34797, 3520}, {186, 7464, 3520}, {186, 10296, 54001}, {376, 15682, 30775}, {403, 10295, 37934}, {403, 35489, 186}, {468, 52301, 37777}, {550, 7574, 2071}, {858, 47308, 376}, {1113, 1114, 35473}, {2070, 5073, 44267}, {3146, 35486, 4}, {3146, 35503, 16868}, {3153, 3522, 15122}, {3153, 44246, 37948}, {3522, 15122, 37948}, {3534, 35480, 35473}, {3534, 47596, 376}, {3543, 37760, 47336}, {3830, 37958, 44961}, {5000, 5001, 37907}, {5073, 32534, 4}, {5094, 35480, 4}, {7464, 7512, 2071}, {7547, 15696, 23040}, {7575, 21844, 186}, {10295, 37934, 35489}, {10296, 30745, 18572}, {10297, 44280, 631}, {10750, 10751, 18566}, {11799, 35503, 186}, {15122, 44246, 3522}, {15160, 15161, 35481}, {15681, 33532, 20}, {15682, 52290, 4}, {18323, 47335, 2}, {18533, 49670, 4}, {18559, 35481, 13596}, {18560, 37458, 4}, {21284, 35001, 378}, {35473, 37969, 186}, {37931, 37943, 186}, {37958, 44961, 37907}, {42789, 42790, 7575}, {44265, 47336, 37760}

X(56370) = X(2)X(3)∩X(98)X(325)

Barycentrics    2*a^8 - 3*a^6*b^2 + 5*a^4*b^4 - 5*a^2*b^6 + b^8 - 3*a^6*c^2 + 2*a^4*b^2*c^2 + a^2*b^4*c^2 - 4*b^6*c^2 + 5*a^4*c^4 + a^2*b^2*c^4 + 6*b^4*c^4 - 5*a^2*c^6 - 4*b^2*c^6 + c^8 : :
X(56370) = 3 X[2] + X[5999], 9 X[2] - X[40236], 3 X[2] - 5 X[40336], X[4] - 3 X[33228], X[20] + 3 X[14041], 5 X[631] - X[11676], 5 X[631] - 3 X[35297], 3 X[1513] - X[40236], X[1513] - 5 X[40336], 3 X[2071] + X[36174], 7 X[3523] - 3 X[13586], 3 X[3524] - X[8598], 3 X[5054] - X[37461], X[5999] + 2 X[10011], 3 X[5999] + X[40236], X[5999] + 5 X[40336], and many others

X(56370) lies on the cubic K460 and these lines: {{2, 3}, {98, 325}, {114, 1503}, {115, 18860}, {141, 13355}, {147, 7925}, {182, 3815}, {183, 48876}, {187, 38737}, {230, 511}, {262, 7792}, {316, 34473}, {385, 34380}, {523, 47570}, {524, 6055}, {538, 11623}, {542, 22110}, {575, 9300}, {576, 5306}, {620, 10256}, {625, 2794}, {1007, 6776}, {1184, 36747}, {1350, 37637}, {1351, 7735}, {1352, 7778}, {1353, 7774}, {1499, 16235}, {1550, 30789}, {1611, 37498}, {2080, 38739}, {2393, 44389}, {2407, 47277}, {2782, 6390}, {2967, 16318}, {2974, 30737}, {3001, 16310}, {3054, 3098}, {3055, 5092}, {3095, 5305}, {3260, 51611}, {3313, 53414}, {3329, 51732}, {3424, 48662}, {3589, 13354}, {5050, 7736}, {5085, 31489}, {5093, 5304}, {5188, 7749}, {5254, 9737}, {5286, 10983}, {5359, 36749}, {5480, 35387}, {5913, 37477}, {5915, 10564}, {5965, 35021}, {6033, 22664}, {6054, 41133}, {6194, 17004}, {6248, 7789}, {6393, 46236}, {6721, 29012}, {7607, 33706}, {7608, 54906}, {7610, 54173}, {7612, 37667}, {7745, 13335}, {7746, 30270}, {7763, 39646}, {7767, 10104}, {7769, 12203}, {7773, 36998}, {7799, 38664}, {7912, 9863}, {8705, 44386}, {9732, 49221}, {9733, 49220}, {9744, 48906}, {9752, 51212}, {9753, 21850}, {9754, 48874}, {9771, 51737}, {10519, 34229}, {11064, 47200}, {11163, 50979}, {11168, 50977}, {11174, 35429}, {11179, 11184}, {11580, 37496}, {11632, 52229}, {11898, 37668}, {13346, 40326}, {13449, 38749}, {14061, 39663}, {14627, 34482}, {14651, 47286}, {14881, 20576}, {15491, 42534}, {15597, 54169}, {15819, 24256}, {16303, 46127}, {16306, 18114}, {16320, 16760}, {18440, 37690}, {19924, 41139}, {22712, 37688}, {23055, 50967}, {23698, 53419}, {25406, 34803}, {26926, 39113}, {29181, 44381}, {31275, 36519}, {31455, 37479}, {31842, 38970}, {32006, 39647}, {32132, 34427}, {32459, 38748}, {35002, 38224}, {35383, 38227}, {37647, 43461}, {37665, 53091}, {37689, 44456}, {38064, 42849}, {38552, 47177}, {38642, 39266}, {44392, 49212}, {44394, 49213}, {44531, 47619}, {47239, 47584}, {47467, 53274}, {49111, 54187}}.

X(56370) = midpoint of X(i) and X(j) for these {i,j}: {3, 15980}, {4, 54996}, {98, 325}, {115, 18860}, {376, 8352}, {858, 36166}, {1350, 53505}, {1513, 5999}, {13449, 38749}, {36196, 54995}, {38642, 39266}, {47619, 53475}
X(56370) = reflection of X(i) in X(j) for these {i,j}: {114, 44377}, {230, 6036}, {381, 8355}, {1513, 10011}, {16320, 16760}, {27088, 549}, {36170, 5159}, {37459, 140}, {47584, 47239}
X(56370) = complement of X(1513)
X(56370) = anticomplement of X(10011)
X(56370) = orthocentroidal-circle-inverse of X(37071)
X(56370) = orthoptic-circle-of-Steiner-inellipse-inverse of X(36163)
X(56370) = X(36051)-anticomplementary conjugate of X(9742)
X(56370) = X(i)-complementary conjugate of X(j) for these (i,j): {40799, 16591}, {41074, 21259}
X(56370) = X(41074)-Ceva conjugate of X(525)
X(56370) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3, 37451}, {2, 4, 37071}, {2, 376, 40248}, {2, 1513, 10011}, {2, 5999, 1513}, {2, 13860, 5}, {2, 37450, 140}, {4, 631, 32973}, {4, 7887, 5}, {5, 140, 7819}, {5, 550, 40279}, {5, 33186, 1656}, {20, 32980, 4}, {262, 7792, 18583}, {631, 11676, 35297}, {858, 7426, 36188}, {1513, 40336, 2}, {5000, 5001, 460}, {5004, 5005, 35296}, {5999, 37455, 10997}, {5999, 40336, 10011}, {6039, 6040, 20}, {6998, 21554, 16917}, {7774, 9755, 1353}, {7778, 9756, 1352}, {10486, 37455, 2}, {14782, 14783, 14001}, {15765, 18585, 8369}, {16434, 19544, 11350}, {32490, 36714, 5}, {32491, 36709, 5}, {32981, 33015, 7807}, {33228, 54996, 4}, {47612, 47613, 441}

X(56371) = X(2)X(3)∩X(4677)X(11910)

Barycentrics    (2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)*(a^8 - a^6*b^2 + 6*a^4*b^4 - 13*a^2*b^6 + 7*b^8 - a^6*c^2 - 11*a^4*b^2*c^2 + 13*a^2*b^4*c^2 - b^6*c^2 + 6*a^4*c^4 + 13*a^2*b^2*c^4 - 12*b^4*c^4 - 13*a^2*c^6 - b^2*c^6 + 7*c^8) : :
X(56371) = 4 X[2] - 3 X[402], X[2] - 3 X[1650], 5 X[2] - 3 X[1651], 7 X[2] - 3 X[4240], 2 X[2] - 3 X[11049], X[2] + 3 X[11050], 17 X[2] - 15 X[15183], 5 X[2] - 6 X[15184], 5 X[2] + 3 X[45289], X[402] - 4 X[1650], 5 X[402] - 4 X[1651], 9 X[402] - 4 X[3081], 7 X[402] - 4 X[4240], X[402] + 4 X[11050], 17 X[402] - 20 X[15183], 5 X[402] - 8 X[15184], and many otrhers

X(563) lies on the cubic K700 and these lines: {2, 3}, {4677, 11910}, {9033, 38240}, {11900, 51071}, {12438, 51066}, {12583, 50993}, {12793, 36767}, {18317, 34297}, {49585, 51109}, {51110, 51712}

X(56371) = midpoint of X(i) and X(j) for these {i,j}: {1650, 11050}, {1651, 45289}, {3543, 46472}
X(56371) = reflection of X(i) in X(j) for these {i,j}: {402, 11049}, {1651, 15184}, {11049, 1650}, {15774, 549}, {34582, 2}
X(56371) = complement of X(3081)
X(56371) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 18870, 3845}, {2, 34582, 402}, {1650, 45289, 15184}, {11049, 34582, 2}

X(56372) = X(2)X(3)∩X(6)X(1632)

Barycentrics    (a^4 - a^2*b^2 - a^2*c^2 + 2*b^2*c^2)*(3*a^4 + b^4 - 2*b^2*c^2 + c^4) : :

X(56372) lies on the cubic K790 and these lines: {2, 3}, {6, 1632}, {154, 11257}, {157, 7668}, {194, 3167}, {264, 34233}, {1853, 9873}, {1974, 20477}, {1975, 9306}, {3164, 19118}, {3168, 3172}, {3186, 15905}, {9747, 9755}, {12110, 17810}, {13567, 36998}, {14712, 21970}, {17809, 32467}, {20065, 41588}, {31859, 51430}, {39646, 42671}, {40821, 40825}

X(56372) = isogonal conjugate of X(43727)
X(56372) = X(6)-Ceva conjugate of X(9755)
X(56372) = X(i)-isoconjugate of X(j) for these (i,j): {1, 43727}, {9255, 40801}, {9258, 40802}
X(56372) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 43727}, {7710, 9307}
X(56372) = barycentric product X(i)*X(j) for these {i,j}: {1958, 4008}, {1975, 7735}, {6776, 9308}, {9306, 40814}, {30476, 35278}
X(56372) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 43727}, {1968, 40801}, {1975, 40824}, {6776, 9289}, {7735, 9307}, {9306, 40802}, {9308, 55972}, {35278, 43188}, {40825, 9292}
X(56372) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 30549, 9307}, {458, 3148, 13860}, {1316, 3148, 458}, {1316, 7473, 37930}, {6620, 37188, 1513}

X(56373) = X(2)X(3)∩X(3917)X(14670)

Barycentrics    a^4*(a^10*b^2 - 5*a^8*b^4 + 10*a^6*b^6 - 10*a^4*b^8 + 5*a^2*b^10 - b^12 + a^10*c^2 - 8*a^8*b^2*c^2 + 14*a^6*b^4*c^2 - 4*a^4*b^6*c^2 - 7*a^2*b^8*c^2 + 4*b^10*c^2 - 5*a^8*c^4 + 14*a^6*b^2*c^4 - 22*a^4*b^4*c^4 + 11*a^2*b^6*c^4 + 2*b^8*c^4 + 10*a^6*c^6 - 4*a^4*b^2*c^6 + 11*a^2*b^4*c^6 - 10*b^6*c^6 - 10*a^4*c^8 - 7*a^2*b^2*c^8 + 2*b^4*c^8 + 5*a^2*c^10 + 4*b^2*c^10 - c^12) : :

X(56373) lies on the cubic K920 and these lines: {2, 3}, {3917, 14670}, {12041, 23217}, {13366, 15786}, {13391, 18114}, {16186, 54042}, {20126, 36829}, {32423, 53246}, {47055, 54044}

X(56373) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 15329, 549}

X(56374) = X(2)X(3)∩X(57)X(162)

Barycentrics     a*(a + b)*(a + c)*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^5 - a^4*b - a*b^4 + b^5 - a^4*c + a^3*b*c + a^2*b^2*c - a*b^3*c + a^2*b*c^2 - b^3*c^2 - a*b*c^3 - b^2*c^3 - a*c^4 + c^5) : :

X(56374) lies on the cubic K972 and these lines: {2, 3}, {55, 14192}, {57, 162}, {92, 107}, {229, 44696}, {610, 2326}, {1621, 38860}, {2062, 7282}, {2184, 40431}, {5285, 52412}, {16547, 46884}, {18613, 52604}, {18743, 36797}, {46103, 52913}, {51762, 53684}

X(56374) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 25443, 5125}, {28, 2074, 7501}, {28, 4183, 1817}, {28, 36011, 17515}, {4223, 37386, 37279}

X(56375) = X(2)X(3)∩X(63)X(162)

Barycentrics   a*(a + b)*(a - b - c)*(a + c)*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^4 - b^4 + a^2*b*c - b^3*c - b*c^3 - c^4) : :

X(56375) lies on the cubic K973 and these lines: {2, 3}, {33, 2326}, {34, 40431}, {63, 162}, {312, 36797}, {1376, 14192}, {2328, 55994}, {15621, 52604}, {41502, 56316}

X(56375) = X(i)-isoconjugate of X(j) for these (i,j): {73, 15314}, {307, 8615}
X(56375) = X(i)-Dao conjugate of X(j) for these (i,j): {34846, 17094}, {46878, 41003}, {52355, 17879}
X(56375) = barycentric product X(i)*X(j) for these {i,j}: {29, 5279}, {645, 54247}, {1172, 7270}, {2064, 2299}, {2322, 4296}, {5285, 31623}, {16612, 36797}
X(56375) = barycentric quotient X(i)/X(j) for these {i,j}: {1172, 15314}, {2204, 8615}, {5279, 307}, {5285, 1214}, {7270, 1231}, {16612, 17094}, {54247, 7178}
X(56375) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {37386, 47511, 11109}

X(56376) = X(2)X(3)∩X(38)X(7224)

Barycentrics   a^8 - a^6*b^2 + 2*a^4*b^4 - a^2*b^6 - b^8 - a^6*c^2 + a^4*b^2*c^2 - a^2*b^4*c^2 + b^6*c^2 + 2*a^4*c^4 - a^2*b^2*c^4 - a^2*c^6 + b^2*c^6 - c^8 : :

X(56376) lies on the cubic K1000 and these lines: {2, 3}, {38, 7224}, {69, 52636}, {99, 40876}, {147, 8841}, {194, 1899}, {325, 19599}, {394, 9863}, {925, 53894}, {1853, 1975}, {1959, 4645}, {2227, 7261}, {2896, 3491}, {3001, 44363}, {3229, 43449}, {3800, 6563}, {5207, 40708}, {7750, 37894}, {7779, 36214}, {7839, 11245}, {9218, 9514}, {9306, 9873}, {9473, 30737}, {11606, 22735}, {20021, 40847}, {22089, 23301}, {32529, 34214}, {40888, 45279}, {45029, 46717}

X(56376) = isogonal conjugate of X(43721)
X(56376) = anticomplement of X(419)
X(56376) = de-Longchamps-circle-inverse of X(1316)
X(56376) = anticomplement of the isogonal conjugate of X(36214)
X(56376) = anticomplement of the isotomic conjugate of X(40708)
X(56376) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {48, 8782}, {63, 25332}, {694, 5905}, {805, 7253}, {1581, 4}, {1916, 21270}, {1934, 11442}, {1967, 193}, {7015, 17794}, {7019, 20554}, {7116, 33888}, {9468, 21216}, {17938, 17498}, {17970, 192}, {18829, 21300}, {36214, 8}, {37134, 850}, {40708, 6327}, {43763, 3060}
X(56376) = X(i)-Ceva conjugate of X(j) for these (i,j): {5207, 7779}, {40708, 2}
X(56376) = X(i)-isoconjugate of X(j) for these (i,j): {1, 43721}, {1910, 51250}
X(56376) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 43721}, {11672, 51250}
X(56376) = barycentric product X(i)*X(j) for these {i,j}: {141, 8928}, {325, 8861}
X(56376) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 43721}, {511, 51250}, {8861, 98}, {8928, 83}
X(56376) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3146, 6620}, {2, 6658, 33336}, {3, 5117, 2}, {5002, 5003, 40236}, {6660, 11007, 420}, {14957, 36163, 40853}, {33314, 37183, 2}, {33314, 50706, 37183}

X(56377) = X(2)X(3)∩X(31)X(3212)

Barycentrics   2*a^8 - a^6*b^2 - a^2*b^6 - a^6*c^2 + a^4*b^2*c^2 - a^2*b^4*c^2 + b^6*c^2 - a^2*b^2*c^4 - 2*b^4*c^4 - a^2*c^6 + b^2*c^6 : :

X(56377) lies on the cubic K1037 and these lines: {2, 3}, {31, 3212}, {51, 7787}, {69, 19571}, {76, 42671}, {154, 1975}, {184, 194}, {263, 52083}, {343, 9863}, {1976, 2998}, {2001, 46717}, {2896, 43653}, {3100, 49530}, {3186, 37893}, {6194, 8922}, {7738, 10329}, {7766, 19222}, {7793, 52144}, {7802, 40876}, {7839, 11402}, {7898, 51431}, {9157, 26233}, {9873, 21243}, {24349, 52134}

X(56377) = anticomplement of X(5117)
X(56377) = anticomplement of the isogonal conjugate of X(43722)
X(56377) = isogonal conjugate of the isotomic conjugate of X(8920)
X(56377) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {3113, 11442}, {3407, 21270}, {18898, 5905}, {33514, 21300}, {43722, 8}
X(56377) = X(18906)-Ceva conjugate of X(7766)
X(56377) = barycentric product X(6)*X(8920)
X(56377) = barycentric quotient X(8920)/X(76)
X(56377) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 419, 2}, {20, 11348, 7396}, {22, 401, 20}, {237, 35926, 3552}, {1316, 46546, 37190}, {4226, 37184, 51350}

X(56378) = X(1)X(7)∩X(171)X(50562)

Barycentrics   (a + b - c)^2*(a - b + c)^2*(a^5 - 2*a^4*b + a^3*b^2 - 2*a^4*c + 3*a^3*b*c + a^2*b^2*c - a*b^3*c - b^4*c + a^3*c^2 + a^2*b*c^2 - 2*a*b^2*c^2 + b^3*c^2 - a*b*c^3 + b^2*c^3 - b*c^4) : :

X(56378) lies on the cubic K221 and these lines: {1, 7}, {171, 50562}, {240, 36118}, {657, 14837}, {658, 896}, {1757, 4566}, {1966, 46406}, {24011, 24013}

X(56378) = X(14837)-line conjugate of X(657)
X(56378) = {X(14189),X(41351)}-harmonic conjugate of X(41355)

X(56379) = X(1)X(7)∩X(56)X(927)

Barycentrics   (a + b - c)*(a - b + c)*(a^5*b - 2*a^4*b^2 + a^3*b^3 + a^5*c - a^4*b*c + a^3*b^2*c - a^2*b^3*c - 2*a^4*c^2 + a^3*b*c^2 + a^2*b^2*c^2 + b^4*c^2 + a^3*c^3 - a^2*b*c^3 - 2*b^3*c^3 + b^2*c^4) : :

X(56379) lies on the cubic K359 and these lines: {1, 7}, {56, 927}, {348, 19888}, {514, 3212}, {573, 34057}, {664, 1362}, {1025, 3501}, {1434, 3110}, {7223, 43671}, {17084, 17758}, {18328, 43672}, {38285, 44043}

X(56380) = X(1)X(7)∩X(101)X(165)

Barycentrics   a*(a^6 - 9*a^4*b^2 + 16*a^3*b^3 - 9*a^2*b^4 + b^6 + 4*a^4*b*c - 8*a^3*b^2*c + 8*a*b^4*c - 4*b^5*c - 9*a^4*c^2 - 8*a^3*b*c^2 + 18*a^2*b^2*c^2 - 8*a*b^3*c^2 + 7*b^4*c^2 + 16*a^3*c^3 - 8*a*b^2*c^3 - 8*b^3*c^3 - 9*a^2*c^4 + 8*a*b*c^4 + 7*b^2*c^4 - 4*b*c^5 + c^6) : :

X(56380) lies on the cubic K609 and these lines: {1, 7}, {101, 165}, {1212, 16112}, {3062, 52705}, {6603, 11495}, {10860, 54474}, {15726, 34522}, {24009, 56309}

X(56380) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 2951, 5527}, {170, 5527, 2951}, {4319, 38459, 1}, {31573, 31574, 43178}

X(56381) = X(1)X(7)∩X(103)X(105)

Barycentrics   a*(a^8*b - 3*a^7*b^2 + 3*a^6*b^3 - a^5*b^4 - a^4*b^5 + 3*a^3*b^6 - 3*a^2*b^7 + a*b^8 + a^8*c - 2*a^5*b^3*c - 4*a^4*b^4*c + 4*a^3*b^5*c + 4*a^2*b^6*c - 2*a*b^7*c - b^8*c - 3*a^7*c^2 + 4*a^5*b^2*c^2 + 5*a^4*b^3*c^2 - 3*a^3*b^4*c^2 - 6*a^2*b^5*c^2 + 2*a*b^6*c^2 + b^7*c^2 + 3*a^6*c^3 - 2*a^5*b*c^3 + 5*a^4*b^2*c^3 - 8*a^3*b^3*c^3 + 5*a^2*b^4*c^3 - 6*a*b^5*c^3 + 3*b^6*c^3 - a^5*c^4 - 4*a^4*b*c^4 - 3*a^3*b^2*c^4 + 5*a^2*b^3*c^4 + 10*a*b^4*c^4 - 3*b^5*c^4 - a^4*c^5 + 4*a^3*b*c^5 - 6*a^2*b^2*c^5 - 6*a*b^3*c^5 - 3*b^4*c^5 + 3*a^3*c^6 + 4*a^2*b*c^6 + 2*a*b^2*c^6 + 3*b^3*c^6 - 3*a^2*c^7 - 2*a*b*c^7 + b^2*c^7 + a*c^8 - b*c^8) : :

X(56381) lies on the cubic K921 and these lines: {1, 7}, {103, 105}, {104, 28848}, {812, 24813}, {971, 17435}, {1001, 44357}, {2082, 38502}, {2724, 12032}, {2808, 52004}, {24411, 24708}, {29015, 41905}

X(56381) = crossdifference of every pair of points on line {657, 9502}

X(56382) = X(1)X(7)∩X(85)X(92)

Barycentrics   (a + b - c)^2*(a - b + c)^2*(b + c)*(a^2 - b^2 - c^2) : :

X(56382) lies on the cubic K974 and these lines: {1, 7}, {2, 2184}, {4, 34059}, {10, 4566}, {21, 934}, {57, 24580}, {63, 348}, {72, 307}, {85, 92}, {86, 40431}, {223, 5813}, {226, 857}, {273, 52248}, {274, 4569}, {306, 1231}, {342, 46353}, {349, 4054}, {377, 9312}, {379, 43035}, {658, 2349}, {908, 40702}, {1020, 3294}, {1071, 1565}, {1088, 18651}, {1119, 7498}, {1212, 39063}, {1214, 20618}, {1427, 5244}, {1434, 1790}, {1441, 39130}, {1729, 51775}, {2167, 17078}, {2475, 38948}, {2741, 24016}, {3665, 34855}, {3868, 9436}, {4208, 31994}, {5226, 30838}, {5273, 9533}, {6604, 11520}, {6611, 16368}, {7282, 52846}, {8767, 14944}, {9856, 41007}, {10431, 56309}, {17079, 56033}, {17106, 31424}, {17181, 51364}, {17205, 44709}, {17880, 20880}, {22125, 22131}, {26125, 27275}, {30032, 30097}, {34060, 37434}, {34168, 36079}, {44708, 52563}, {45227, 51150}, {46273, 46406}, {46330, 54311}, {53237, 55108}

X(56382) = isogonal conjugate of X(2332)
X(56382) = isotomic conjugate of X(2322)
X(56382) = isotomic conjugate of the anticomplement of X(18643)
X(56382) = isotomic conjugate of the isogonal conjugate of X(52373)
X(56382) = isotomic conjugate of the polar conjugate of X(3668)
X(56382) = X(i)-Ceva conjugate of X(j) for these (i,j): {85, 1446}, {4569, 4025}, {7056, 1439}, {30705, 1427}
X(56382) = X(i)-isoconjugate of X(j) for these (i,j): {1, 2332}, {6, 4183}, {8, 2204}, {9, 2299}, {19, 2328}, {21, 607}, {25, 2287}, {27, 1253}, {28, 220}, {29, 41}, {31, 2322}, {33, 284}, {42, 2326}, {55, 1172}, {58, 7079}, {81, 7071}, {112, 3900}, {162, 657}, {200, 1474}, {210, 2189}, {212, 8748}, {228, 36421}, {250, 36197}, {270, 1334}, {281, 2194}, {286, 14827}, {294, 37908}, {333, 2212}, {346, 2203}, {480, 1396}, {608, 56182}, {648, 8641}, {692, 17926}, {1021, 8750}, {1043, 1973}, {1096, 2327}, {1098, 2333}, {1260, 5317}, {1333, 7046}, {1783, 21789}, {1792, 2207}, {1802, 8747}, {1812, 6059}, {1824, 7054}, {1857, 2193}, {1880, 6061}, {1896, 52425}, {2150, 53008}, {2175, 31623}, {2206, 7101}, {2341, 52427}, {3063, 36797}, {3194, 7367}, {3239, 32676}, {3709, 52914}, {4578, 43925}, {4636, 55206}, {5379, 14936}, {5546, 18344}, {7073, 41502}, {7156, 52158}, {7252, 56183}, {8736, 23609}, {9447, 44130}, {14024, 51858}, {18889, 52891}, {44100, 56204}
X(56382) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 2322}, {3, 2332}, {6, 2328}, {9, 4183}, {10, 7079}, {37, 7046}, {125, 657}, {223, 1172}, {226, 9}, {478, 2299}, {647, 52335}, {1086, 17926}, {1214, 281}, {1427, 1249}, {3160, 29}, {4988, 42069}, {6337, 1043}, {6503, 2327}, {6505, 2287}, {6609, 1474}, {10001, 36797}, {15267, 2333}, {15526, 3239}, {16583, 6554}, {17113, 27}, {26932, 1021}, {34591, 3900}, {36908, 19}, {39006, 21789}, {40586, 7071}, {40590, 33}, {40591, 220}, {40592, 2326}, {40593, 31623}, {40603, 7101}, {40611, 607}, {40618, 7253}, {40622, 3064}, {40837, 8748}, {47345, 1857}, {51574, 200}, {52870, 52891}, {55066, 8641}, {56325, 53008}
X(56382) = cevapoint of X(i) and X(j) for these (i,j): {7, 18633}, {525, 17216}, {1214, 1439}, {3668, 36908}, {4466, 17094}, {6356, 37755}
X(56382) = trilinear pole of line {656, 8057}
X(56382) = barycentric product X(i)*X(j) for these {i,j}: {7, 307}, {10, 7056}, {57, 1231}, {63, 1446}, {65, 7182}, {69, 3668}, {72, 1088}, {73, 6063}, {75, 1439}, {76, 52373}, {77, 1441}, {85, 1214}, {86, 6356}, {222, 349}, {225, 7055}, {226, 348}, {269, 20336}, {273, 52385}, {274, 37755}, {278, 52565}, {279, 306}, {304, 1427}, {305, 1042}, {310, 1425}, {313, 7053}, {321, 7177}, {331, 40152}, {332, 6046}, {333, 20618}, {479, 3710}, {525, 658}, {561, 1410}, {647, 46406}, {656, 4569}, {664, 17094}, {934, 14208}, {1020, 15413}, {1119, 52396}, {1275, 4466}, {1407, 40071}, {1409, 20567}, {1434, 26942}, {1461, 3267}, {1847, 3998}, {2321, 30682}, {3261, 52610}, {3265, 36118}, {3694, 23062}, {4025, 4566}, {4064, 4616}, {4077, 6516}, {4554, 51664}, {4605, 15419}, {4626, 52355}, {4635, 55232}, {6354, 17206}, {6355, 8822}, {7099, 27801}, {7125, 52575}, {7183, 40149}, {8611, 36838}, {13149, 24018}, {17216, 55346}, {18589, 30705}, {20235, 56359}, {23067, 52621}, {30805, 52607}, {34403, 36908}, {36620, 50563}, {40702, 52037}, {41804, 52392}, {52390, 52421}
X(56382) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 4183}, {2, 2322}, {3, 2328}, {6, 2332}, {7, 29}, {10, 7046}, {12, 53008}, {27, 36421}, {37, 7079}, {42, 7071}, {56, 2299}, {57, 1172}, {63, 2287}, {65, 33}, {69, 1043}, {71, 220}, {72, 200}, {73, 55}, {77, 21}, {78, 56182}, {81, 2326}, {85, 31623}, {125, 52335}, {201, 210}, {222, 284}, {225, 1857}, {226, 281}, {227, 40971}, {228, 1253}, {269, 28}, {273, 1896}, {278, 8748}, {279, 27}, {283, 6061}, {306, 346}, {307, 8}, {321, 7101}, {326, 1792}, {348, 333}, {349, 7017}, {394, 2327}, {514, 17926}, {525, 3239}, {603, 2194}, {604, 2204}, {647, 657}, {656, 3900}, {658, 648}, {664, 36797}, {738, 1396}, {810, 8641}, {905, 1021}, {934, 162}, {1014, 270}, {1020, 1783}, {1042, 25}, {1088, 286}, {1106, 2203}, {1119, 8747}, {1214, 9}, {1231, 312}, {1254, 1824}, {1323, 52891}, {1332, 7259}, {1400, 607}, {1402, 2212}, {1407, 1474}, {1409, 41}, {1410, 31}, {1412, 2189}, {1414, 52914}, {1425, 42}, {1426, 1096}, {1427, 19}, {1434, 46103}, {1435, 5317}, {1439, 1}, {1441, 318}, {1442, 11107}, {1443, 17515}, {1444, 1098}, {1446, 92}, {1447, 14024}, {1458, 37908}, {1459, 21789}, {1461, 112}, {1464, 52427}, {1790, 7054}, {1804, 283}, {1813, 5546}, {2003, 41502}, {2197, 1334}, {2200, 14827}, {2318, 480}, {3120, 42069}, {3267, 52622}, {3668, 4}, {3671, 461}, {3682, 1260}, {3694, 728}, {3695, 4082}, {3708, 36197}, {3710, 5423}, {3914, 1863}, {3949, 4515}, {3990, 1802}, {3998, 3692}, {4017, 18344}, {4025, 7253}, {4077, 44426}, {4091, 23090}, {4303, 8021}, {4320, 4206}, {4341, 30733}, {4350, 4233}, {4466, 1146}, {4551, 56183}, {4561, 7256}, {4566, 1897}, {4569, 811}, {4635, 55231}, {5088, 15146}, {5930, 44695}, {6046, 225}, {6063, 44130}, {6354, 1826}, {6355, 39130}, {6356, 10}, {6357, 52956}, {6516, 643}, {7045, 5379}, {7053, 58}, {7055, 332}, {7056, 86}, {7066, 2318}, {7099, 1333}, {7125, 2193}, {7138, 228}, {7147, 1880}, {7176, 14006}, {7177, 81}, {7178, 3064}, {7182, 314}, {7183, 1812}, {7216, 6591}, {7591, 6726}, {8611, 4130}, {8808, 7003}, {8811, 7007}, {8812, 3183}, {13149, 823}, {14208, 4397}, {14256, 41083}, {14429, 4528}, {15556, 56316}, {17094, 522}, {17206, 7058}, {17216, 2968}, {17441, 4319}, {18210, 2310}, {18589, 6554}, {20336, 341}, {20618, 226}, {21207, 21666}, {22097, 46889}, {22341, 212}, {23067, 3939}, {23603, 16054}, {23620, 30706}, {23973, 4241}, {24459, 4148}, {26942, 2321}, {28786, 56146}, {30456, 7156}, {30682, 1434}, {30705, 40411}, {30805, 15411}, {32714, 24019}, {34855, 54407}, {36079, 1301}, {36118, 107}, {36908, 1249}, {37583, 41503}, {37755, 37}, {39791, 14547}, {40152, 219}, {40933, 204}, {40961, 40987}, {41003, 46878}, {41087, 7367}, {41353, 4238}, {41393, 40967}, {41804, 5081}, {42289, 28044}, {42309, 31926}, {46406, 6331}, {51640, 1946}, {51645, 2202}, {51664, 650}, {52023, 1855}, {52037, 282}, {52354, 6555}, {52355, 4163}, {52370, 6602}, {52373, 6}, {52384, 7008}, {52385, 78}, {52390, 7073}, {52391, 52371}, {52392, 6740}, {52396, 1265}, {52565, 345}, {52609, 6558}, {52610, 101}, {53321, 8750}, {53545, 8735}, {53560, 3119}, {55205, 4631}, {55230, 4524}, {55232, 4171}, {55234, 3709}
X(56382) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 77, 18650}, {7, 347, 18655}, {7, 3160, 20}, {7, 3188, 4292}, {307, 50563, 72}, {348, 7056, 7177}, {1231, 52565, 306}, {1323, 4292, 3188}, {1439, 6356, 307}, {10884, 17170, 18650}

X(56383) = X(1)X(7)∩X(657)X(4091)

Barycentrics   a*(a + b - c)*(a - b + c)*(a^5*b - 2*a^4*b^2 + 2*a^2*b^4 - a*b^5 + a^5*c - 2*a^2*b^3*c - a*b^4*c + 2*b^5*c - 2*a^4*c^2 + 2*a^2*b^2*c^2 + 2*a*b^3*c^2 - 2*b^4*c^2 - 2*a^2*b*c^3 + 2*a*b^2*c^3 + 2*a^2*c^4 - a*b*c^4 - 2*b^2*c^4 - a*c^5 + 2*b*c^5) : :

X(56383) lies on the cubic K1076 and these lines: {1, 7}, {657, 4091}, {658, 2635}, {1414, 23692}, {1804, 24320}, {4617, 36002}, {6516, 23693}, {14943, 36101}

X(56383) =crossdifference of every pair of points on line {657, 4336}
X(56383) =X(i)-line conjugate of X(j) for these (i,j): {1, 4336}, {4091, 657}
X(56383) ={X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 51308, 77}, {3000, 41355, 14189}

X(56384) = X(1)X(2)∩X(37)X(589)

Barycentrics   1 + 2*Sin[A] : :
Barycentrics   a*(b*c + 2*S) : :

X(56384) lies on these lines: {1, 2}, {11, 15234}, {12, 15233}, {33, 55475}, {34, 55476}, {37, 589}, {40, 21567}, {55, 1600}, {56, 1599}, {81, 7968}, {176, 5905}, {192, 37881}, {326, 32793}, {329, 17805}, {394, 3297}, {481, 26842}, {482, 17483}, {495, 1592}, {496, 1591}, {517, 16440}, {940, 44636}, {999, 1583}, {1015, 8962}, {1038, 55897}, {1040, 55893}, {1056, 6806}, {1058, 6805}, {1060, 1590}, {1062, 1589}, {1124, 1993}, {1267, 44179}, {1270, 55391}, {1271, 55392}, {1335, 5422}, {1385, 16441}, {1398, 15198}, {1482, 16432}, {1584, 3295}, {1585, 1870}, {1586, 6198}, {1659, 31053}, {1994, 3299}, {2066, 55566}, {3100, 55883}, {3218, 13389}, {3219, 30556}, {3298, 10601}, {3301, 34545}, {3553, 7586}, {3554, 7585}, {3576, 21566}, {3593, 55456}, {3595, 55457}, {3640, 4430}, {3641, 4661}, {3681, 45714}, {3873, 45713}, {4296, 55888}, {4383, 44635}, {5408, 35769}, {5409, 35808}, {5483, 31583}, {6502, 55567}, {6767, 55577}, {7071, 15201}, {7373, 55579}, {7969, 32911}, {7982, 21568}, {8148, 21561}, {9538, 55894}, {9776, 17802}, {10222, 21492}, {10246, 16433}, {10247, 21548}, {11398, 15188}, {11399, 15187}, {12702, 21560}, {13388, 27003}, {13390, 31019}, {15066, 55409}, {15178, 21553}, {15192, 52427}, {15325, 55865}, {16200, 21569}, {16777, 31473}, {17484, 31538}, {17597, 45476}, {18447, 55890}, {18455, 55885}, {18992, 37685}, {20060, 31533}, {20075, 30333}, {21547, 37624}, {21555, 33179}, {27065, 30557}, {37696, 55882}, {37697, 55881}, {37729, 55892}, {55389, 55425}, {55390, 55424}, {55403, 55436}, {55404, 55464}

X(56384) = anticomplement of X(6347)
X(56384) = X(i)-isoconjugate of X(j) for these (i,j): {6, 3300}, {2963, 3301}
X(56384) = X(i)-Dao conjugate of X(j) for these (i,j): {9, 3300}, {600, 1}, {10639, 42679}, {10640, 42681}
X(56384) = barycentric product X(i)*X(j) for these {i,j}: {1, 32791}, {75, 3299}, {302, 42676}, {303, 42678}
X(56384) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 3300}, {61, 42681}, {62, 42679}, {2964, 3301}, {3083, 39312}, {3299, 1}, {3302, 2962}, {32791, 75}, {38004, 39316}, {42676, 17}, {42678, 18}
X(56384) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3083, 2}, {33, 55475, 55569}, {34, 55476, 55573}, {1124, 55410, 1993}, {1125, 6348, 2}, {5405, 55876, 2}, {13389, 55398, 3218}, {30556, 55397, 3219}, {55391, 55427, 1270}, {55392, 55426, 1271}, {55409, 55442, 15066}

X(56385) = X(1)X(2)∩X(7)X(1270)

Barycentrics   1 + Cot[A/2] : :
Barycentrics   a^2 - b^2 - c^2 - 2*b*c - 2*S : :

X(56385) lies on these lines: {1, 2}, {7, 1270}, {9, 7348}, {63, 488}, {69, 1267}, {75, 492}, {100, 16440}, {264, 55458}, {280, 55894}, {312, 7090}, {317, 55429}, {318, 1586}, {319, 491}, {320, 32801}, {321, 486}, {326, 55427}, {329, 31548}, {332, 2066}, {333, 14121}, {345, 13425}, {346, 15892}, {391, 30413}, {517, 2048}, {585, 3210}, {586, 41839}, {590, 17362}, {591, 4363}, {594, 615}, {637, 31550}, {908, 13387}, {956, 16433}, {966, 6352}, {1271, 32099}, {1585, 5081}, {1659, 4417}, {2047, 5814}, {2345, 3069}, {2886, 45444}, {2968, 55885}, {2975, 16441}, {3068, 5839}, {3536, 7046}, {3593, 32087}, {3713, 31473}, {3758, 45421}, {4000, 5590}, {4361, 45472}, {4371, 26361}, {4385, 7388}, {4388, 52805}, {4445, 45473}, {4644, 5860}, {4969, 32787}, {5015, 7389}, {5391, 32805}, {5564, 32792}, {5687, 16432}, {5739, 55397}, {5744, 46421}, {5749, 7586}, {6351, 17314}, {10538, 55883}, {13453, 50559}, {13458, 28808}, {13637, 50077}, {13701, 51583}, {13973, 44417}, {14555, 30557}, {17360, 32809}, {17369, 32788}, {17740, 35775}, {19066, 37642}, {21296, 32814}, {26098, 49347}, {30479, 42013}, {30568, 31595}, {30699, 53593}, {32795, 32806}, {32796, 32812}, {32797, 32810}, {32932, 52808}, {37646, 49232}, {37662, 49233}, {45872, 48636}, {46891, 53122}, {55385, 55423}, {55386, 55452}, {55387, 55421}, {55388, 55450}, {55393, 55474}, {55394, 55479}

X(56385) = isotomic conjugate of X(1659)
X(56385) = anticomplement of X(5393)
X(56385) = isotomic conjugate of the complement of X(46422)
X(56385) = isotomic conjugate of the isogonal conjugate of X(2066)
X(56385) = isotomic conjugate of the polar conjugate of X(14121)
X(56385) = X(69)-Ceva conjugate of X(31547)
X(56385) = X(i)-isoconjugate of X(j) for these (i,j): {4, 53063}, {6, 2362}, {19, 2067}, {25, 13388}, {31, 1659}, {34, 5414}, {56, 7133}, {278, 53066}, {513, 54018}, {604, 7090}, {608, 30557}, {1123, 53064}, {1805, 1880}, {2066, 13438}, {13437, 53065}, {16232, 34121}
X(56385) = X(i)-Dao conjugate of X(j) for these (i,j): {1, 7133}, {2, 1659}, {6, 2067}, {9, 2362}, {3161, 7090}, {6505, 13388}, {11517, 5414}, {13388, 57}, {30556, 6204}, {36033, 53063}, {39026, 54018}, {40626, 54017}
X(56385) = cevapoint of X(i) and X(j) for these (i,j): {2, 46422}, {8, 30412}, {63, 3083}
X(56385) = trilinear pole of line {6332, 54019}
X(56385) = barycentric product X(i)*X(j) for these {i,j}: {69, 14121}, {75, 30556}, {76, 2066}, {190, 54019}, {304, 42013}, {312, 13389}, {313, 1806}, {345, 13390}, {561, 53065}, {1267, 7090}, {1659, 13425}, {3596, 6502}, {3718, 16232}, {28659, 53064}, {30557, 46744}, {31547, 40699}
X(56385) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2362}, {2, 1659}, {3, 2067}, {8, 7090}, {9, 7133}, {48, 53063}, {63, 13388}, {78, 30557}, {101, 54018}, {212, 53066}, {219, 5414}, {283, 1805}, {605, 53064}, {1124, 6502}, {1659, 13437}, {1806, 58}, {2066, 6}, {2362, 13438}, {3083, 13389}, {5414, 34121}, {6212, 16232}, {6332, 54017}, {6502, 56}, {7090, 1123}, {13386, 13390}, {13389, 57}, {13390, 278}, {14121, 4}, {16232, 34}, {30556, 1}, {30557, 6213}, {31535, 482}, {31547, 175}, {34908, 46433}, {42013, 19}, {53064, 604}, {53065, 31}, {54016, 32674}, {54019, 514}
X(56385) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 5405, 2}, {10, 49624, 1}, {63, 13386, 31547}, {319, 32791, 491}, {329, 46422, 31548}, {1270, 32793, 7}, {6348, 55877, 2}, {32805, 42696, 5391}

X(56386) = X(1)X(2)∩X(63)X(487)

Barycentrics   1 - Cot[A/2] : :
Barycentrics   a^2 - b^2 - c^2 - 2*b*c + 2*S : :

X(56386) lies on these lines: {1, 2}, {7, 1271}, {9, 7347}, {63, 487}, {69, 5391}, {75, 491}, {100, 16441}, {264, 55428}, {280, 55898}, {312, 14121}, {317, 55459}, {318, 1585}, {319, 492}, {320, 32802}, {321, 485}, {326, 55457}, {329, 31547}, {332, 5414}, {333, 7090}, {345, 13458}, {346, 15891}, {355, 2048}, {391, 30412}, {585, 41839}, {586, 3210}, {590, 594}, {615, 17362}, {638, 31549}, {908, 13386}, {956, 16432}, {966, 6351}, {1267, 32806}, {1270, 32099}, {1586, 5081}, {1991, 4363}, {2047, 5295}, {2345, 3068}, {2886, 45445}, {2968, 55890}, {2975, 16440}, {3069, 5839}, {3535, 7046}, {3595, 32087}, {3758, 45420}, {4000, 5591}, {4361, 45473}, {4371, 26362}, {4385, 7389}, {4388, 52808}, {4417, 13390}, {4445, 45472}, {4644, 5861}, {4969, 32788}, {5015, 7388}, {5564, 32791}, {5687, 16433}, {5739, 55398}, {5744, 46422}, {5749, 7585}, {6352, 17314}, {7133, 30479}, {7595, 11687}, {10538, 55888}, {13425, 28808}, {13436, 50559}, {13461, 32851}, {13757, 50077}, {13821, 51583}, {13911, 44417}, {14555, 30556}, {17360, 32808}, {17369, 32787}, {17740, 35774}, {19065, 37642}, {26098, 49348}, {30568, 31594}, {30699, 53595}, {32795, 32813}, {32796, 32805}, {32798, 32811}, {32804, 32807}, {32932, 52805}, {37646, 49233}, {37662, 49232}, {45871, 48636}, {46892, 53122}, {55385, 55453}, {55386, 55422}, {55387, 55451}, {55388, 55420}, {55393, 55480}, {55394, 55473}

X(56386) = isotomic conjugate of X(13390)
X(56386) = anticomplement of X(5405)
X(56386) = isotomic conjugate of the complement of X(46421)
X(56386) = isotomic conjugate of the isogonal conjugate of X(5414)
X(56386) = isotomic conjugate of the polar conjugate of X(7090)
X(56386) = X(69)-Ceva conjugate of X(31548)
X(56386) = X(i)-isoconjugate of X(j) for these (i,j): {4, 53064}, {6, 16232}, {19, 6502}, {25, 13389}, {31, 13390}, {34, 2066}, {56, 42013}, {278, 53065}, {513, 54016}, {604, 14121}, {608, 30556}, {1336, 53063}, {1806, 1880}, {2362, 34125}, {5414, 13460}, {13459, 53066}
X(56386) = X(i)-Dao conjugate of X(j) for these (i,j): {1, 42013}, {2, 13390}, {6, 6502}, {9, 16232}, {3161, 14121}, {6505, 13389}, {11517, 2066}, {13389, 57}, {30557, 6203}, {36033, 53064}, {39026, 54016}, {40626, 54019}
X(56386) = cevapoint of X(i) and X(j) for these (i,j): {2, 46421}, {8, 30413}, {63, 3084}
X(56386) = trilinear pole of line {6332, 54017}
X(56386) = barycentric product X(i)*X(j) for these {i,j}: {69, 7090}, {75, 30557}, {76, 5414}, {190, 54017}, {304, 7133}, {312, 13388}, {313, 1805}, {345, 1659}, {561, 53066}, {2067, 3596}, {2362, 3718}, {5391, 14121}, {13390, 13458}, {28659, 53063}, {30556, 46745}, {31548, 40700}
X(56386) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 16232}, {2, 13390}, {3, 6502}, {8, 14121}, {9, 42013}, {48, 53064}, {63, 13389}, {78, 30556}, {101, 54016}, {212, 53065}, {219, 2066}, {283, 1806}, {606, 53063}, {1335, 2067}, {1659, 278}, {1805, 58}, {2066, 34125}, {2067, 56}, {2362, 34}, {3084, 13388}, {5414, 6}, {6213, 2362}, {6332, 54019}, {7090, 4}, {7133, 19}, {13387, 1659}, {13388, 57}, {13390, 13459}, {14121, 1336}, {16232, 13460}, {30556, 6212}, {30557, 1}, {31534, 481}, {31548, 176}, {34907, 46434}, {53063, 604}, {53066, 31}, {54017, 514}, {54018, 32674}
X(56386) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 5393, 2}, {10, 49625, 1}, {63, 13387, 31548}, {319, 32792, 492}, {329, 46421, 31547}, {1271, 32794, 7}, {6347, 55876, 2}, {32806, 42696, 1267}

X(56387) = X(1)X(2)∩X(46)X(214)

Barycentrics   Cot[A] + Cos[A]*Cot[A] - 2*Sin[A] : :
Barycentrics   a*(a - b - c)*(3*a^2 - 3*b^2 + 4*b*c - 3*c^2) : :
X(56387) = X[8] - 3 X[5552], 3 X[499] - 4 X[1125], 7 X[3622] - 3 X[10529], 12 X[20107] - 13 X[34595], 3 X[11928] - 5 X[18493]

X(56387) lies on these lines: {1, 2}, {3, 11682}, {9, 3897}, {20, 51423}, {21, 13384}, {40, 54192}, {46, 214}, {63, 1385}, {65, 35262}, {72, 10246}, {77, 320}, {100, 7982}, {224, 1537}, {326, 7190}, {355, 30852}, {404, 3340}, {474, 50194}, {480, 15570}, {517, 4855}, {518, 1388}, {758, 37618}, {908, 944}, {956, 3984}, {960, 34471}, {999, 1259}, {1260, 7373}, {1317, 32049}, {1319, 12635}, {1320, 2136}, {1329, 37740}, {1376, 11011}, {1420, 3868}, {1467, 18467}, {1482, 5440}, {1697, 5330}, {1837, 3847}, {2093, 4188}, {2096, 10884}, {2098, 3895}, {2099, 10107}, {2646, 5250}, {2975, 3951}, {3035, 41687}, {3100, 4779}, {3158, 3885}, {3306, 17614}, {3333, 34195}, {3419, 5901}, {3434, 13464}, {3436, 5882}, {3486, 41012}, {3555, 51379}, {3576, 3869}, {3577, 6915}, {3601, 3877}, {3612, 3878}, {3650, 33858}, {3685, 7221}, {3689, 10912}, {3713, 3723}, {3814, 37711}, {3816, 37724}, {3825, 37721}, {3871, 7962}, {3899, 37616}, {3913, 5048}, {3927, 28451}, {3940, 37624}, {3962, 11194}, {3965, 16884}, {4004, 16417}, {4018, 4930}, {4187, 37739}, {4193, 5727}, {4297, 11415}, {4311, 5905}, {4323, 6904}, {4742, 23528}, {4848, 6921}, {4867, 21842}, {4881, 15803}, {5057, 6261}, {5086, 8227}, {5128, 13587}, {5204, 44663}, {5227, 17438}, {5253, 11529}, {5439, 35272}, {5560, 45764}, {5563, 12559}, {5687, 10222}, {5691, 6224}, {5692, 24926}, {5734, 17784}, {5794, 15950}, {5837, 6910}, {5855, 24914}, {5881, 11681}, {6603, 55337}, {6909, 7971}, {7082, 30538}, {7269, 52709}, {7280, 45392}, {7290, 44694}, {7354, 34647}, {8715, 30323}, {9580, 11015}, {9613, 31053}, {9624, 11680}, {9643, 10538}, {10074, 45393}, {10247, 10914}, {10595, 55108}, {10680, 11517}, {10698, 49163}, {10950, 25681}, {11009, 54286}, {11041, 17567}, {11376, 44669}, {11522, 52367}, {11523, 54391}, {11928, 18493}, {12514, 37525}, {12526, 30389}, {12607, 37738}, {12735, 55016}, {13253, 17100}, {13607, 21075}, {14923, 16200}, {16126, 37587}, {16371, 50193}, {17360, 55392}, {17757, 37727}, {17880, 18156}, {18446, 31789}, {18480, 45770}, {18481, 41543}, {18526, 37700}, {18802, 19907}, {18990, 31164}, {22759, 42843}, {25415, 25440}, {25716, 30806}, {31266, 37737}, {31730, 40257}, {37281, 37533}, {38316, 41228}, {41229, 51111}, {51714, 51816}
X(56387) = X(56)-isoconjugate of X(43734)
X(56387) = X(i)-Dao conjugate of X(j) for these (i,j): {1, 43734}, {16885, 31231}
X(56387) = barycentric product X(i)*X(j) for these {i,j}: {333, 4018}, {4930, 30608}
X(56387) = barycentric quotient X(i)/X(j) for these {i,j}: {9, 43734}, {4018, 226}, {4930, 5219}, {51577, 31231}
X(56387) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 78, 3872}, {1, 200, 4861}, {1, 997, 19860}, {1, 3811, 36846}, {1, 4511, 78}, {1, 6765, 38460}, {1, 19861, 54392}, {1, 22836, 3870}, {1, 30144, 19861}, {1, 47623, 28011}, {8, 27383, 27525}, {8, 27525, 6735}, {145, 27383, 6735}, {145, 27525, 8}, {551, 6737, 10527}, {1385, 5730, 63}, {2646, 5289, 5250}, {3244, 6745, 8}, {3576, 3869, 4652}, {3576, 54290, 5303}, {3612, 3878, 35258}, {3689, 33176, 10912}, {3869, 5303, 54290}, {5128, 45036, 13587}, {5303, 54290, 4652}, {13384, 15829, 21}, {21740, 37611, 10884}, {44179, 55391, 77}

X(56388) = X(3)X(6)∩X(163)X(14599)

Barycentrics   a^3*(a + b)*(a + c)*(a^2*b^2 + a^2*b*c - a*b^2*c + a^2*c^2 - a*b*c^2 - b^2*c^2) : :

X(56388) lies on the cubic K1021 and these lines: {3, 6}, {163, 14599}, {172, 757}, {593, 2205}, {2106, 51331}, {4567, 4590}, {6043, 51319}, {9454, 18268}, {20796, 21788}, {24727, 52680}

X(56388) = isogonal conjugate of X(43685)
X(56388) = isogonal conjugate of the isotomic conjugate of X(2106)
X(56388) = isogonal conjugate of the polar conjugate of X(15148)
X(56388) = X(i)-isoconjugate of X(j) for these (i,j): {1, 43685}, {10, 39925}, {75, 54980}, {76, 2107}, {313, 51333}, {321, 2665}, {661, 53216}, {1577, 53624}
X(56388) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 43685}, {206, 54980}, {27854, 16732}, {36830, 53216}, {39056, 313}, {39057, 561}
X(56388) = crossdifference of every pair of points on line {523, 53478}
X(56388) = barycentric product X(i)*X(j) for these {i,j}: {3, 15148}, {6, 2106}, {28, 20796}, {31, 2669}, {32, 40874}, {58, 2664}, {81, 21788}, {560, 41535}, {593, 21897}, {1333, 17759}, {2206, 52049}, {5009, 40796}, {18268, 39916}, {37128, 51331}
X(56388) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 43685}, {32, 54980}, {110, 53216}, {560, 2107}, {1333, 39925}, {1576, 53624}, {2106, 76}, {2206, 2665}, {2664, 313}, {2669, 561}, {15148, 264}, {17759, 27801}, {20796, 20336}, {21788, 321}, {21897, 28654}, {40874, 1502}, {41535, 1928}, {51331, 3948}

X(56389) = X(3)X(6)∩X(112)X(3565)

Barycentrics   a^2*(a^2 - b^2)*(a^2 - c^2)*(a^2 - b^2 - c^2)*(2*a^4 - a^2*b^2 + b^4 - a^2*c^2 - 2*b^2*c^2 + c^4) : :

X(56389) lies on the cubic K658 and these lines: {3, 6}, {112, 3565}, {1576, 1625}, {1634, 35324}, {2421, 2715}, {2501, 30512}, {2974, 12829}, {3564, 53783}, {4226, 55267}, {4558, 8552}, {5477, 35067}, {7418, 10313}, {10097, 32662}, {15329, 23357}, {36830, 52603}
X(56389) = isogonal conjugate of the polar conjugate of X(4226)
X(56389) = X(i)-Ceva conjugate of X(j) for these (i,j): {250, 51335}, {2715, 32661}, {32697, 110}
X(56389) = X(i)-isoconjugate of X(j) for these (i,j): {92, 35364}, {115, 36105}, {661, 35142}, {1109, 32697}, {1577, 3563}, {2501, 8773}, {2987, 24006}, {14618, 36051}
X(56389) = X(i)-Dao conjugate of X(j) for these (i,j): {114, 14618}, {22391, 35364}, {34156, 43665}, {35067, 850}, {36830, 35142}, {39001, 115}, {39069, 24006}, {39072, 2501}, {41181, 339}, {55152, 2970}
X(56389) = trilinear pole of line {47406, 52144}
X(56389) = crossdifference of every pair of points on line {523, 8754}
X(56389) = barycentric product X(i)*X(j) for these {i,j}: {3, 4226}, {99, 52144}, {110, 3564}, {114, 43754}, {230, 4558}, {1692, 4563}, {1733, 4575}, {2966, 47406}, {3292, 52035}, {4230, 53783}, {4592, 8772}, {6782, 38414}, {6783, 38413}, {17932, 51335}, {32661, 51481}, {32697, 35067}, {42663, 47389}
X(56389) = barycentric quotient X(i)/X(j) for these {i,j}: {110, 35142}, {184, 35364}, {230, 14618}, {1101, 36105}, {1576, 3563}, {1692, 2501}, {3564, 850}, {4226, 264}, {4558, 8781}, {4575, 8773}, {8772, 24006}, {23357, 32697}, {32661, 2987}, {42663, 8754}, {43754, 40428}, {44102, 52476}, {47390, 10425}, {47406, 2799}, {51335, 16230}, {52035, 46111}, {52144, 523}, {55122, 2970}

X(56390) = X(4)X(147)∩X(25)X(648)

Barycentrics   (-a^2 - b^2 + c^2)*(a^2 - b^2 + c^2)*(a^4*b^2 - 2*a^2*b^4 + a^4*c^2 + b^4*c^2 - 2*a^2*c^4 + b^2*c^4) : :

X(56390) lies on the cubic K484 and these lines: {4, 147}, {25, 648}, {230, 231}, {264, 2970}, {427, 8754}, {1112, 1843}, {3186, 4232}, {6531, 36822}, {10295, 53793}, {36156, 52951}

X(56390) = reflection of X(47211) in X(2493)
X(56390) = polar conjugate of X(35146)
X(56390) = polar conjugate of the isotomic conjugate of X(5969)
X(56390) = polar conjugate of the isogonal conjugate of X(5106)
X(56390) = X(i)-isoconjugate of X(j) for these (i,j): {48, 35146}, {63, 5970}, {4592, 14606}
X(56390) = X(i)-Dao conjugate of X(j) for these (i,j): {1249, 35146}, {3162, 5970}, {5139, 14606}, {35077, 69}
X(56390) = barycentric product X(i)*X(j) for these {i,j}: {4, 5969}, {264, 5106}, {648, 11182}, {2501, 14607}, {17983, 45330}, {17984, 51494}
X(56390) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 35146}, {25, 5970}, {419, 47646}, {2489, 14606}, {5106, 3}, {5969, 69}, {11182, 525}, {14607, 4563}, {45330, 6390}, {51494, 36214}
X(56390) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {648, 36898, 25}, {2971, 41676, 5186}, {6103, 41360, 468}

X(56391) = X(3)X(541)∩X(230)X(231)

Barycentrics   2*a^12 - 15*a^8*b^4 + 24*a^6*b^6 - 12*a^4*b^8 + b^12 + 24*a^8*b^2*c^2 - 22*a^6*b^4*c^2 - 10*a^4*b^6*c^2 + 10*a^2*b^8*c^2 - 2*b^10*c^2 - 15*a^8*c^4 - 22*a^6*b^2*c^4 + 44*a^4*b^4*c^4 - 10*a^2*b^6*c^4 - b^8*c^4 + 24*a^6*c^6 - 10*a^4*b^2*c^6 - 10*a^2*b^4*c^6 + 4*b^6*c^6 - 12*a^4*c^8 + 10*a^2*b^2*c^8 - b^4*c^8 - 2*b^2*c^10 + c^12 : :

X(56391) lies on the cubic K816 and these lines: {3, 541}, {125, 14685}, {230, 231}, {574, 35282}, {5094, 53568}, {14220, 34291}, {14919, 32247}, {15118, 44889}, {35278, 35485}, {41376, 46949}

X(56391) = X(541)-line conjugate of X(3)

X(56392) = X(2)X(41339)∩X(187)X(237)

Barycentrics   a^2*(a^10*b^6 - 3*a^8*b^8 + 3*a^6*b^10 - a^4*b^12 + 2*a^10*b^4*c^2 - 5*a^8*b^6*c^2 + 3*a^6*b^8*c^2 + 2*a^10*b^2*c^4 - 2*a^8*b^4*c^4 + 3*a^6*b^6*c^4 + a^4*b^8*c^4 - 2*a^2*b^10*c^4 + b^12*c^4 + a^10*c^6 - 5*a^8*b^2*c^6 + 3*a^6*b^4*c^6 - 6*a^4*b^6*c^6 + 2*a^2*b^8*c^6 - 4*b^10*c^6 - 3*a^8*c^8 + 3*a^6*b^2*c^8 + a^4*b^4*c^8 + 2*a^2*b^6*c^8 + 6*b^8*c^8 + 3*a^6*c^10 - 2*a^2*b^4*c^10 - 4*b^6*c^10 - a^4*c^12 + b^4*c^12) : :

X(56392) lies on the cubic K508 and these lines: {2, 41330}, {30, 11673}, {187, 237}, {263, 52446}, {3580, 18322}, {6785, 37988}, {14957, 43453}, {15993, 51441}, {18321, 37465}, {31848, 37338}, {38230, 44215}

X(56392) = reflection of X(i) in X(j) for these {i,j}: {237, 47638}, {33873, 21531}
X(56392) = X(41330)-line conjugate of X(2)

X(56393) = X(23)X(94)∩X(187)X(237)

Barycentrics   a^4*(a^8*b^4 - 3*a^6*b^6 + 3*a^4*b^8 - a^2*b^10 - a^4*b^6*c^2 + a^2*b^8*c^2 + a^8*c^4 + 2*a^4*b^4*c^4 - a^2*b^6*c^4 - b^8*c^4 - 3*a^6*c^6 - a^4*b^2*c^6 - a^2*b^4*c^6 + 2*b^6*c^6 + 3*a^4*c^8 + a^2*b^2*c^8 - b^4*c^8 - a^2*c^10) : :

X(56393) lies on the cubic K592 and these lines: {23, 94}, {184, 14966}, {187, 237}, {1576, 9418}, {5926, 36180}, {7669, 33983}, {9419, 14567}, {11332, 34417}, {15080, 15920}, {17938, 17970}, {22463, 52128}, {26714, 32730}, {46272, 52169}

X(56393) = X(43654)-Ceva conjugate of X(6)
X(56393) = X(75)-isoconjugate of X(43654)
X(56393) = X(206)-Dao conjugate of X(43654)
X(56393) = barycentric quotient X(32)/X(43654)
X(56393) = {X(237),X(669)}-harmonic conjugate of X(1495)

X(56394) = X(3)X(34290)∩X(187)X(237)

Barycentrics   a^4*(b - c)*(b + c)*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6 + a^6*c^2 - 4*a^4*b^2*c^2 + 4*a^2*b^4*c^2 - 3*b^6*c^2 - 2*a^4*c^4 + 4*a^2*b^2*c^4 + 2*b^4*c^4 + a^2*c^6 - 3*b^2*c^6) : :
X(56394) = 4 X[21531] - 5 X[31279]

X(56394) lies on the cubic K593 and these lines: {3, 34290}, {30, 31176}, {187, 237}, {523, 1634}, {1084, 3049}, {5652, 11328}, {11182, 14096}, {11183, 37338}, {14957, 23301}, {20775, 22260}, {21531, 31279}, {35364, 38354}, {35606, 53327}, {44445, 46518}, {53247, 53365}

X(56394) = midpoint of X(44445) and X(46518)
X(56394) = reflection of X(i) in X(j) for these {i,j}: {669, 237}, {14957, 23301}

X(56395) = X(2)X(49)∩X(6)X(13)

Barycentrics   (2*a^2 - b^2 - c^2)*(a^2 - a*b + b^2 - c^2)*(a^2 + a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^2 - b^2 + a*c + c^2) : :

X(56395) lies on the cubic K055 and these lines: {2, 249}, {4, 38395}, {6, 13}, {30, 2088}, {32, 23967}, {39, 51254}, {51, 512}, {94, 598}, {187, 1648}, {262, 18316}, {328, 22486}, {476, 843}, {524, 43084}, {1995, 15539}, {2420, 10413}, {3148, 52153}, {3815, 5915}, {5099, 5967}, {5627, 35906}, {5968, 50711}, {7603, 41939}, {7745, 14254}, {7812, 35139}, {8176, 18883}, {9143, 52668}, {10630, 52449}, {11005, 23969}, {11179, 53768}, {11555, 11556}, {13851, 39563}, {14357, 51429}, {14560, 19136}, {14591, 37943}, {15538, 34365}, {16461, 16462}, {16770, 39405}, {16771, 39404}, {18907, 34209}, {19780, 51274}, {19781, 51267}, {22826, 22827}, {23895, 41746}, {23896, 41745}, {34288, 51349}, {51479, 52038}, {53771, 54131}

X(56395) = reflection of X(45901) in X(7753)
X(56395) = isogonal conjugate of the anticomplement of X(13162)
X(56395) = isogonal conjugate of the isotomic conjugate of X(43084)
X(56395) = X(i)-isoconjugate of X(j) for these (i,j): {50, 46277}, {75, 52668}, {323, 897}, {340, 36060}, {526, 36085}, {662, 9213}, {671, 6149}, {691, 32679}, {892, 2624}, {895, 52414}, {923, 7799}, {1577, 51478}, {3268, 36142}, {10411, 23894}, {36128, 52437}
X(56395) = X(i)-Dao conjugate of X(j) for these (i,j): {206, 52668}, {1084, 9213}, {1560, 340}, {1648, 45808}, {2482, 7799}, {6593, 323}, {14993, 671}, {15295, 111}, {21905, 2088}, {23992, 3268}, {38988, 526}, {48317, 44427}
X(56395) = cevapoint of X(9115) and X(9117)
X(56395) = trilinear pole of line {351, 33919}
X(56395) = crossdifference of every pair of points on line {323, 526}
X(56395) = barycentric product X(i)*X(j) for these {i,j}: {6, 43084}, {13, 52040}, {14, 52039}, {94, 187}, {110, 51479}, {265, 468}, {328, 44102}, {351, 35139}, {476, 690}, {523, 14559}, {524, 1989}, {896, 2166}, {1141, 41586}, {1648, 39295}, {2642, 32680}, {3266, 11060}, {3292, 6344}, {4235, 14582}, {5467, 10412}, {5468, 15475}, {5627, 5642}, {5967, 14356}, {6390, 18384}, {9717, 14254}, {12028, 12828}, {14357, 52449}, {14560, 35522}, {14567, 20573}, {14583, 36890}, {18316, 32225}, {18817, 23200}, {22105, 46155}, {23968, 50942}, {30454, 36310}, {30455, 36307}, {37778, 50433}, {44146, 52153}, {45662, 54554}
X(56395) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 52668}, {94, 18023}, {187, 323}, {265, 30786}, {351, 526}, {468, 340}, {476, 892}, {512, 9213}, {524, 7799}, {690, 3268}, {922, 6149}, {1576, 51478}, {1649, 45808}, {1989, 671}, {2166, 46277}, {2642, 32679}, {2682, 3258}, {3292, 52437}, {5467, 10411}, {5642, 6148}, {6344, 46111}, {8014, 52750}, {8015, 52751}, {9115, 14922}, {9117, 14921}, {9155, 51383}, {10412, 52632}, {11060, 111}, {14273, 44427}, {14417, 45792}, {14559, 99}, {14560, 691}, {14567, 50}, {14582, 14977}, {14583, 9214}, {15475, 5466}, {18384, 17983}, {21839, 42701}, {21906, 2088}, {23200, 22115}, {23968, 50941}, {32225, 52149}, {32678, 36085}, {35139, 53080}, {39295, 52940}, {40355, 9139}, {41586, 1273}, {43084, 76}, {44102, 186}, {51479, 850}, {52039, 299}, {52040, 298}, {52153, 895}, {52449, 52551}, {54274, 44814}
X(56395) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13, 14, 14356}, {8014, 8015, 14583}, {21466, 21467, 476}

X(56396) = X(6)X(13)∩X(187)X(476)

Barycentrics   (a^2 - a*b + b^2 - c^2)*(a^2 + a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^2 - b^2 + a*c + c^2)*(a^8 - 2*a^6*b^2 + a^4*b^4 - 2*a^6*c^2 + 3*a^4*b^2*c^2 - a^2*b^4*c^2 - b^6*c^2 + a^4*c^4 - a^2*b^2*c^4 + 2*b^4*c^4 - b^2*c^6) : :

X(56396) lies on the cubic K222 and these lines: {6, 13}, {32, 14254}, {94, 23588}, {112, 6344}, {187, 476}, {230, 34209}, {248, 32650}, {385, 35139}, {1637, 14270}, {5627, 48451}, {6781, 52056}, {7735, 51835}, {7737, 52449}, {7746, 39170}, {7748, 51254}, {9160, 15544}, {14910, 39375}, {18316, 48453}, {23969, 43654}, {47229, 51479}

X(56396) = X(i)-isoconjugate of X(j) for these (i,j): {2624, 53192}, {9160, 32679}
X(56396) = crossdifference of every pair of points on line {526, 34834}
X(56396) = barycentric product X(i)*X(j) for these {i,j}: {94, 32761}, {1989, 40879}
X(56396) = barycentric quotient X(i)/X(j) for these {i,j}: {476, 53192}, {14560, 9160}, {32761, 323}, {40879, 7799}
X(56396) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {265, 1989, 115}, {1989, 41392, 11060}

X(56397) = X(6)X(13)∩X(94)X(110)

Barycentrics   (a^2 - a*b + b^2 - c^2)*(a^2 + a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^2 - b^2 + a*c + c^2)*(a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6 - 3*a^8*c^2 + 5*a^6*b^2*c^2 - 3*a^4*b^4*c^2 + 2*a^2*b^6*c^2 - b^8*c^2 + 3*a^6*c^4 - 3*a^4*b^2*c^4 - 2*a^2*b^4*c^4 + b^6*c^4 - a^4*c^6 + 2*a^2*b^2*c^6 + b^4*c^6 - b^2*c^8) : :
X(56397) = X[265] - 3 X[1989]

X(56397) lies on the cubic K223 and these lines: {6, 13}, {74, 39290}, {94, 110}, {125, 18883}, {182, 43084}, {264, 3043}, {328, 15462}, {476, 1495}, {511, 53768}, {1141, 9160}, {1503, 51847}, {2410, 52772}, {3448, 30529}, {5961, 13289}, {6000, 12028}, {8754, 12140}, {10264, 49006}, {10706, 18316}, {14254, 46261}, {14560, 43087}, {14582, 14697}, {14595, 46818}, {18381, 53168}, {18576, 46686}, {20573, 44155}, {21650, 39139}, {22265, 39295}, {29012, 53771}, {34209, 46817}, {41204, 46456}, {41512, 52153}

X(56398) = X(6)X(13)∩X(476)X(10412)

Barycentrics   (a^2 - b^2)*(a^2 - c^2)*(a^2 - a*b + b^2 - c^2)*(a^2 + a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^2 - b^2 + a*c + c^2)*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6 + a^6*c^2 - 2*b^6*c^2 - 2*a^4*c^4 + 4*b^4*c^4 + a^2*c^6 - 2*b^2*c^6) : :

X(5698) lies on the cubic K229 and these lines: {6, 13}, {476, 10412}, {523, 2410}, {4230, 46456}, {5467, 39295}, {14380, 39290}, {18867, 38393}, {53267, 53768}

X(56398) = X(32679)-isoconjugate of X(32730)
X(56398) = crossdifference of every pair of points on line {526, 18334}
X(56398) = barycentric product X(i)*X(j) for these {i,j}: {110, 52983}, {3016, 35139}
X(56398) = barycentric quotient X(i)/X(j) for these {i,j}: {3016, 526}, {14560, 32730}, {23966, 32731}, {41392, 52763}, {52983, 850}

X(56399) = X(6)X(13)∩X(94)X(264)

Barycentrics   (a^2 - b^2 - c^2)*(a^2 - a*b + b^2 - c^2)*(a^2 + a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^2 - b^2 + a*c + c^2)*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4) : :

X(56399) lies on the cubic K260 and these lines: {2, 39290}, {6, 13}, {30, 51545}, {94, 264}, {184, 14595}, {206, 14560}, {216, 647}, {393, 23964}, {476, 46869}, {577, 32662}, {1249, 51835}, {1495, 3081}, {1531, 3284}, {1539, 39176}, {1990, 14254}, {2088, 16310}, {2420, 52945}, {3589, 43084}, {4550, 11074}, {4846, 12028}, {5158, 10217}, {6103, 41512}, {6794, 34298}, {8918, 8919}, {15454, 32761}, {18316, 54585}, {31670, 53768}, {36430, 36435}, {40578, 40579}, {40947, 52153}, {45778, 45779}, {46262, 47050}, {48905, 53771}, {48906, 51847}

X(56399) = complement of the isotomic conjugate of X(15454)
X(56399) = isotomic conjugate of the polar conjugate of X(14583)
X(56399) = isogonal conjugate of the polar conjugate of X(14254)
X(56399) = polar conjugate of the isotomic conjugate of X(51254)
X(56399) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 39170}, {15454, 2887}, {51965, 20305}, {52552, 21235}
X(56399) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 39170}, {94, 30}, {12028, 52153}, {14254, 14583}, {23588, 32662}, {39290, 43083}, {41392, 18558}, {41512, 512}
X(56399) = X(i)-isoconjugate of X(j) for these (i,j): {74, 52414}, {92, 14385}, {186, 2349}, {323, 36119}, {340, 2159}, {1304, 32679}, {2624, 16077}, {3268, 36131}, {6149, 16080}, {14165, 35200}, {33805, 34397}, {35201, 40384}, {36034, 44427}
X(56399) = X(i)-Dao conjugate of X(j) for these (i,j): {30, 14920}, {133, 14165}, {1511, 323}, {1650, 5664}, {3163, 340}, {3258, 44427}, {8552, 23965}, {14993, 16080}, {15295, 8749}, {22391, 14385}, {38999, 8552}, {39008, 3268}, {39170, 2}, {52869, 14918}
X(56399) = cevapoint of X(i) and X(j) for these (i,j): {1636, 39008}, {3163, 52945}
X(56399) = trilinear pole of line {9409, 18558}
X(56399) = crossdifference of every pair of points on line {186, 526}
X(56399) = barycentric product X(i)*X(j) for these {i,j}: {3, 14254}, {4, 51254}, {30, 265}, {69, 14583}, {94, 3284}, {112, 18557}, {113, 12028}, {328, 1495}, {476, 9033}, {525, 41392}, {648, 18558}, {1141, 1568}, {1531, 18316}, {1636, 46456}, {1989, 11064}, {2407, 14582}, {2420, 14592}, {2631, 32680}, {3260, 52153}, {4240, 43083}, {5627, 16163}, {6148, 14595}, {6344, 51394}, {9409, 35139}, {10272, 15392}, {11079, 36789}, {13754, 39375}, {14356, 35912}, {14401, 39290}, {14993, 20123}, {15454, 39170}, {17702, 51349}, {32662, 41079}, {34334, 50464}, {36035, 36061}, {36298, 40709}, {36299, 40710}, {40427, 47405}, {46106, 50433}, {51457, 51847}
X(56399) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 340}, {184, 14385}, {265, 1494}, {476, 16077}, {1495, 186}, {1531, 52149}, {1568, 1273}, {1636, 8552}, {1637, 44427}, {1989, 16080}, {1990, 14165}, {2173, 52414}, {2420, 14590}, {2631, 32679}, {3163, 14920}, {3284, 323}, {9033, 3268}, {9407, 34397}, {9408, 39176}, {9409, 526}, {11060, 8749}, {11064, 7799}, {11074, 40391}, {11079, 40384}, {12028, 40423}, {14254, 264}, {14391, 41078}, {14398, 47230}, {14401, 5664}, {14560, 1304}, {14581, 52418}, {14582, 2394}, {14583, 4}, {14595, 5627}, {15475, 18808}, {16163, 6148}, {18557, 3267}, {18558, 525}, {23347, 53176}, {32662, 44769}, {36298, 470}, {36299, 471}, {41077, 45792}, {41392, 648}, {41995, 6111}, {41996, 6110}, {42074, 35201}, {43083, 34767}, {47405, 34834}, {50433, 14919}, {51254, 69}, {51394, 52437}, {52153, 74}, {52945, 14918}
X(56399) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10217, 10218, 39170}, {36298, 36299, 14583}, {51270, 51277, 14356}

X(56400) = X(3)X(476)∩X64)X(13)

Barycentrics   (a^2 - a*b + b^2 - c^2)*(a^2 + a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^2 - b^2 + a*c + c^2)*(a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6 - 3*a^6*c^2 + 9*a^4*b^2*c^2 - 4*a^2*b^4*c^2 - 2*b^6*c^2 + 3*a^4*c^4 - 4*a^2*b^2*c^4 + 4*b^4*c^4 - a^2*c^6 - 2*b^2*c^6) : :

X(56400) lies on the cubic K297 and these lines: {2, 34209}, {3, 476}, {5, 14611}, {6, 13}, {30, 52449}, {94, 31861}, {183, 35139}, {378, 6344}, {382, 51254}, {1141, 21308}, {1656, 39170}, {3258, 16535}, {3534, 14583}, {5054, 14993}, {5055, 5627}, {5070, 53137}, {10620, 41512}, {14702, 52153}, {15688, 51345}, {18316, 54807}, {36193, 52772}, {37924, 53267}, {44438, 52415}, {51479, 53266}

X(56400) = X(32679)-isoconjugate of X(32732)
X(56400) = barycentric product X(94)*X(37477)
X(56400) = barycentric quotient X(i)/X(j) for these {i,j}: {14560, 32732}, {37477, 323}
X(56400) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 51835, 34209}, {265, 5655, 41390}, {265, 14356, 381}, {381, 34810, 399}

X(56401) = X(3)X(476)∩X23)X(94)

Barycentrics   (a^2 - a*b + b^2 - c^2)*(a^2 + a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^2 - b^2 + a*c + c^2)*(a^4 - a^2*b^2 - a^2*c^2 - 2*b^2*c^2) : :

X(56401) lies on the cubic K302 and these lines: {3, 30542}, {6, 13}, {23, 94}, {30, 15364}, {95, 99}, {114, 18883}, {147, 30529}, {300, 5981}, {301, 5980}, {671, 18316}, {804, 10412}, {2782, 13233}, {2788, 43082}, {2790, 2980}, {2793, 14662}, {2799, 43083}, {5613, 8838}, {5617, 8836}, {5961, 7502}, {6055, 47596}, {6321, 14980}, {6344, 32085}, {6770, 16771}, {6771, 40710}, {6773, 16770}, {6774, 40709}, {11169, 38664}, {11177, 52449}, {11623, 39170}, {14254, 45819}, {14486, 18384}, {14639, 18300}, {14651, 18478}, {14830, 52056}, {14854, 15535}, {18572, 39818}, {20774, 23956}, {32305, 53267}, {34209, 44266}, {34218, 53274}, {35139, 43664}, {39295, 43532}, {39809, 52842}, {43088, 55122}, {43090, 44961}, {43535, 54554}, {46039, 48983}, {52772, 53346}

X(56401) = midpoint of X(12188) and X(15928)
X(56401) = X(i)-isoconjugate of X(j) for these (i,j): {262, 6149}, {323, 2186}, {2290, 42300}, {3402, 7799}, {26714, 32679}, {43718, 52414}, {51444, 51801}
X(56401) = X(i)-Dao conjugate of X(j) for these (i,j): {14993, 262}, {15295, 263}, {38997, 526}, {51580, 7799}
X(56401) = trilinear pole of line {3288, 45321}
X(56401) = barycentric product X(i)*X(j) for these {i,j}: {94, 182}, {183, 1989}, {265, 458}, {328, 10311}, {476, 23878}, {2166, 52134}, {3288, 35139}, {5627, 51372}, {11060, 20023}, {14356, 46806}, {20573, 34396}, {44144, 52153}
X(56401) = barycentric quotient X(i)/X(j) for these {i,j}: {94, 327}, {182, 323}, {183, 7799}, {265, 42313}, {458, 340}, {1141, 42300}, {1989, 262}, {3288, 526}, {6784, 2088}, {10311, 186}, {11060, 263}, {11077, 51444}, {14356, 46807}, {14560, 26714}, {23878, 3268}, {23968, 36885}, {33971, 14165}, {34396, 50}, {39530, 14918}, {50433, 54032}, {51372, 6148}, {51542, 14355}, {52153, 43718}
X(56401) = {X(265),X(1989)}-harmonic conjugate of X(14356)

X(56402) = X(1)X(30)∩X(6)X(13)

Barycentrics   (a^2 + a*b + b^2 - c^2)*(a^2 - b^2 + a*c + c^2)*(2*a^3 - a^2*b - 2*a*b^2 + b^3 - a^2*c - 2*a*b*c - b^2*c - 2*a*c^2 - b*c^2 + c^3) : :
X(56402) = 2 X[13408] + X[48903], X[48916] - 4 X[49743]

X(56402) lies on the cubic K383 and these lines: {1, 30}, {2, 582}, {3, 52375}, {6, 13}, {57, 50462}, {94, 54679}, {226, 54613}, {376, 52393}, {519, 6757}, {541, 7986}, {942, 52390}, {999, 26700}, {1789, 16370}, {2160, 37584}, {3120, 11699}, {3241, 6742}, {3524, 24936}, {3534, 48868}, {3545, 24883}, {3578, 48887}, {3579, 27577}, {3746, 47749}, {4388, 50215}, {4653, 28460}, {5055, 24880}, {5663, 5902}, {5722, 34301}, {5886, 14844}, {6186, 14636}, {10247, 53794}, {11334, 52153}, {13743, 51748}, {14158, 51340}, {15699, 24902}, {21674, 50821}, {28194, 46617}, {28202, 32167}, {28368, 50415}, {30602, 39948}, {38430, 50301}, {41930, 52381}, {43682, 54526}, {44229, 48857}, {46441, 52269}, {48877, 50256}

X(56402) = midpoint of X(48877) and X(50256)
X(56402) = reflection of X(i) in X(j) for these {i,j}: {500, 37631}, {3578, 48887}
X(56402) = X(6149)-isoconjugate of X(54528)
X(56402) = X(14993)-Dao conjugate of X(54528)
X(56402) = crossdifference of every pair of points on line {526, 9404}
X(56402) = barycentric product X(i)*X(j) for these {i,j}: {79, 54357}, {24929, 30690}
X(56402) = barycentric quotient X(i)/X(j) for these {i,j}: {1989, 54528}, {15670, 3578}, {15762, 445}, {24929, 3219}, {54357, 319}
X(56402) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 79, 52382}, {13, 14, 8818}, {381, 3017, 45926}, {381, 45923, 3017}, {3017, 45924, 381}, {3019, 45924, 45923}, {45923, 45924, 45926}

X(56403) = X(4)X(40388)∩X(6)X(13)

Barycentrics   (a^2 - a*b + b^2 - c^2)*(a^2 + a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^2 - b^2 + a*c + c^2)*(a^4*b^2 - 2*a^2*b^4 + b^6 + a^4*c^2 + 2*a^2*b^2*c^2 - b^4*c^2 - 2*a^2*c^4 - b^2*c^4 + c^6) : :

X(56403) lies on the cubic K429 and these lines: {4, 40388}, {6, 13}, {53, 2501}, {94, 34289}, {141, 43084}, {157, 52153}, {231, 2420}, {571, 32662}, {1974, 14560}, {2088, 39235}, {3003, 34104}, {5063, 51254}, {5627, 34288}, {8014, 36298}, {8015, 36299}, {10413, 52945}, {10733, 14910}, {11074, 11080}, {11079, 51964}, {12383, 52557}, {15441, 15442}, {15475, 22260}, {21850, 51847}, {32223, 53274}, {39295, 54925}, {40158, 40159}, {46264, 53768}, {48910, 53771}, {52552, 54395}, {54556, 54557}

X(56403) = polar conjugate of the isotomic conjugate of X(39170)
X(56403) = orthic-isogonal conjugate of X(14583)
X(56403) = X(i)-Ceva conjugate of X(j) for these (i,j): {4, 14583}, {1989, 3003}
X(56403) = X(i)-isoconjugate of X(j) for these (i,j): {63, 38936}, {75, 52557}, {323, 36053}, {662, 15470}, {2349, 39371}, {2624, 18878}, {2986, 6149}, {5504, 52414}, {8552, 36114}, {10420, 32679}
X(56403) = X(i)-Dao conjugate of X(j) for these (i,j): {113, 323}, {206, 52557}, {1084, 15470}, {3003, 6148}, {3162, 38936}, {6334, 23965}, {14993, 2986}, {15295, 14910}, {16178, 44427}, {34834, 7799}, {39005, 8552}, {39021, 3268}
X(56403) = crossdifference of every pair of points on line {526, 15470}
X(56403) = barycentric product X(i)*X(j) for these {i,j}: {4, 39170}, {94, 3003}, {113, 5627}, {265, 403}, {328, 44084}, {476, 55121}, {523, 41512}, {686, 46456}, {1725, 2166}, {1989, 3580}, {6344, 13754}, {10412, 15329}, {12825, 48374}, {14254, 14264}, {14356, 52451}, {14582, 16237}, {14993, 18781}, {21731, 35139}, {34209, 39985}, {39290, 55265}, {44138, 52153}
X(56403) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 38936}, {32, 52557}, {94, 40832}, {113, 6148}, {403, 340}, {476, 18878}, {512, 15470}, {686, 8552}, {1495, 39371}, {1989, 2986}, {3003, 323}, {3580, 7799}, {5627, 40423}, {6334, 45792}, {11060, 14910}, {13754, 52437}, {14254, 52552}, {14560, 10420}, {14582, 15421}, {14583, 15454}, {14595, 12028}, {15329, 10411}, {15475, 15328}, {18384, 1300}, {21731, 526}, {32662, 43755}, {34209, 39988}, {39170, 69}, {39290, 55264}, {40355, 10419}, {41512, 99}, {44084, 186}, {47236, 44427}, {51821, 14385}, {52153, 5504}, {55121, 3268}, {55265, 5664}
X(56403) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1989, 41392, 3018}, {11080, 11085, 14583}, {14595, 34417, 14583}

X(56404) = X(6)X(13)∩X(51)X(14595)

Barycentrics   (a^2 - a*b + b^2 - c^2)*(a^2 + a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^2 - b^2 + a*c + c^2)*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6 - 3*a^4*c^2 - a^2*b^2*c^2 + b^4*c^2 + 3*a^2*c^4 + b^2*c^4 - c^6) : :

X(56404) lies on the cubic K486 and these lines: {6, 13}, {51, 14595}, {69, 43084}, {1117, 11071}, {2965, 32662}, {5627, 11074}, {8014, 11085}, {8015, 11080}, {8929, 8930}, {10413, 11063}, {13483, 16771}, {13484, 16770}, {15538, 39170}, {18316, 54827}, {31670, 53771}, {32002, 46456}, {34325, 34326}, {48906, 53768}

X(56404) = X(i)-Ceva conjugate of X(j) for these (i,j): {249, 41512}, {39295, 47053}
X(56404) = X(i)-isoconjugate of X(j) for these (i,j): {323, 51804}, {1291, 32679}, {6149, 13582}, {43704, 52414}
X(56404) = X(i)-Dao conjugate of X(j) for these (i,j): {14993, 13582}, {15295, 14579}, {16336, 54461}, {53989, 44427}
X(56404) = barycentric product X(i)*X(j) for these {i,j}: {13, 51274}, {14, 51267}, {94, 11063}, {265, 37943}, {476, 45147}, {1749, 2166}, {1989, 37779}, {3470, 14254}, {5627, 10272}, {6140, 35139}, {6344, 50461}, {10412, 47053}, {10413, 39295}, {14451, 14993}, {14583, 46751}
X(56404) = barycentric quotient X(i)/X(j) for these {i,j}: {1989, 13582}, {6140, 526}, {10272, 6148}, {11060, 14579}, {11063, 323}, {14560, 1291}, {14583, 3471}, {14595, 15392}, {37779, 7799}, {37943, 340}, {45147, 3268}, {47053, 10411}, {50461, 52437}, {51267, 299}, {51274, 298}, {52153, 43704}

X(56405) = X(1)X(60)∩X(6)X(13)

Barycentrics   a*(a + b)*(a + c)*(a^2 - a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^3 + a^2*b - a*b^2 - b^3 + a^2*c - a*b*c - b^2*c - a*c^2 - b*c^2 - c^3) : :

X(56405) lies on the cubics K058 and K498 and these lines: {1, 60}, {6, 13}, {10, 36927}, {58, 2771}, {80, 502}, {81, 6126}, {125, 24880}, {519, 6740}, {1793, 5692}, {1807, 40602}, {2361, 5127}, {3448, 24883}, {3751, 41741}, {4653, 16164}, {5620, 39140}, {11699, 15955}, {12047, 24624}, {13605, 37791}, {15059, 24902}, {15065, 47318}, {43700, 52391}

X(56405) = isogonal conjugate of X(39149)
X(56405) = X(80)-Ceva conjugate of X(759)
X(56405) = X(i)-isoconjugate of X(j) for these (i,j): {1, 39149}, {36, 502}, {267, 758}, {1029, 2245}, {2250, 41910}, {3218, 21353}, {3444, 3936}, {3724, 44188}, {4053, 40143}
X(56405) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 39149}, {81, 320}, {15898, 502}
X(56405) = crossdifference of every pair of points on line {526, 2610}
X(56405) = barycentric product X(i)*X(j) for these {i,j}: {80, 40592}, {191, 24624}, {501, 18359}, {759, 2895}, {1030, 14616}, {2341, 41808}, {2906, 52351}, {6740, 47057}, {20932, 34079}, {31947, 47318}
X(56405) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 39149}, {191, 3936}, {501, 3218}, {759, 1029}, {859, 41910}, {1030, 758}, {2161, 502}, {2895, 35550}, {2906, 17923}, {6187, 21353}, {8614, 18593}, {24624, 44188}, {31947, 4707}, {34079, 267}, {40592, 320}, {42653, 2610}, {47057, 41804}
X(56405) = {X(1),X(52380)}-harmonic conjugate of X(759)

X(56406) = X(6)X(13)∩X(141)X(46155)

Barycentrics   (a^2 - a*b + b^2 - c^2)*(a^2 + a*b + b^2 - c^2)*(b^2 + c^2)*(a^2 - b^2 - a*c + c^2)*(a^2 - b^2 + a*c + c^2)*(a^4 + a^2*b^2 - 2*b^4 + a^2*c^2 + b^2*c^2 - 2*c^4) : :

X(56406) lies on the cubic K975 and these lines: {6, 13}, {141, 46155}, {308, 35139}, {1176, 14560}, {10412, 31065}, {11119, 11120}, {15107, 38393}, {35222, 52153}

X(56406) =X(51360)-Dao conjugate of X(1511)

X(56407) = X(3)X(94)∩X(6)X(13)

Barycentrics   (a^2 - a*b + b^2 - c^2)*(a^2 + a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^2 - b^2 + a*c + c^2)*(a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6 - 3*a^6*c^2 + 3*a^4*b^2*c^2 + 2*a^2*b^4*c^2 - 2*b^6*c^2 + 3*a^4*c^4 + 2*a^2*b^2*c^4 + 4*b^4*c^4 - a^2*c^6 - 2*b^2*c^6) : :

X(56407) lies on the cubic K1057 and these lines: {3, 94}, {5, 30529}, {6, 13}, {25, 6344}, {183, 20573}, {476, 1141}, {567, 9222}, {1656, 18883}, {2166, 18524}, {3830, 18316}, {3843, 18300}, {7545, 14254}, {7574, 51847}, {12028, 18859}, {18386, 23956}, {18494, 52415}, {20304, 30685}, {23181, 38587}, {37924, 53768}, {39290, 44715}, {44275, 51835}

X(56407) = X(6149)-isoconjugate of X(9221)
X(56407) = X(14993)-Dao conjugate of X(9221)
X(56407) = barycentric product X(94)*X(567)
X(56407) = barycentric quotient X(i)/X(j) for these {i,j}: {567, 323}, {1989, 9221}

X(56408) = X(6)X(13)∩X(141)X(328)

Barycentrics   (a^2 - a*b + b^2 - c^2)*(a^2 + a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^2 - b^2 + a*c + c^2)*(a^4*b^2 - 2*a^2*b^4 + b^6 + a^4*c^2 - a^2*b^2*c^2 - b^4*c^2 - 2*a^2*c^4 - b^2*c^4 + c^6) : :

X(56408) lies on the cubic K1284 and these lines: {6, 13}, {53, 6344}, {94, 3580}, {141, 328}, {216, 8579}, {476, 47275}, {1141, 14533}, {1609, 31676}, {3569, 10412}, {5627, 51544}, {6748, 23956}, {10733, 38872}, {11063, 34448}, {18316, 51545}, {18573, 39170}, {18877, 40389}, {32227, 44529}, {34209, 47322}

X(56408) = X(6149)-isoconjugate of X(7578)
X(56408) = X(i)-Dao conjugate of X(j) for these (i,j): {566, 52149}, {14993, 7578}
X(56408) = barycentric product X(i)*X(j) for these {i,j}: {94, 566}, {265, 7577}, {5627, 51391}, {6344, 23039}, {10412, 36829}, {14356, 52190}, {18117, 35139}
X(56408) = barycentric quotient X(i)/X(j) for these {i,j}: {566, 323}, {1989, 7578}, {7577, 340}, {18117, 526}, {23039, 52437}, {36829, 10411}, {51391, 6148}
X(56408) = {X(265),X(1989)}-harmonic conjugate of X(6)

X(56409) = X(6)X(13)∩X(76)X(5641)

Barycentrics   (a^2 - a*b + b^2 - c^2)*(a^2 + a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^2 - b^2 + a*c + c^2)*(a^6 - a^4*b^2 + 2*a^2*b^4 - 2*b^6 - a^4*c^2 + 3*a^2*b^2*c^2 - b^4*c^2 + 2*a^2*c^4 - b^2*c^4 - 2*c^6) : :

X(56409) lies on the cubic K1316 and these lines: {6, 13}, {76, 5641}, {476, 36194}, {599, 46155}, {826, 15475}, {3407, 18316}, {7884, 14355}, {11178, 43087}, {11328, 52153}, {14458, 39295}, {14560, 19127}, {43453, 52449}

X(56409) = X(6149)-isoconjugate of X(55009)
X(56409) = X(14993)-Dao conjugate of X(55009)
X(56409) = barycentric product X(94)*X(35002)
X(56409) = barycentric quotient X(i)/X(j) for these {i,j}: {1989, 55009}, {35002, 323}

X(56410) = X(1)X(3)∩X(108)X(13397)

Barycentrics   a^2*(a - b)*(a - c)*(a + b - c)*(a - b + c)*(a^2 - b^2 - c^2)*(a^3*b - a^2*b^2 - a*b^3 + b^4 + a^3*c + a*b^2*c - a^2*c^2 + a*b*c^2 - 2*b^2*c^2 - a*c^3 + c^4) : :

X(56410) lies on the cubic K658 and these lines: {1, 3}, {108, 13397}, {109, 36082}, {912, 53786}, {1331, 1813}, {2720, 6099}, {7335, 22457}, {12832, 34332}

X(56410) = X(2720)-Ceva conjugate of X(36059)
X(56410) = X(i)-isoconjugate of X(j) for these (i,j): {11, 36106}, {29, 3657}, {522, 915}, {650, 37203}, {663, 46133}, {913, 4391}, {2990, 3064}, {4858, 32698}, {7649, 45393}, {32655, 46110}, {36052, 44426}
X(56410) = X(i)-Dao conjugate of X(j) for these (i,j): {119, 44426}, {39002, 11}, {39175, 43728}
X(56410) = trilinear pole of line {2252, 47408}
X(56410) = crossdifference of every pair of points on line {650, 6506}
X(56410) = barycentric product X(i)*X(j) for these {i,j}: {109, 914}, {190, 51649}, {651, 912}, {664, 2252}, {1214, 3658}, {1332, 18838}, {1737, 1813}, {6516, 8609}, {36059, 48380}, {44717, 55126}, {47408, 54953}
X(56410) = barycentric quotient X(i)/X(j) for these {i,j}: {109, 37203}, {651, 46133}, {906, 45393}, {912, 4391}, {914, 35519}, {1409, 3657}, {1415, 915}, {1737, 46110}, {2149, 36106}, {2252, 522}, {3658, 31623}, {8609, 44426}, {18838, 17924}, {32660, 36052}, {36059, 2990}, {47408, 2804}, {51649, 514}

X(56411) = X(1)X(3)∩X(33)X(2222)

Barycentrics   a*(a^8 - 2*a^7*b + 4*a^5*b^3 - 4*a^4*b^4 - 2*a^3*b^5 + 4*a^2*b^6 - b^8 - 2*a^7*c + 7*a^6*b*c - 7*a^5*b^2*c - 4*a^4*b^3*c + 12*a^3*b^4*c - 5*a^2*b^5*c - 3*a*b^6*c + 2*b^7*c - 7*a^5*b*c^2 + 18*a^4*b^2*c^2 - 10*a^3*b^3*c^2 - 6*a^2*b^4*c^2 + 5*a*b^5*c^2 + 4*a^5*c^3 - 4*a^4*b*c^3 - 10*a^3*b^2*c^3 + 14*a^2*b^3*c^3 - 2*a*b^4*c^3 - 2*b^5*c^3 - 4*a^4*c^4 + 12*a^3*b*c^4 - 6*a^2*b^2*c^4 - 2*a*b^3*c^4 + 2*b^4*c^4 - 2*a^3*c^5 - 5*a^2*b*c^5 + 5*a*b^2*c^5 - 2*b^3*c^5 + 4*a^2*c^6 - 3*a*b*c^6 + 2*b*c^7 - c^8) : :

X(56411) lies on the cubic K817 and these lines: {1, 3}, {33, 2222}, {43, 2957}, {59, 9637}, {513, 1709}, {614, 37815}, {1699, 3259}, {1768, 2807}, {2817, 10058}, {7680, 47270}, {11124, 42757}, {44425, 44670}

X(56412) = X(1)X(3)∩X(5)X(30493)

Barycentrics   a*(a + b - c)*(a - b + c)*(a^3 - a*b^2 + a*b*c - b^2*c - a*c^2 - b*c^2)*(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4) : :

X(56412) lies on the cubic K976 and these lines: {1, 3}, {5, 30493}, {54, 36059}, {109, 37806}, {276, 18026}, {1210, 20122}, {1361, 5901}, {1393, 18180}, {1425, 43043}, {1887, 13369}, {6906, 45022}, {29958, 52659}

X(56412) = X(18026)-Ceva conjugate of X(17496)
X(56412) = X(i)-isoconjugate of X(j) for these (i,j): {34434, 44687}, {35196, 51870}
X(56412) = barycentric product X(i)*X(j) for these {i,j}: {5, 17074}, {1393, 14829}, {1414, 52322}, {11109, 44708}, {14570, 51662}, {17167, 37558}, {18180, 52358}
X(56412) = barycentric quotient X(i)/X(j) for these {i,j}: {572, 44687}, {1393, 2051}, {17074, 95}, {18180, 46880}, {37558, 56246}, {51662, 15412}, {52322, 4086}, {52358, 56189}, {55323, 56254}

X(56413) = X(1)X(3)∩X(31)X(3212)

Barycentrics   a*(a + b - c)*(a - b + c)*(a^2 - b*c)*(a^2*b - a*b^2 + a^2*c - a*b*c + b^2*c - a*c^2 + b*c^2) : :

X(56413) lies on the cubic K989 and these lines: {1, 3}, {31, 3212}, {109, 43040}, {238, 242}, {239, 51329}, {1447, 3747}, {1966, 18033}, {3501, 52657}, {4433, 34253}, {9285, 51917}, {12194, 55086}, {19222, 51902}, {20967, 24579}, {24578, 52635}, {34252, 51903}, {51246, 51909}

X(56413) = isogonal conjugate of X(43748)
X(56413) = X(31)-Ceva conjugate of X(51935)
X(56413) = X(i)-isoconjugate of X(j) for these (i,j): {1, 43748}, {2, 51995}, {694, 39936}, {3500, 4876}, {7077, 54128}
X(56413) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 43748}, {32664, 51995}, {39043, 39936}
X(56413) = crossdifference of every pair of points on line {650, 20359}
X(56413) = X(1)-line conjugate of X(20359)
X(56413) = barycentric product X(i)*X(j) for these {i,j}: {1, 39930}, {75, 51956}, {1423, 14199}, {1428, 17786}, {1429, 32937}, {1447, 3501}, {1966, 51986}, {8927, 39940}, {10030, 34247}, {13588, 16609}, {18033, 51949}
X(56413) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 43748}, {31, 51995}, {1428, 3500}, {1429, 54128}, {1580, 39936}, {3501, 4518}, {13588, 36800}, {14199, 27424}, {34247, 4876}, {39930, 75}, {51949, 7077}, {51956, 1}, {51986, 1581}

X(56414) = X(1)X(3)∩X(20)X(108)

Barycentrics   a^2*(a + b - c)*(a - b + c)*(a^2 - b^2 - c^2)*(a^4 - b^4 + 2*a^2*b*c - 2*a*b^2*c - 2*a*b*c^2 + 2*b^2*c^2 - c^4) : :

X(56414) lies on the cubic K1324 and these lines: {1, 3}, {12, 34120}, {20, 108}, {34, 37034}, {68, 53786}, {73, 7125}, {78, 7111}, {109, 3556}, {123, 3436}, {197, 21147}, {198, 15905}, {222, 1425}, {225, 37241}, {307, 1804}, {577, 2178}, {859, 53995}, {958, 51368}, {1012, 11399}, {1066, 52218}, {1092, 7078}, {1259, 23067}, {1359, 11827}, {1394, 40212}, {1396, 27652}, {1398, 1465}, {1415, 10316}, {1437, 19349}, {1455, 9798}, {1887, 37696}, {2933, 53321}, {2968, 12513}, {3157, 7335}, {3435, 3827}, {3869, 39167}, {3911, 34823}, {3926, 6516}, {4296, 11337}, {5226, 25909}, {5253, 25876}, {6759, 52830}, {6827, 54200}, {7099, 33587}, {7114, 22350}, {7952, 37404}, {8283, 18481}, {10106, 34822}, {10571, 22119}, {11500, 38554}, {13273, 18404}, {14257, 16049}, {15524, 52097}, {17306, 55118}, {18531, 18961}, {18641, 46009}, {19365, 36754}, {19366, 36742}, {20122, 36746}, {21773, 36748}, {22479, 37259}, {26377, 37397}, {28405, 28773}, {28407, 28771}, {36029, 44696}, {37179, 54366}, {40944, 56294}, {43742, 52366}, {52389, 55117}, {54081, 54083}

X(56414) = isogonal conjugate of X(43742)
X(56414) = isotomic conjugate of the polar conjugate of X(478)
X(56414) = X(i)-Ceva conjugate of X(j) for these (i,j): {69, 222}, {16049, 21147}
X(56414) = X(i)-isoconjugate of X(j) for these (i,j): {1, 43742}, {19, 34277}, {29, 43703}, {33, 8048}, {158, 39167}, {281, 42467}, {318, 3435}, {522, 40097}, {3064, 46640}, {15385, 24026}, {40454, 46878}
X(56414) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 43742}, {6, 34277}, {56, 4}, {123, 44426}, {1147, 39167}, {6588, 23978}
X(56414) = barycentric product X(i)*X(j) for these {i,j}: {7, 22132}, {63, 21147}, {69, 478}, {77, 1766}, {123, 1262}, {197, 348}, {205, 7182}, {222, 3436}, {394, 14257}, {603, 20928}, {1214, 16049}, {1231, 52143}, {1813, 21186}, {3926, 17408}, {6516, 6588}, {41364, 52385}, {47410, 55346}
X(56414) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 34277}, {6, 43742}, {123, 23978}, {197, 281}, {205, 33}, {222, 8048}, {478, 4}, {577, 39167}, {603, 42467}, {1409, 43703}, {1415, 40097}, {1766, 318}, {3436, 7017}, {6588, 44426}, {14257, 2052}, {16049, 31623}, {17408, 393}, {21147, 92}, {21186, 46110}, {22132, 8}, {23979, 15385}, {36059, 46640}, {41364, 1896}, {47410, 2968}, {52143, 1172}, {52411, 3435}
X(56414) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 999, 17102}, {1398, 37257, 1465}

X(56415) = X(1)X(5)∩X(44)X(655)

Barycentrics   (a + b - c)*(a - b + c)*(a^2 - a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^5 - a^4*b - a^3*b^2 + a^2*b^3 - a^4*c + a^3*b*c + a^2*b^2*c - b^4*c - a^3*c^2 + a^2*b*c^2 - 2*a*b^2*c^2 + b^3*c^2 + a^2*c^3 + b^2*c^3 - b*c^4) : :

X(56415) lies on the cubic K137 and these lines: {1, 5}, {44, 655}, {239, 35174}, {651, 16732}, {654, 10015}, {1086, 52392}, {1146, 52351}, {18359, 23592}

X(56415) = X(10015)-line conjugate of X(654)

X(56416) = X(1)X(5)∩X(10)X(522)

Barycentrics   (a^2 - a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^2*b - b^3 + a^2*c - 2*a*b*c + b^2*c + b*c^2 - c^3) : :

X(56416) lies on the cubic K259 and these lines: {1, 5}, {2, 36590}, {3, 2222}, {4, 7012}, {8, 51562}, {10, 522}, {30, 23703}, {35, 45828}, {40, 29374}, {45, 14358}, {55, 39173}, {56, 47051}, {79, 46821}, {109, 10742}, {169, 2161}, {220, 35113}, {221, 18542}, {318, 7141}, {517, 35015}, {651, 10711}, {655, 5657}, {759, 38903}, {942, 43947}, {1145, 26611}, {1168, 24864}, {1500, 23980}, {1512, 22464}, {1737, 53525}, {2804, 37629}, {3120, 6797}, {3259, 14260}, {3295, 38938}, {3585, 18360}, {3673, 18815}, {3679, 36909}, {4075, 15065}, {5697, 13756}, {5790, 14629}, {6376, 20566}, {6702, 52537}, {6788, 17054}, {7004, 12619}, {10703, 19914}, {11010, 51886}, {12611, 53530}, {14010, 17757}, {14628, 31397}, {15325, 41343}, {18480, 33649}, {18524, 38945}, {18545, 34046}, {21290, 28829}, {23058, 36910}, {24929, 40172}, {24984, 25005}, {25413, 34242}, {33298, 35174}, {34040, 45631}, {35004, 52391}, {38950, 51631}

X(56416) = complement of X(36944)
X(56416) = complement of the isogonal conjugate of X(14260)
X(56416) = X(i)-complementary conjugate of X(j) for these (i,j): {106, 517}, {517, 121}, {859, 34587}, {1417, 44675}, {1457, 1145}, {1769, 3259}, {2183, 16594}, {8752, 26011}, {9456, 3911}, {14260, 10}, {17109, 45247}, {52031, 141}
X(56416) = X(i)-Ceva conjugate of X(j) for these (i,j): {80, 517}, {36590, 80}, {51562, 2804}
X(56416) = X(i)-isoconjugate of X(j) for these (i,j): {36, 104}, {214, 10428}, {320, 34858}, {654, 37136}, {909, 3218}, {1309, 22379}, {1443, 2342}, {1795, 1870}, {1983, 2401}, {2323, 34051}, {2423, 4585}, {2720, 3738}, {3904, 32669}, {3960, 32641}, {7113, 34234}, {8648, 54953}, {11570, 15381}, {13136, 21758}, {14578, 17923}, {16586, 41933}, {16944, 36944}, {18816, 52434}, {36037, 53314}, {36123, 52407}, {51565, 52440}
X(56416) = X(i)-Dao conjugate of X(j) for these (i,j): {517, 34586}, {1145, 4511}, {3259, 53314}, {3911, 41801}, {15898, 104}, {16586, 320}, {23980, 3218}, {25640, 1870}, {36909, 51565}, {38981, 3738}, {40613, 36}, {46398, 4453}, {55153, 3904}
X(56416) = cevapoint of X(i) and X(j) for these (i,j): {1145, 17757}, {1769, 3259}, {23757, 35015}, {23980, 51377}
X(56416) = trilinear pole of line {21801, 42763}
X(56416) = crossdifference of every pair of points on line {654, 7113}
X(56416) = barycentric product X(i)*X(j) for these {i,j}: {8, 52212}, {80, 908}, {517, 18359}, {655, 2804}, {1465, 52409}, {1769, 36804}, {1785, 52351}, {2006, 6735}, {2161, 3262}, {2183, 20566}, {10015, 51562}, {14616, 21801}, {17757, 24624}, {22464, 36910}, {24029, 52356}, {26611, 40437}, {35174, 46393}, {36590, 52659}, {46398, 46649}, {46405, 53549}, {51975, 52031}
X(56416) = barycentric quotient X(i)/X(j) for these {i,j}: {80, 34234}, {517, 3218}, {655, 54953}, {908, 320}, {1145, 51583}, {1411, 34051}, {1465, 1443}, {1769, 3960}, {1785, 17923}, {2161, 104}, {2183, 36}, {2222, 37136}, {2804, 3904}, {3262, 20924}, {3310, 53314}, {3326, 46398}, {6187, 909}, {6735, 32851}, {10015, 4453}, {14260, 40215}, {14571, 1870}, {14584, 40218}, {15507, 27950}, {17757, 3936}, {18359, 18816}, {21801, 758}, {22350, 22128}, {22464, 17078}, {23980, 34586}, {24028, 16586}, {32675, 2720}, {34857, 2250}, {36910, 51565}, {41215, 38353}, {42753, 53546}, {42754, 4089}, {46393, 3738}, {51362, 27757}, {51377, 2245}, {51562, 13136}, {52031, 52553}, {52212, 7}, {52371, 52663}, {52409, 36795}, {52431, 1795}, {52659, 41801}, {53549, 654}
X(56416) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 80, 14584}, {1, 14584, 34232}, {1, 52005, 34586}, {80, 52383, 45926}

X(56417) = X(1)X(5)∩X(2)X(52409)

Barycentrics   (a^2 - a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^3 + a^2*b - a*b^2 - b^3 + a^2*c + b^2*c - a*c^2 + b*c^2 - c^3) : :

X(56417) lies on the cubic K491 and these lines: {1, 5}, {2, 52409}, {37, 1989}, {79, 18360}, {171, 16152}, {498, 15065}, {499, 51975}, {759, 4228}, {915, 1785}, {1319, 38954}, {1478, 11700}, {1720, 34257}, {1725, 17734}, {1737, 33129}, {1784, 37770}, {2161, 17699}, {3085, 18359}, {3193, 21077}, {3582, 36909}, {3583, 51361}, {3664, 52392}, {3672, 18815}, {4862, 56287}, {7040, 7952}, {10058, 51889}, {10260, 54064}, {13273, 33649}, {17322, 20566}

X(56417) = X(i)-isoconjugate of X(j) for these (i,j): {36, 90}, {1069, 1870}, {1443, 7072}, {2164, 3218}, {2361, 7318}, {2994, 7113}, {3738, 36082}, {6513, 52413}, {7040, 52407}, {20570, 52434}, {36626, 52440}
X(56417) = X(i)-Dao conjugate of X(j) for these (i,j): {15898, 90}, {36909, 36626}
X(56417) = trilinear pole of line {21853, 46389}
X(56417) = barycentric product X(i)*X(j) for these {i,j}: {46, 18359}, {80, 5905}, {1068, 52351}, {2006, 5552}, {2161, 20930}, {2178, 20566}, {14616, 21853}, {21077, 24624}, {21188, 51562}, {31631, 52383}, {35174, 46389}, {36804, 51648}
X(56417) = barycentric quotient X(i)/X(j) for these {i,j}: {46, 3218}, {80, 2994}, {1068, 17923}, {1807, 6513}, {2006, 7318}, {2161, 90}, {2178, 36}, {3157, 22128}, {5552, 32851}, {5905, 320}, {6187, 2164}, {18359, 20570}, {20930, 20924}, {21077, 3936}, {21188, 4453}, {21853, 758}, {32675, 36082}, {36910, 36626}, {46389, 3738}, {51648, 3960}, {52033, 1870}, {52431, 1069}, {55214, 53527}
X(56417) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {119, 45946, 1718}, {1807, 52383, 80}, {45926, 52371, 80}

X(56418) = X(1)X(5)∩X(6)X(57)

Barycentrics   a*(a + b - c)*(a - b + c)*(a^3 + a^2*b - a*b^2 - b^3 + a^2*c - 4*a*b*c + b^2*c - a*c^2 + b*c^2 - c^3) : :

X(56418) lies on the cubic K502 and these lines: {1, 5}, {2, 914}, {6, 57}, {7, 17012}, {34, 386}, {42, 34036}, {43, 8270}, {46, 36754}, {73, 34489}, {77, 3911}, {165, 2361}, {198, 51413}, {226, 3946}, {227, 16466}, {278, 52033}, {582, 1399}, {651, 4850}, {990, 2635}, {995, 998}, {997, 54292}, {1038, 3216}, {1079, 3338}, {1103, 1697}, {1193, 21147}, {1203, 37550}, {1214, 1723}, {1445, 18593}, {1453, 37583}, {1456, 37541}, {1480, 5119}, {1490, 33178}, {1708, 17080}, {1722, 37558}, {1724, 54320}, {1728, 37565}, {1758, 16468}, {1877, 48837}, {2051, 5307}, {2078, 7290}, {2264, 15851}, {2324, 31142}, {3240, 4318}, {3305, 16577}, {3306, 43048}, {3666, 34048}, {3914, 34029}, {3995, 28996}, {4646, 34040}, {4654, 7274}, {4846, 50527}, {5018, 17779}, {5222, 8776}, {5226, 17011}, {5316, 25930}, {5398, 15803}, {5435, 17020}, {5709, 54301}, {6510, 25934}, {6848, 15836}, {7269, 17013}, {7308, 40937}, {8758, 15299}, {9370, 37592}, {10571, 54418}, {10964, 16215}, {14997, 37787}, {15297, 34977}, {17073, 26005}, {17147, 28997}, {17495, 28968}, {23511, 31231}, {25939, 55432}, {28780, 33077}, {28830, 40863}, {31019, 37771}, {31187, 54390}, {34050, 34492}, {39943, 40407}

X(56418) = X(i)-isoconjugate of X(j) for these (i,j): {9, 7284}, {1481, 36916}
X(56418) = X(i)-Dao conjugate of X(j) for these (i,j): {478, 7284}, {3306, 28808}
X(56418) = crossdifference of every pair of points on line {654, 3900}
X(56418) = barycentric product X(i)*X(j) for these {i,j}: {7, 5119}, {57, 31018}
X(56418) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 7284}, {1480, 3872}, {5119, 8}, {31018, 312}
X(56418) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5400, 9817}, {6, 1465, 57}, {222, 3752, 57}, {223, 2999, 57}, {1427, 52424, 57}, {5396, 37697, 1}, {5718, 5723, 37695}, {5718, 37695, 5219}, {17080, 32911, 1708}, {17720, 52659, 5219}

X(56419) = X(1)X(5)∩X(4)X(2964)

Barycentrics   (a^2 - a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^2*b - b^3 + a^2*c + a*b*c + b^2*c + b*c^2 - c^3) : :

X(56419) lies on the cubic K588 and these lines: {1, 5}, {4, 2964}, {10, 18359}, {58, 3585}, {201, 18395}, {225, 2166}, {484, 2161}, {759, 4225}, {1698, 52351}, {1737, 18815}, {2323, 31160}, {3120, 11571}, {3254, 46821}, {3582, 40437}, {3584, 54528}, {4792, 33136}, {6187, 38938}, {6702, 16586}, {6734, 52409}, {9780, 41226}, {10894, 16473}, {10895, 36750}, {11219, 46820}, {15932, 47054}, {19875, 36910}, {29675, 40172}, {33140, 40109}

X(56419) = X(54528)-Ceva conjugate of X(80)
X(56419) = X(36)-isoconjugate of X(15175)
X(56419) = X(i)-Dao conjugate of X(j) for these (i,j): {15898, 15175}, {17057, 4511}
X(56419) = barycentric product X(i)*X(j) for these {i,j}: {80, 31019}, {3822, 24624}, {5902, 18359}
X(56419) = barycentric quotient X(i)/X(j) for these {i,j}: {2161, 15175}, {3822, 3936}, {5902, 3218}, {17057, 27757}, {23758, 23884}, {31019, 320}
X(56419) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {80, 2006, 1}, {37718, 51310, 80}, {45926, 52383, 80}

X(56420) = X(1)X(5)∩X(4)X(38954)

Barycentrics   (a^2 - a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^5*b - 2*a^3*b^3 + a*b^5 + a^5*c - 4*a^4*b*c + 4*a^3*b^2*c + 3*a^2*b^3*c - 5*a*b^4*c + b^5*c + 4*a^3*b*c^2 - 8*a^2*b^2*c^2 + 4*a*b^3*c^2 - 2*a^3*c^3 + 3*a^2*b*c^3 + 4*a*b^2*c^3 - 2*b^3*c^3 - 5*a*b*c^4 + a*c^5 + b*c^5) : :
X(56420) = 3 X[5587] - X[52005], 3 X[381] - X[14260]

X(56420) lies on the cubic K594 and these lines: {1, 5}, {4, 38954}, {381, 14260}, {513, 18480}, {517, 51975}, {1482, 51562}, {2222, 6924}, {3656, 36909}, {5903, 18302}, {6911, 40437}, {14923, 52409}, {17753, 35174}, {36944, 38617}

X(56421) = X(1)X(5)∩X(56)X(40577)

Barycentrics   (2*a - b - c)*(a + b - c)*(a - b + c)*(a^3*b + a^2*b^2 - a*b^3 - b^4 + a^3*c - 6*a^2*b*c + 2*a*b^2*c + a^2*c^2 + 2*a*b*c^2 + 2*b^2*c^2 - a*c^3 - c^4) : :

X(56421) lies on the cubic K666 and these lines: {1, 5}, {56, 40577}, {65, 13756}, {946, 38385}, {1319, 14028}, {1647, 40663}, {2099, 45247}, {3649, 4017}, {5298, 23703}, {10106, 39752}, {10222, 31841}, {11717, 18976}, {13751, 17705}, {15326, 41343}, {21630, 52537}, {23243, 24928}, {24871, 25028}, {28174, 46820}, {41801, 55082}

X(56421) = X(52537)-Dao conjugate of X(8)
X(56421) = barycentric product X(i)*X(j) for these {i,j}: {3911, 21630}, {14628, 52537}
X(56421) = barycentric quotient X(21630)/X(4997)
X(56421) = {X(1),X(14584)}-harmonic conjugate of X(1317)

X(56422) = X(1)X(5)∩X(74)X(484)

Barycentrics   a*(a^2 - a*b + b^2 - c^2)*(a^2 - b^2 - b*c - c^2)*(a^2 - b^2 - a*c + c^2) : :

X(56422) lies on the cubic K668 and these lines: {1, 5}, {35, 35194}, {59, 10091}, {74, 484}, {78, 52409}, {104, 46821}, {269, 52392}, {759, 5293}, {1250, 46077}, {2161, 3731}, {2166, 35320}, {2324, 36910}, {3065, 52377}, {3678, 35193}, {3811, 18359}, {3961, 40172}, {4354, 4420}, {5010, 10260}, {6740, 15065}, {7150, 10638}, {7161, 52380}, {7190, 18815}, {7280, 10623}, {7984, 14513}, {10090, 46820}, {13146, 35338}, {16110, 52242}, {17104, 47378}, {24433, 35204}, {41684, 45272}

X(56422) = X(i)-isoconjugate of X(j) for these (i,j): {36, 79}, {94, 52059}, {320, 6186}, {654, 38340}, {758, 52375}, {1443, 7073}, {1464, 3615}, {1789, 1835}, {1870, 7100}, {2160, 3218}, {2245, 52393}, {2323, 52374}, {3179, 41225}, {3738, 26700}, {4282, 43682}, {4511, 52372}, {6742, 53314}, {7113, 30690}, {13486, 53527}, {15455, 21758}, {17515, 52390}, {20565, 52434}, {39152, 39153}, {47317, 53046}, {52344, 52440}, {52381, 52413}
X(56422) = X(i)-Dao conjugate of X(j) for these (i,j): {8287, 4453}, {15898, 79}, {36909, 52344}, {55042, 3738}
X(56422) = barycentric product X(i)*X(j) for these {i,j}: {1, 41226}, {35, 18359}, {80, 3219}, {319, 2161}, {655, 35057}, {759, 3969}, {1411, 42033}, {1442, 36910}, {1807, 52412}, {2003, 52409}, {2006, 4420}, {2174, 20566}, {2341, 40999}, {2605, 36804}, {3678, 24624}, {6187, 33939}, {6198, 52351}, {6740, 16577}, {9404, 35174}, {14838, 51562}, {15065, 40214}, {17095, 52371}, {18815, 52405}, {34016, 34857}
X(56422) = barycentric quotient X(i)/X(j) for these {i,j}: {35, 3218}, {80, 30690}, {319, 20924}, {759, 52393}, {1411, 52374}, {1442, 17078}, {1807, 52381}, {2003, 1443}, {2161, 79}, {2174, 36}, {2222, 38340}, {2341, 3615}, {2594, 18593}, {2605, 3960}, {3219, 320}, {3678, 3936}, {3969, 35550}, {4420, 32851}, {6187, 2160}, {6198, 17923}, {7202, 4089}, {9404, 3738}, {14838, 4453}, {14975, 52413}, {16577, 41804}, {17454, 4973}, {18359, 20565}, {21741, 1464}, {32675, 26700}, {33939, 40075}, {34079, 52375}, {34857, 8818}, {35057, 3904}, {36910, 52344}, {41226, 75}, {41502, 17515}, {42624, 3179}, {47054, 26842}, {51562, 15455}, {52371, 7110}, {52383, 43682}, {52405, 4511}, {52408, 22128}, {52431, 7100}, {53542, 53546}, {55210, 53527}
X(56422) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5400, 38458}, {80, 1807, 1}, {1807, 52371, 80}, {6740, 51562, 15065}

X(56423) = X(1)X(5)∩X(100)X(24026)

Barycentrics   a^9 - 2*a^8*b + 3*a^6*b^3 - 3*a^5*b^4 + 2*a^3*b^6 - a^2*b^7 - 2*a^8*c + 6*a^7*b*c - 5*a^6*b^2*c - 4*a^5*b^3*c + 11*a^4*b^4*c - 6*a^3*b^5*c - 3*a^2*b^6*c + 4*a*b^7*c - b^8*c - 5*a^6*b*c^2 + 15*a^5*b^2*c^2 - 11*a^4*b^3*c^2 - 9*a^3*b^4*c^2 + 17*a^2*b^5*c^2 - 8*a*b^6*c^2 + b^7*c^2 + 3*a^6*c^3 - 4*a^5*b*c^3 - 11*a^4*b^2*c^3 + 26*a^3*b^3*c^3 - 13*a^2*b^4*c^3 - 4*a*b^5*c^3 + 3*b^6*c^3 - 3*a^5*c^4 + 11*a^4*b*c^4 - 9*a^3*b^2*c^4 - 13*a^2*b^3*c^4 + 16*a*b^4*c^4 - 3*b^5*c^4 - 6*a^3*b*c^5 + 17*a^2*b^2*c^5 - 4*a*b^3*c^5 - 3*b^4*c^5 + 2*a^3*c^6 - 3*a^2*b*c^6 - 8*a*b^2*c^6 + 3*b^3*c^6 - a^2*c^7 + 4*a*b*c^7 + b^2*c^7 - b*c^8 : :

X(56423) lies on the cubic K817 and these lines: {1, 5}, {100, 24026}, {104, 53610}, {108, 10090}, {153, 25436}, {523, 34464}, {900, 1768}, {2771, 18342}, {2801, 15343}, {3520, 18861}, {5494, 10265}, {5691, 38950}, {8674, 34462}, {10777, 35015}, {10778, 21635}, {14130, 35451}, {17100, 22467}, {24410, 53742}, {34460, 47227}, {43655, 47270}, {43728, 43940}

X(56423) = reflection of X(i) in X(j) for these {i,j}: {153, 25436}, {5691, 38950}, {18341, 10265}, {47270, 43655}
X(56423) = reflection of X(34464) in the Euler line

X(56424) = X(1)X(5)∩X(4)X(522)

Barycentrics   2*a^10 - 3*a^9*b - a^8*b^2 + 5*a^7*b^3 - 7*a^6*b^4 + 3*a^5*b^5 + 7*a^4*b^6 - 9*a^3*b^7 + a^2*b^8 + 4*a*b^9 - 2*b^10 - 3*a^9*c + 8*a^8*b*c - 6*a^7*b^2*c - 2*a^6*b^3*c + 12*a^5*b^4*c - 18*a^4*b^5*c + 6*a^3*b^6*c + 10*a^2*b^7*c - 9*a*b^8*c + 2*b^9*c - a^8*c^2 - 6*a^7*b*c^2 + 18*a^6*b^2*c^2 - 15*a^5*b^3*c^2 - 3*a^4*b^4*c^2 + 24*a^3*b^5*c^2 - 20*a^2*b^6*c^2 - 3*a*b^7*c^2 + 6*b^8*c^2 + 5*a^7*c^3 - 2*a^6*b*c^3 - 15*a^5*b^2*c^3 + 28*a^4*b^3*c^3 - 21*a^3*b^4*c^3 - 10*a^2*b^5*c^3 + 23*a*b^6*c^3 - 8*b^7*c^3 - 7*a^6*c^4 + 12*a^5*b*c^4 - 3*a^4*b^2*c^4 - 21*a^3*b^3*c^4 + 38*a^2*b^4*c^4 - 15*a*b^5*c^4 - 4*b^6*c^4 + 3*a^5*c^5 - 18*a^4*b*c^5 + 24*a^3*b^2*c^5 - 10*a^2*b^3*c^5 - 15*a*b^4*c^5 + 12*b^5*c^5 + 7*a^4*c^6 + 6*a^3*b*c^6 - 20*a^2*b^2*c^6 + 23*a*b^3*c^6 - 4*b^4*c^6 - 9*a^3*c^7 + 10*a^2*b*c^7 - 3*a*b^2*c^7 - 8*b^3*c^7 + a^2*c^8 - 9*a*b*c^8 + 6*b^2*c^8 + 4*a*c^9 + 2*b*c^9 - 2*c^10 : :

X(56424) lies on the cubic K858 and these lines: {1, 5}, {4, 522}, {34, 13999}, {515, 36944}, {5136, 54243}, {5691, 34464}, {5693, 31847}, {16554, 23058}

X(56424) = {X(14584),X(45950)}-harmonic conjugate of X(1)

X(56425) = X(1)X(5)∩X(89)X(8046)

Barycentrics   (a^2 - a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(3*a^3 - a^2*b - 3*a*b^2 + b^3 - a^2*c + 5*a*b*c - b^2*c - 3*a*c^2 - b*c^2 + c^3) : :

X(56425) lies on the cubic K915 and these lines: {1, 5}, {89, 8046}, {145, 51975}, {1168, 5425}, {2222, 5563}, {3241, 36909}, {3244, 51562}, {4977, 14812}, {5559, 52377}, {6126, 41558}, {6224, 52537}, {10222, 38954}, {11009, 51886}, {13606, 46821}, {36590, 51071}, {36975, 53525}, {40437, 52640}

X(56425) = X(36)-isoconjugate of X(13143)
X(56425) = X(15898)-Dao conjugate of X(13143)
X(56425) = barycentric quotient X(i)/X(j) for these {i,j}: {2161, 13143}, {33812, 51583}
X(56425) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 14584, 80}, {14584, 34232, 1}

X(56426) = X(1)X(5)∩X(44)X(517)

Barycentrics   a*(a^2 - a*b + b^2 - c^2)*(a^2 - b^2 + 4*b*c - c^2)*(a^2 - b^2 - a*c + c^2) : :

X(56426) lies on the cubic K1075 and these lines: {1, 5}, {3, 6187}, {13, 11072}, {14, 11073}, {30, 8481}, {44, 517}, {88, 104}, {109, 6797}, {244, 12773}, {265, 1245}, {381, 49487}, {515, 15898}, {678, 12331}, {759, 1293}, {899, 35459}, {1010, 6740}, {1054, 38602}, {1443, 17895}, {1480, 40587}, {1482, 34857}, {2153, 52202}, {2154, 52201}, {2166, 52372}, {2222, 5126}, {3120, 10742}, {3527, 52391}, {3576, 39963}, {3577, 16670}, {3656, 49494}, {3753, 35281}, {3924, 18525}, {3938, 50798}, {4285, 48848}, {4642, 13743}, {4674, 12515}, {4695, 35000}, {4696, 52409}, {5297, 24808}, {6914, 17601}, {7052, 19551}, {7126, 33655}, {7292, 39572}, {9324, 33814}, {9623, 36910}, {9955, 15955}, {10246, 40172}, {15934, 53531}, {16615, 52380}, {17595, 22758}, {18526, 28082}, {19860, 37150}, {24297, 52377}, {24443, 26321}, {24624, 54933}, {26727, 34311}, {28204, 30117}, {29820, 50824}, {30588, 54528}, {34242, 50193}, {36590, 38460}, {37611, 54390}, {44414, 52431}, {49682, 50796}

X(56426) = X(i)-isoconjugate of X(j) for these (i,j): {36, 1000}, {320, 34446}, {1443, 52429}, {1464, 56107}, {30680, 52413}, {51564, 53314}
X(56426) = X(i)-Dao conjugate of X(j) for these (i,j): {45, 27757}, {15898, 1000}, {52148, 4511}
X(56426) = crossdifference of every pair of points on line {654, 53535}
X(56426) = barycentric product X(i)*X(j) for these {i,j}: {80, 3306}, {759, 4054}, {999, 18359}, {1411, 28808}, {2006, 3872}, {2161, 42697}, {3753, 24624}, {6187, 20925}, {17079, 52371}, {18815, 55432}
X(56426) = barycentric quotient X(i)/X(j) for these {i,j}: {999, 3218}, {1807, 30680}, {2161, 1000}, {2341, 56107}, {3306, 320}, {3753, 3936}, {3872, 32851}, {4054, 35550}, {20925, 40075}, {35281, 4585}, {40587, 27757}, {42697, 20924}, {52371, 36916}, {52428, 2323}, {55432, 4511}
X(56426) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 80, 52371}, {1, 52371, 1807}, {80, 1411, 1807}, {1411, 52371, 1}, {39150, 39151, 2161}

X(56427) = X(1)X(2)∩X(37)X(588)

Barycentrics   1 - 2*Sin[A] : :
Barycentrics   a*(b*c - 2*S) : :

X(56427) lies on these lines: {1, 2}, {11, 15233}, {12, 15234}, {33, 55481}, {34, 55482}, {37, 588}, {40, 21566}, {55, 1599}, {56, 1600}, {81, 7969}, {175, 5905}, {326, 32794}, {329, 17802}, {394, 3298}, {481, 17483}, {482, 26842}, {495, 1591}, {496, 1592}, {517, 16441}, {940, 44635}, {999, 1584}, {1038, 55893}, {1040, 55897}, {1056, 6805}, {1058, 6806}, {1060, 1589}, {1062, 1590}, {1124, 5422}, {1270, 55392}, {1271, 55391}, {1335, 1993}, {1385, 16440}, {1398, 15201}, {1482, 16433}, {1500, 8962}, {1583, 3295}, {1585, 6198}, {1586, 1870}, {1659, 31019}, {1994, 3301}, {2067, 55566}, {3100, 55888}, {3218, 13388}, {3219, 30557}, {3297, 10601}, {3299, 34545}, {3553, 7585}, {3554, 7586}, {3576, 21567}, {3593, 55427}, {3595, 55426}, {3640, 4661}, {3641, 4430}, {3681, 45713}, {3873, 45714}, {4296, 55883}, {4383, 44636}, {5391, 44179}, {5408, 35809}, {5409, 35768}, {5414, 55567}, {5483, 31582}, {6767, 55579}, {7071, 15198}, {7373, 55577}, {7968, 32911}, {7982, 21565}, {8148, 21558}, {8968, 9632}, {9538, 55898}, {9776, 17805}, {10222, 21553}, {10246, 16432}, {10247, 21547}, {11398, 15187}, {11399, 15188}, {12702, 21559}, {13389, 27003}, {13390, 31053}, {15066, 55410}, {15178, 21492}, {15191, 52427}, {15325, 55878}, {16200, 21564}, {16884, 31473}, {17484, 31539}, {17597, 45477}, {18447, 55885}, {18455, 55890}, {18991, 37685}, {20060, 31532}, {20075, 30334}, {21548, 37624}, {21552, 33179}, {27065, 30556}, {32582, 45716}, {37696, 55881}, {37697, 55882}, {37729, 55887}, {55389, 55455}, {55390, 55454}, {55403, 55465}, {55404, 55435}

X(56427) = anticomplement of X(6348)
X(56427) = X(i)-isoconjugate of X(j) for these (i,j): {6, 3302}, {2963, 3299}
X(56427) = X(i)-Dao conjugate of X(j) for these (i,j): {9, 3302}, {5507, 1}, {10639, 42676}, {10640, 42678}
X(56427) = barycentric product X(i)*X(j) for these {i,j}: {1, 32792}, {75, 3301}, {302, 42679}, {303, 42681}
X(56427) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 3302}, {61, 42678}, {62, 42676}, {2964, 3299}, {3300, 2962}, {3301, 1}, {32792, 75}, {42679, 17}, {42681, 18}
X(56427) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3084, 2}, {33, 55481, 55573}, {34, 55482, 55569}, {1125, 6347, 2}, {1335, 55409, 1993}, {5393, 55877, 2}, {13388, 55397, 3218}, {30557, 55398, 3219}, {55391, 55457, 1271}, {55392, 55456, 1270}, {55410, 55441, 15066}

X(56428) = X(2)X(6)∩X(159)X(20998)

Barycentrics   a^2*(a^4*b^2 + a^2*b^4 + a^4*c^2 - 3*a^2*b^2*c^2 - b^4*c^2 + a^2*c^4 - b^2*c^4) : :

X(56428) lies on the cubic K076 and these lines: {2, 6}, {159, 20998}, {182, 6310}, {1176, 30496}, {1691, 1968}, {1915, 19137}, {3053, 11326}, {3124, 12220}, {3229, 20794}, {3291, 6467}, {3981, 11574}, {5085, 35687}, {5640, 31390}, {6375, 11328}, {8770, 9924}, {9225, 52016}, {9230, 11333}, {18278, 21778}, {19132, 32445}, {19133, 34251}, {22138, 43183}, {34249, 41396}, {34811, 41328}, {48262, 55697}

X(56428) = X(53059)-Ceva conjugate of X(6)
X(56428) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 21001, 69}, {6, 38303, 6144}, {597, 16285, 6}, {3051, 51171, 6}, {26206, 42295, 6}

X(56429) = X(2)X(6)∩X(99)X(1499)

Barycentrics   (a^2 - b^2)*(a^2 - c^2)*(2*a^6 - 6*a^4*b^2 + 9*a^2*b^4 - b^6 - 6*a^4*c^2 - 3*b^4*c^2 + 9*a^2*c^4 - 3*b^2*c^4 - c^6) : :
X(56429) = 2 X[37746] - 3 X[41133]

X(56428) lies on the cubic K088 and these lines: {2, 6}, {99, 1499}, {110, 6082}, {523, 9124}, {843, 47077}, {892, 4563}, {1975, 15098}, {2696, 35575}, {6077, 16092}, {6390, 11006}, {14588, 35356}, {34169, 44956}, {50567, 53136}

X(56429) = reflection of X(i) in X(j) for these {i,j}: {843, 47077}, {5912, 5108}, {22329, 37745}, {34169, 44956}
X(56429) = isotomic conjugate of X(43667)
X(56429) = antitomic image of X(52235)
X(56429) = psi-transform of X(47047)
X(56429) = X(i)-isoconjugate of X(j) for these (i,j): {31, 43667}, {661, 9136}, {798, 9487}
X(56429) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 43667}, {31998, 9487}, {36830, 9136}, {39075, 512}
X(56429) = barycentric product X(670)*X(9486)
X(56429) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 43667}, {99, 9487}, {110, 9136}, {5468, 37860}, {9486, 512}, {52233, 9178}, {52235, 43674}
X(56429) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5468, 9182, 14999}, {5468, 14607, 9182}

X(56430) = X(2)X(6)∩X(23)X(4576)

Barycentrics   a^6 - a^4*b^2 - a^4*c^2 + 3*a^2*b^2*c^2 - b^4*c^2 - b^2*c^4 : :

X(56430) lies on the cubic K223 and these lines: {2, 6}, {23, 4576}, {32, 35275}, {74, 9150}, {76, 5651}, {99, 1495}, {110, 2868}, {125, 37803}, {182, 11059}, {305, 9306}, {316, 51360}, {419, 18020}, {450, 44132}, {468, 6393}, {511, 4563}, {538, 35279}, {669, 3265}, {698, 20998}, {732, 9225}, {805, 2373}, {858, 5207}, {1078, 5650}, {1799, 3819}, {1915, 16951}, {1975, 35259}, {1976, 17932}, {1995, 18906}, {2366, 9091}, {2482, 35295}, {3094, 26257}, {3917, 33651}, {4074, 16950}, {4176, 6353}, {5642, 7799}, {5972, 37804}, {6331, 41204}, {6337, 35260}, {6340, 32064}, {6394, 44436}, {7760, 40130}, {7782, 35268}, {7783, 35301}, {7793, 35288}, {7809, 13857}, {7998, 26233}, {8627, 13586}, {9146, 15107}, {9888, 48991}, {10330, 35265}, {11056, 24206}, {11206, 19583}, {11326, 37889}, {11459, 37334}, {12036, 51224}, {13414, 46810}, {13415, 46813}, {19577, 53475}, {30793, 39141}, {31101, 33796}, {32223, 50567}, {32269, 51374}, {32741, 52501}, {34336, 34397}, {34405, 52249}, {35277, 37512}, {35575, 53704}, {43363, 53624}, {47582, 51438}

X(56430) = isogonal conjugate of X(16098)
X(56430) = isogonal conjugate of the isotomic conjugate of X(16084)
X(56430) = isotomic conjugate of the polar conjugate of X(15014)
X(56430) = X(2366)-Ceva conjugate of X(69)
X(56430) = X(i)-isoconjugate of X(j) for these (i,j): {1, 16098}, {661, 9091}, {798, 53202}
X(56430) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 16098}, {31998, 53202}, {36830, 9091}
X(56430) = crossdifference of every pair of points on line {512, 1196}
X(56430) = barycentric product X(i)*X(j) for these {i,j}: {6, 16084}, {69, 15014}, {99, 9035}, {865, 34537}, {4563, 47206}
X(56430) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 16098}, {99, 53202}, {110, 9091}, {865, 3124}, {9035, 523}, {15014, 4}, {16084, 76}, {47206, 2501}
X(56430) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {110, 3266, 12215}, {5468, 5971, 39099}, {5972, 51371, 37804}

X(56431) = X(2)X(6)∩X(31)X(8033)

Barycentrics   (a + b)*(a + c)*(a^3*b + a^3*c - a^2*b*c - b^2*c^2) : :

X(56431) lies on the cubic K224 and these lines: {2, 6}, {31, 8033}, {42, 7304}, {99, 902}, {100, 2669}, {106, 4615}, {171, 873}, {238, 799}, {310, 24259}, {669, 4367}, {675, 805}, {750, 51314}, {1326, 4610}, {1458, 4573}, {1621, 39915}, {1911, 4589}, {2054, 17930}, {2239, 40017}, {3011, 51370}, {3218, 18827}, {3747, 40874}, {4038, 40439}, {4039, 4600}, {4576, 20045}, {6384, 27631}, {7191, 32010}, {16690, 34022}, {17103, 17126}, {17122, 33779}, {17763, 52137}, {26247, 36800}, {52899, 56053}

X(56431) = isotomic conjugate of the polar conjugate of X(15147)
X(56431) = X(2368)-Ceva conjugate of X(86)
X(56431) = X(798)-isoconjugate of X(53195)
X(56431) = X(31998)-Dao conjugate of X(53195)
X(56431) = crossdifference of every pair of points on line {512, 21838}
X(56431) = barycentric product X(i)*X(j) for these {i,j}: {69, 15147}, {86, 40859}
X(56431) = barycentric quotient X(i)/X(j) for these {i,j}: {99, 53195}, {15147, 4}, {40859, 10}

X(56432) = X(2)X(6)∩X(99)X(1055)

Barycentrics   (a + b)*(a + c)*(a^4*b - a^3*b^2 + a^4*c - a^3*b*c + a^2*b^2*c - a^3*c^2 + a^2*b*c^2 + a*b^2*c^2 - b^3*c^2 - b^2*c^3) : :

X(56432) lies on the cubic K225 and these lines: {2, 6}, {99, 1055}, {101, 5209}, {350, 662}, {645, 672}, {669, 7253}, {805, 1311}, {811, 2202}, {1326, 4368}, {2291, 9150}, {4594, 41882}, {4620, 34537}, {5011, 38477}, {17499, 27698}, {20863, 56154}, {26279, 32010}, {53624, 53707}

X(56432) = barycentric product X(1)*X(14195)
X(56432) = barycentric quotient X(14195)/X(75)
X(56432) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {}

X(56433) = X(2)X(6)∩X(75)X(517)

Barycentrics   a^4*b + a^3*b^2 - a^2*b^3 - a*b^4 + a^4*c - a^3*b*c - 2*a^2*b^2*c - a*b^3*c - b^4*c + a^3*c^2 - 2*a^2*b*c^2 - 4*a*b^2*c^2 - b^3*c^2 - a^2*c^3 - a*b*c^3 - b^2*c^3 - a*c^4 - b*c^4 : :

X(56433) lies on the cubic K386 and these lines: {2, 6}, {8, 3264}, {56, 54429}, {75, 517}, {104, 1310}, {320, 31997}, {991, 3883}, {995, 4357}, {1444, 4216}, {2274, 50295}, {3879, 30116}, {3966, 9025}, {4352, 4389}, {4360, 20037}, {4643, 37596}, {4690, 25125}, {10449, 30939}, {17139, 34284}, {17152, 42697}, {17183, 44140}, {17196, 48838}, {17272, 49997}, {19257, 49716}, {37617, 50296}

X(56434) = X(2)X(6)∩X(187)X(48657)

Barycentrics   a^6 - 7*a^4*b^2 + 5*a^2*b^4 - 2*b^6 - 7*a^4*c^2 + 3*a^2*b^2*c^2 + 2*b^4*c^2 + 5*a^2*c^4 + 2*b^2*c^4 - 2*c^6 : : X(56434) = 5 X[6] - 8 X[230], X[6] - 4 X[15993], 5 X[69] + X[50248], 2 X[230] - 5 X[15993], 2 X[385] + X[40341], 5 X[599] - 2 X[7840], 2 X[3630] + X[50249], 4 X[3631] - X[7779], 5 X[3763] - 2 X[39099], 5 X[21358] - 4 X[41133], 5 X[32113] - 2 X[47154], 5 X[47448] - 8 X[47559]

X(564) lies on the cubic K487 and these lines: {2, 6}, {187, 48657}, {511, 38732}, {523, 47445}, {542, 2076}, {1634, 11063}, {5017, 50955}, {5104, 11645}, {5116, 50977}, {5965, 15561}, {6034, 15514}, {7812, 44530}, {9225, 32225}, {11082, 22826}, {11087, 22827}, {11178, 13330}, {11646, 19924}, {14537, 43150}, {15360, 20998}, {18362, 37517}, {18365, 23967}, {19780, 22998}, {19781, 22997}, {25214, 25217}, {32113, 47154}, {44532, 51224}, {47237, 47465}, {47448, 47559}

X(56434) = crossdifference of every pair of points on line {512, 50664}
X(56434) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {599, 40341, 7788}

X(56435) = X(2)X(6)∩X(4)X(10748)

Barycentrics   a^6 + a^4*b^2 - a^2*b^4 - b^6 + a^4*c^2 + 16*a^2*b^2*c^2 - 3*b^4*c^2 - a^2*c^4 - 3*b^2*c^4 - c^6 : :
X(56435) = X[14360] + 2 X[34166], 5 X[3091] - 2 X[14262]

X(56435) lies on the cubic K582 and these lines: {2, 6}, {4, 10748}, {111, 34511}, {126, 7775}, {316, 11059}, {1383, 32985}, {1995, 6390}, {3091, 14262}, {3266, 11185}, {3524, 6031}, {3926, 16042}, {6337, 14002}, {6719, 7764}, {7664, 7763}, {7752, 14246}, {7758, 39576}, {7813, 8585}, {9146, 20423}, {9464, 52713}, {10989, 32827}, {13608, 38698}, {19583, 37349}, {31125, 33006}, {31128, 33007}, {32829, 52300}

X(56435) = anticomplement of X(20481)
X(56435) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 193, 11580}

X(56436) = X(2)X(6)∩X(3)X(33979)

Barycentrics   a^2*(a^4 + 14*a^2*b^2 + b^4 + 14*a^2*c^2 - 58*b^2*c^2 + c^4) : :

X(56436) lies on the cubic K765 and these lines: {2, 6}, {3, 33979}, {111, 31884}, {353, 55684}, {1350, 21448}, {5024, 5646}, {5585, 20998}, {11477, 22111}, {13192, 55591}, {14924, 44500}, {15603, 32237}, {15655, 41424}, {16187, 21309}, {39576, 53097}

X(56436) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8617, 20481, 46949}, {20481, 46949, 6}

X(56437) = X(2)X(6)∩X(3)X(9292)

Barycentrics   a^2*(a^4 - a^2*b^2 - a^2*c^2 + 2*b^2*c^2)*(a^2*b^2 - b^4 + a^2*c^2 - c^4) : :

X(56437) lies on the cubic K783 and these lines: {2, 6}, {3, 9292}, {99, 3331}, {154, 10607}, {217, 7763}, {232, 36790}, {237, 51337}, {538, 45938}, {669, 684}, {805, 1297}, {1498, 6461}, {1625, 6390}, {1971, 4558}, {1987, 43705}, {2211, 6393}, {2451, 17215}, {3491, 11326}, {6337, 32445}, {6786, 9418}, {9150, 26717}, {9419, 51373}, {9475, 36212}, {9737, 23098}, {12215, 46272}, {13335, 32518}

X(56437) = isotomic conjugate of the polar conjugate of X(15143)
X(56437) = X(3)-Ceva conjugate of X(36790)
X(56437) = X(i)-isoconjugate of X(j) for these (i,j): {98, 9258}, {1821, 9292}, {1910, 9307}, {6531, 9255}, {36120, 51336}
X(56437) = X(i)-Dao conjugate of X(j) for these (i,j): {11672, 9307}, {30476, 51404}, {40601, 9292}, {46094, 51336}, {48316, 523}
X(56437) = crossdifference of every pair of points on line {512, 3767}
X(56437) = X(3)-line conjugate of X(9292)
X(56437) = barycentric product X(i)*X(j) for these {i,j}: {69, 15143}, {325, 9306}, {394, 40887}, {511, 1975}, {877, 22089}, {1958, 1959}, {1968, 6393}, {2396, 2451}, {2421, 30476}, {9308, 36212}, {17893, 23997}
X(56437) = barycentric quotient X(i)/X(j) for these {i,j}: {237, 9292}, {511, 9307}, {1755, 9258}, {1957, 36120}, {1958, 1821}, {1968, 6531}, {1975, 290}, {2421, 43188}, {2451, 2395}, {3289, 51336}, {9306, 98}, {9308, 16081}, {15143, 4}, {22089, 879}, {30476, 43665}, {36212, 9289}, {40887, 2052}
X(56437) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {232, 51386, 36790}, {325, 2421, 3289}

X(56438) = X(2)X(6)∩X(110)X(41359)

Barycentrics   3*a^10 - 7*a^8*b^2 + 6*a^6*b^4 - 4*a^4*b^6 + 3*a^2*b^8 - b^10 - 7*a^8*c^2 + 15*a^6*b^2*c^2 - 8*a^4*b^4*c^2 + 5*a^2*b^6*c^2 - b^8*c^2 + 6*a^6*c^4 - 8*a^4*b^2*c^4 - 8*a^2*b^4*c^4 + 2*b^6*c^4 - 4*a^4*c^6 + 5*a^2*b^2*c^6 + 2*b^4*c^6 + 3*a^2*c^8 - b^2*c^8 - c^10 : :

X(56438) lies on the cubic K818 and these lines: {2, 6}, {110, 41359}, {1352, 16188}, {1499, 18556}, {1550, 11180}, {2709, 40118}, {2715, 53186}, {7471, 16334}, {38970, 44956}, {40915, 48540}

X(56439) = X(1)X(1098)∩X(2)X(6)

Barycentrics   a*(a + b)*(a + c)*(a^3 - a^2*b - a*b^2 + b^3 - a^2*c - a*b*c - a*c^2 + c^3) : :

X(56439) lies on the cubic K972 and these lines: {1, 1098}, {2, 6}, {7, 52361}, {8, 46441}, {21, 12635}, {55, 2651}, {57, 662}, {58, 22836}, {60, 3868}, {63, 2185}, {75, 7058}, {92, 648}, {110, 3873}, {191, 37029}, {326, 757}, {448, 33296}, {593, 4558}, {643, 3870}, {645, 18743}, {758, 9275}, {894, 42708}, {1088, 4573}, {1326, 4650}, {1762, 18714}, {1836, 19642}, {2194, 5208}, {2363, 54421}, {3218, 40214}, {3219, 4053}, {3751, 6043}, {3758, 14534}, {3874, 17104}, {4273, 25059}, {4360, 18662}, {4658, 30143}, {5221, 35991}, {5228, 24378}, {5902, 11116}, {6061, 11020}, {6626, 23151}, {11101, 34195}, {11102, 35637}, {11684, 37032}, {12649, 52360}, {13739, 39772}, {14570, 17147}, {14628, 47318}, {17728, 25533}, {24473, 51420}, {24624, 31053}, {24929, 51290}, {30606, 32939}, {35145, 54951}, {49168, 56018}

X(56439) = reflection of X(17512) in X(9275)
X(56439) = isotomic conjugate of X(43683)
X(56439) = isotomic conjugate of the polar conjugate of X(13739)
X(56439) = X(4573)-Ceva conjugate of X(31603)
X(56439) = X(i)-isoconjugate of X(j) for these (i,j): {6, 41501}, {19, 43708}, {31, 43683}, {42, 37887}, {661, 6011}, {1400, 6598}
X(56439) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 43683}, {6, 43708}, {9, 41501}, {8286, 3700}, {35193, 9}, {35583, 2610}, {36830, 6011}, {40582, 6598}, {40592, 37887}
X(56439) = trilinear pole of line {6003, 27086}
X(56439) = barycentric product X(i)*X(j) for these {i,j}: {69, 13739}, {81, 33116}, {86, 34772}, {99, 6003}, {261, 15556}, {314, 37583}, {643, 31603}, {1444, 5174}, {7182, 41503}, {8286, 24041}, {14616, 27086}, {39772, 40412}
X(56439) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 41501}, {2, 43683}, {3, 43708}, {21, 6598}, {81, 37887}, {110, 6011}, {229, 41495}, {5174, 41013}, {6003, 523}, {8286, 1109}, {11101, 34243}, {13739, 4}, {15556, 12}, {27086, 758}, {31603, 4077}, {33116, 321}, {34772, 10}, {37583, 65}, {39772, 442}, {41503, 33}, {41547, 3649}, {56316, 53008}
X(56439) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {81, 1812, 86}, {81, 26637, 42028}, {81, 37783, 2}, {81, 40571, 333}, {81, 41610, 41629}, {333, 40882, 4417}

X(56440) = X(2)X(6)∩X(8)X(13746)

Barycentrics   a*(a + b)*(a - b - c)*(a + c)*(a^2 - b^2 - b*c - c^2) : :

X(56440) lies on the cubic K973 and these lines: {2, 6}, {8, 13746}, {9, 2185}, {21, 56177}, {60, 3876}, {63, 662}, {72, 51420}, {78, 1098}, {110, 3681}, {200, 643}, {312, 645}, {319, 52412}, {409, 12635}, {758, 11116}, {1043, 7072}, {1326, 7262}, {1376, 2651}, {2003, 17095}, {2174, 3219}, {2194, 3786}, {2323, 4886}, {2363, 54386}, {2982, 55096}, {3173, 33298}, {3678, 17104}, {3969, 41226}, {4273, 25058}, {4420, 35193}, {4573, 31627}, {4653, 22836}, {5440, 51290}, {5692, 17512}, {5905, 52361}, {6061, 41228}, {6514, 55965}, {9275, 10176}, {9780, 46441}, {11107, 31938}, {11684, 37405}, {15792, 37029}, {17781, 18653}, {19642, 24703}, {24624, 27131}, {32939, 39767}, {35195, 52126}, {42033, 52405}, {46877, 52680}

X(56440) = isotomic conjugate of X(43682)
X(56440) = isotomic conjugate of the isogonal conjugate of X(35192)
X(56440) = isotomic conjugate of the polar conjugate of X(11107)
X(56440) = X(24041)-Ceva conjugate of X(643)
X(56440) = X(i)-isoconjugate of X(j) for these (i,j): {6, 52382}, {19, 52390}, {31, 43682}, {37, 52372}, {42, 52374}, {56, 8818}, {65, 2160}, {79, 1400}, {109, 55236}, {181, 52393}, {226, 6186}, {512, 38340}, {604, 6757}, {608, 52388}, {661, 26700}, {1042, 7110}, {1402, 30690}, {1427, 7073}, {1464, 1989}, {1637, 36064}, {1880, 7100}, {2171, 52375}, {2643, 35049}, {3669, 56193}, {6742, 7180}, {11060, 41804}, {15455, 51641}, {20982, 55017}, {32678, 51663}
X(56440) = X(i)-Dao conjugate of X(j) for these (i,j): {1, 8818}, {2, 43682}, {6, 52390}, {9, 52382}, {11, 55236}, {1100, 3649}, {3161, 6757}, {3700, 1109}, {5249, 55010}, {8287, 7178}, {18334, 51663}, {34544, 1464}, {36830, 26700}, {39054, 38340}, {40582, 79}, {40589, 52372}, {40592, 52374}, {40602, 2160}, {40604, 18593}, {40605, 30690}, {55042, 661}
X(56440) = cevapoint of X(4420) and X(52405)
X(56440) = barycentric product X(i)*X(j) for these {i,j}: {9, 34016}, {21, 319}, {35, 314}, {69, 11107}, {75, 35193}, {76, 35192}, {81, 42033}, {86, 4420}, {99, 35057}, {261, 3678}, {274, 52405}, {284, 33939}, {304, 41502}, {312, 40214}, {332, 6198}, {333, 3219}, {340, 1793}, {643, 4467}, {644, 16755}, {645, 14838}, {650, 55235}, {799, 9404}, {1043, 1442}, {1098, 40999}, {1792, 7282}, {1812, 52412}, {2174, 28660}, {2185, 3969}, {2287, 17095}, {2328, 52421}, {2341, 7799}, {2605, 7257}, {2611, 6064}, {3596, 17104}, {4102, 17190}, {4600, 53524}, {4612, 7265}, {4631, 55210}, {5546, 18160}, {6741, 24041}, {7058, 16577}, {10411, 52356}, {31938, 40412}, {35195, 46750}, {44130, 52408}
X(56440) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 52382}, {2, 43682}, {3, 52390}, {8, 6757}, {9, 8818}, {21, 79}, {35, 65}, {58, 52372}, {60, 52375}, {78, 52388}, {81, 52374}, {110, 26700}, {186, 1835}, {249, 35049}, {283, 7100}, {284, 2160}, {314, 20565}, {319, 1441}, {323, 18593}, {333, 30690}, {526, 51663}, {643, 6742}, {645, 15455}, {650, 55236}, {662, 38340}, {1043, 52344}, {1098, 3615}, {1399, 1042}, {1442, 3668}, {1793, 265}, {1812, 52381}, {2003, 1427}, {2174, 1400}, {2185, 52393}, {2194, 6186}, {2287, 7110}, {2328, 7073}, {2341, 1989}, {2594, 1254}, {2605, 4017}, {2611, 1365}, {3024, 2611}, {3219, 226}, {3647, 3649}, {3678, 12}, {3939, 56193}, {3969, 6358}, {4420, 10}, {4467, 4077}, {4631, 55209}, {4636, 13486}, {5379, 34922}, {6149, 1464}, {6198, 225}, {6740, 2166}, {6741, 1109}, {7202, 53545}, {9404, 661}, {11107, 4}, {14838, 7178}, {15776, 34301}, {16577, 6354}, {16585, 55010}, {16755, 24002}, {17095, 1446}, {17104, 56}, {17190, 553}, {22342, 1425}, {31938, 442}, {33939, 349}, {34016, 85}, {35057, 523}, {35192, 6}, {35193, 1}, {35195, 3336}, {36034, 36064}, {40214, 57}, {41502, 19}, {42033, 321}, {52126, 11263}, {52356, 10412}, {52405, 37}, {52408, 73}, {52412, 40149}, {53524, 3120}, {53542, 53540}, {53554, 53551}, {55235, 4554}
X(56440) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {645, 7058, 312}, {1812, 2287, 333}