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This is PART 36: Centers X(70001) - X(72000)

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(70001) = X(2)X(59429)∩X(3)X(1495)

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

X(70001) lies on the cubics K009 and K488 and these lines: {2, 59429}, {3, 1495}, {4, 9064}, {32, 18877}, {378, 69877}, {541, 51471}, {1272, 6337}, {1593, 58082}, {3088, 52452}, {5063, 47649}, {7527, 52497}, {10564, 68660}, {13352, 65322}, {13608, 34156}, {14357, 51475}, {39175, 54236}, {44274, 64615}, {69942, 69985}

X(70001) = midpoint of X(69942) and X(69985)
X(70001) = isogonal conjugate of X(39263)
X(70001) = complement of X(59429)
X(70001) = isotomic conjugate of the polar conjugate of X(47649)
X(70001) = isogonal conjugate of the polar conjugate of X(69877)
X(70001) = X(i)-Ceva conjugate of X(j) for these (i,j): {9064, 8675}, {69877, 47649}
X(70001) = X(i)-isoconjugate of X(j) for these (i,j): {1, 39263}, {75, 69942}, {14206, 40385}
X(70001) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 39263}, {206, 69942}, {8675, 53832}
X(70001) = barycentric product X(i)*X(j) for these {i,j}: {3, 69877}, {69, 47649}, {3426, 15066}, {5063, 36889}, {8675, 65322}, {44134, 51990}, {52497, 61459}, {56270, 68659}
X(70001) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 39263}, {32, 69942}, {378, 52147}, {3426, 34289}, {5063, 376}, {15066, 44133}, {40352, 40385}, {42660, 9209}, {44080, 40138}, {47649, 4}, {51990, 4846}, {52438, 26864}, {65322, 65284}, {69877, 264}
X(70001) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 3426, 52168}, {3, 52168, 61448}

X(70002) = X(4)X(2854)∩X(30)X(111)

Barycentrics   (a^4 - b^4 + 4*b^2*c^2 - c^4)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - 4*a^4*c^2 + 9*a^2*b^2*c^2 - b^4*c^2 - 4*a^2*c^4 - b^2*c^4 + c^6)*(a^6 - 4*a^4*b^2 - 4*a^2*b^4 + b^6 - a^4*c^2 + 9*a^2*b^2*c^2 - b^4*c^2 - a^2*c^4 - b^2*c^4 + c^6) : :

X(70002) lies on the cubics K025 and K479 and these lines: {4, 2854}, {30, 111}, {265, 34171}, {1296, 30739}, {1995, 5512}, {7426, 61452}, {16063, 55029}, {34174, 52447}, {34175, 47103}, {43448, 52484}

X(70002) = midpoint of X(16063) and X(66869)
X(70002) = reflection of X(i) in X(j) for these {i,j}: {1296, 30739}, {1995, 5512}
X(70002) = isogonal conjugate of X(61443)
X(70002) = antigonal image of X(1995)
X(70002) = symgonal image of X(30739)
X(70002) = X(1)-isoconjugate of X(61443)
X(70002) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 61443}, {5512, 2780}
X(70002) = barycentric product X(1995)*X(55973)
X(70002) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 61443}, {1995, 41617}, {2696, 65324}, {14262, 52496}, {68778, 2780}

X(70003) = X(3)X(11636)∩X(4)X(575)

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

X(70003) lies on the cubics K028 and K914 and these lines: {3, 11636}, {4, 575}, {76, 35138}, {1383, 5007}, {6179, 51541}, {12105, 52692}, {37909, 61345}, {54459, 64982}

X(70003) = X(i)-Dao conjugate of X(j) for these (i,j): {5008, 15810}, {46657, 3906}
X(70003) = crosssum of X(17414) and X(17416)
X(70003) = barycentric product X(i)*X(j) for these {i,j}: {598, 7492}, {1383, 7850}
X(70003) = barycentric quotient X(i)/X(j) for these {i,j}: {7492, 599}, {7850, 9464}

X(70004) = X(3)X(13868)∩X(36)X(1459)

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

X(70004) lies on the cubics K039 and K274 and these lines: {3, 13868}, {36, 1459}, {186, 953}, {901, 37311}, {2245, 32641}, {3259, 37168}, {3285, 47420}, {5440, 67518}

X(70004) = isogonal conjugate of X(38950)
X(70004) = circumcircle-inverse of X(43692)
X(70004) = isogonal conjugate of the anticomplement of X(56749)
X(70004) = X(i)-isoconjugate of X(j) for these (i,j): {1, 38950}, {3109, 4674}
X(70004) = X(3)-Dao conjugate of X(38950)
X(70004) = trilinear pole of line {17455, 22086}
X(70004) = barycentric product X(16704)*X(43692)
X(70004) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 38950}, {3285, 3109}, {43692, 4080}, {47420, 45922}, {53612, 65336}

X(70005) = X(3)X(32618)∩X(98)X(5003)

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

X(70005) lies on the cubics K039 and K336, the curve Q049, and these lines: {3, 32618}, {98, 5003}, {186, 57027}, {230, 5000}, {248, 32619}, {511, 1976}, {5001, 19165}, {31635, 44781}, {34239, 40895}

X(70005) = isogonal conjugate of X(42809)
X(70005) = circumcircle-inverse of X(32618)
X(70005) = X(98)-Ceva conjugate of X(32618)
X(70005) = X(1)-isoconjugate of X(42809)
X(70005) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 42809}, {41199, 325}
X(70005) = cevapoint of X(41197) and X(52144)
X(70005) = crosspoint of X(57027) and X(57742)
X(70005) = crosssum of X(3564) and X(47612)
X(70005) = barycentric quotient X(6)/X(42809)

X(70006) = X(3)X(32619)∩X(98)X(5002)

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

X(70006) lies on the cubics K039 and K336, the curve Q049, and these lines: {3, 32619}, {98, 5002}, {186, 57028}, {230, 5001}, {248, 32618}, {511, 1976}, {5000, 19165}, {31635, 44780}, {34240, 40894}

X(70006) = isogonal conjugate of X(42810)
X(70006) = circumcircle-inverse of X(32619)
X(70006) = X(98)-Ceva conjugate of X(32619)
X(70006) = X(1)-isoconjugate of X(42810)
X(70006) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 42810}, {41198, 325}
X(70006) = cevapoint of X(41196) and X(52144)
X(70006) = crosspoint of X(57028) and X(57742)
X(70006) = crosssum of X(3564) and X(47613)
X(70006) = barycentric quotient X(6)/X(42810)

X(70007) = X(1)X(971)∩X(55)X(19605)

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

X(70007) lies on the cubics K040 and K980 and these lines: {1, 971}, {55, 19605}, {105, 56718}, {390, 10405}, {497, 3599}, {516, 1360}, {1155, 61240}, {3900, 54255}, {7079, 15837}, {41339, 42077}, {52653, 63165}

X(70007) = incircle-inverse of X(10939)
X(70007) = X(910)-cross conjugate of X(41339)
X(70007) = X(i)-isoconjugate of X(j) for these (i,j): {103, 3160}, {165, 43736}, {651, 68267}, {911, 31627}, {1419, 36101}, {1815, 67169}, {2338, 9533}, {2424, 65165}, {3207, 52156}, {58877, 65538}
X(70007) = X(i)-Dao conjugate of X(j) for these (i,j): {23972, 31627}, {38991, 68267}, {50441, 16284}
X(70007) = crossdifference of every pair of points on line {1419, 68267}
X(70007) = X(1)-line conjugate of X(1419)
X(70007) = barycentric product X(i)*X(j) for these {i,j}: {516, 19605}, {910, 63165}, {3062, 40869}, {10405, 41339}, {36620, 51418}, {46392, 53640}, {56718, 56900}
X(70007) = barycentric quotient X(i)/X(j) for these {i,j}: {516, 31627}, {663, 68267}, {910, 3160}, {1456, 9533}, {3062, 52156}, {11051, 43736}, {19605, 18025}, {30807, 50560}, {40869, 16284}, {41339, 144}, {43035, 50561}, {51418, 64083}, {53622, 65245}, {56718, 56668}, {61240, 65294}, {63165, 57996}, {64980, 67128}, {65664, 7658}

X(70008) = X(2)X(55847)∩X(6)X(468)

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

X(70008) lies on the cubics K043 and K260 and these lines: {2, 55847}, {6, 468}, {67, 10354}, {69, 65324}, {111, 55029}, {187, 13608}, {577, 2482}, {1249, 51831}, {3087, 60266}, {30247, 41719}, {51239, 62373}, {60317, 62992}

X(70008) = complement of X(55848)
X(70008) = complement of the isogonal conjugate of X(38532)
X(70008) = complement of the isotomic conjugate of X(34165)
X(70008) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 13608}, {34165, 2887}, {38532, 10}
X(70008) = X(2)-Ceva conjugate of X(13608)
X(70008) = X(14209)-isoconjugate of X(39382)
X(70008) = X(13608)-Dao conjugate of X(2)
X(70008) = crosspoint of X(2) and X(34165)
X(70008) = barycentric product X(i)*X(j) for these {i,j}: {5486, 7493}, {13608, 34165}
X(70008) = barycentric quotient X(i)/X(j) for these {i,j}: {7493, 11185}, {13608, 55848}, {19153, 1995}, {38532, 14262}

X(70009) = X(6)X(8852)∩X(32)X(56556)

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

X(70009) lies on the cubics K1921 and K1033 and these lines: {6, 8852}, {32, 56556}, {163, 5280}, {184, 69912}, {894, 4027}, {1967, 2210}, {7122, 19575}, {9454, 64215}, {16985, 39933}, {41534, 56441}

X(70009) = isogonal conjugate of X(69914)
X(70009) = isogonal conjugate of the isotomic conjugate of X(41534)
X(70009) = X(14602)-cross conjugate of X(7122)
X(70009) = X(i)-isoconjugate of X(j) for these (i,j): {1, 69914}, {2, 52135}, {75, 40873}, {76, 41532}, {256, 17789}, {257, 4645}, {561, 41882}, {1281, 1916}, {1502, 67145}, {1581, 18037}, {1934, 19557}, {3509, 7018}, {4071, 32010}, {4458, 27805}, {8868, 69956}, {17493, 52085}, {17798, 44187}, {18786, 51859}, {18896, 19561}
X(70009) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 69914}, {206, 40873}, {19576, 18037}, {32664, 52135}, {39031, 1281}, {40368, 41882}
X(70009) = barycentric product X(i)*X(j) for these {i,j}: {6, 41534}, {31, 7061}, {32, 40846}, {171, 8852}, {172, 3512}, {385, 66999}, {1580, 30648}, {1691, 24479}, {1933, 63875}, {7122, 7261}, {8875, 67073}, {14602, 63895}, {51614, 56242}
X(70009) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 69914}, {31, 52135}, {32, 40873}, {172, 17789}, {560, 41532}, {1501, 41882}, {1691, 18037}, {1917, 67145}, {1933, 1281}, {3512, 44187}, {7061, 561}, {7122, 4645}, {8852, 7018}, {14602, 19557}, {18902, 18038}, {24479, 18896}, {30648, 1934}, {40846, 1502}, {41534, 76}, {56242, 4458}, {63895, 44160}, {66973, 51859}, {66999, 1916}

X(70010) = X(13)X(275)∩X(54)X(62)

Barycentrics   a^2*(a^2 - b^2 - c^2)*(a^4 - 2*a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2)*(a^4 - a^2*b^2 - 2*a^2*c^2 - b^2*c^2 + c^4)*(3*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2) + 4*S*(Sqrt[3]*a^2 + S)) : :

X(70010) lies on the cubics K112 and K261a and these lines: {13, 275}, {14, 1141}, {15, 3484}, {54, 62}, {61, 20412}, {95, 619}, {97, 44712}, {216, 5961}, {539, 52204}, {1298, 5995}, {5612, 39377}, {8884, 38943}, {11083, 37505}, {11601, 55495}, {19210, 50465}, {38414, 44713}, {40709, 57875}

X(70010) = isogonal conjugate of X(6117)
X(70010) = isogonal conjugate of the polar conjugate of X(51275)
X(70010) = X(i)-cross conjugate of X(j) for these (i,j): {16, 39377}, {32585, 47481}, {36296, 51275}
X(70010) = X(i)-isoconjugate of X(j) for these (i,j): {1, 6117}, {14, 51801}, {19, 33529}, {53, 65569}, {158, 44711}, {298, 2181}, {324, 2151}, {470, 1953}, {2154, 14918}, {3384, 52670}, {6116, 51806}, {8739, 14213}, {34394, 62273}
X(70010) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 6117}, {6, 33529}, {1147, 44711}, {40578, 324}, {40581, 14918}
X(70010) = cevapoint of X(3) and X(64464)
X(70010) = trilinear pole of line {23286, 46113}
X(70010) = barycentric product X(i)*X(j) for these {i,j}: {3, 51275}, {13, 97}, {16, 65326}, {54, 40709}, {95, 36296}, {299, 11077}, {300, 14533}, {471, 50463}, {1141, 44719}, {2153, 62277}, {3457, 34386}, {5995, 62428}, {15412, 38414}, {23286, 23895}, {39377, 43768}, {46113, 46138}, {50465, 51268}, {60009, 64516}
X(70010) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 33529}, {6, 6117}, {13, 324}, {16, 14918}, {54, 470}, {97, 298}, {300, 62274}, {577, 44711}, {2152, 51801}, {2169, 65569}, {3457, 53}, {5995, 35360}, {8737, 13450}, {11077, 14}, {11081, 6116}, {11083, 52671}, {11136, 20412}, {11142, 52670}, {14533, 15}, {15958, 17402}, {19210, 44718}, {20578, 23290}, {23286, 23870}, {33629, 44700}, {34395, 11062}, {36296, 5}, {36306, 65183}, {38414, 14570}, {39377, 62722}, {40709, 311}, {44713, 45793}, {44719, 1273}, {46088, 60010}, {46113, 1154}, {50433, 44714}, {50463, 40710}, {50465, 33530}, {51275, 264}, {54034, 8739}, {58308, 6137}, {60009, 41078}, {62256, 46112}, {62267, 2151}, {62270, 34394}, {65326, 301}

X(70011) = X(13)X(1141)∩X(54)X(61)

Barycentrics   a^2*(a^2 - b^2 - c^2)*(a^4 - 2*a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2)*(a^4 - a^2*b^2 - 2*a^2*c^2 - b^2*c^2 + c^4)*(3*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2) - 4*(Sqrt[3]*a^2 - S)*S) : :

X(70011) lies on the cubics K112 and K261b and these lines: {13, 1141}, {14, 275}, {16, 3484}, {54, 61}, {62, 20411}, {95, 618}, {97, 44711}, {216, 5961}, {539, 52203}, {1298, 5994}, {5616, 39378}, {8884, 38944}, {11088, 37505}, {11600, 55494}, {19210, 50466}, {38413, 44714}, {40710, 57875}

X(70011) = isogonal conjugate of X(6116)
X(70011) = isogonal conjugate of the polar conjugate of X(51268)
X(70011) = X(i)-cross conjugate of X(j) for these (i,j): {15, 39378}, {32586, 47482}, {36297, 51268}
X(70011) = X(i)-isoconjugate of X(j) for these (i,j): {1, 6116}, {13, 51801}, {19, 33530}, {53, 65570}, {158, 44712}, {299, 2181}, {324, 2152}, {471, 1953}, {2153, 14918}, {3375, 52671}, {6117, 51805}, {8740, 14213}, {34395, 62273}
X(70011) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 6116}, {6, 33530}, {1147, 44712}, {40579, 324}, {40580, 14918}
X(70011) = cevapoint of X(3) and X(64465)
X(70011) = trilinear pole of line {23286, 46112}
X(70011) = barycentric product X(i)*X(j) for these {i,j}: {3, 51268}, {14, 97}, {15, 65326}, {54, 40710}, {95, 36297}, {298, 11077}, {301, 14533}, {470, 50463}, {1141, 44718}, {2154, 62277}, {3458, 34386}, {5994, 62428}, {15412, 38413}, {23286, 23896}, {39378, 43768}, {46112, 46138}, {50466, 51275}, {60010, 64516}
X(70011) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 33530}, {6, 6116}, {14, 324}, {15, 14918}, {54, 471}, {97, 299}, {301, 62274}, {577, 44712}, {2151, 51801}, {2169, 65570}, {3458, 53}, {5994, 35360}, {8738, 13450}, {11077, 13}, {11086, 6117}, {11088, 52670}, {11135, 20411}, {11141, 52671}, {14533, 16}, {15958, 17403}, {19210, 44719}, {20579, 23290}, {23286, 23871}, {33629, 44701}, {34394, 11062}, {36297, 5}, {36309, 65183}, {38413, 14570}, {39378, 62722}, {40710, 311}, {44714, 45793}, {44718, 1273}, {46088, 60009}, {46112, 1154}, {50433, 44713}, {50463, 40709}, {50466, 33529}, {51268, 264}, {54034, 8740}, {58308, 6138}, {60010, 41078}, {62256, 46113}, {62267, 2152}, {62270, 34395}, {65326, 300}

X(70012) = X(4)X(12175)∩X(5)X(44028)

Barycentrics   (a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - 5*a^4*c^2 + 3*a^2*b^2*c^2 - 5*b^4*c^2 + 7*a^2*c^4 + 7*b^2*c^4 - 3*c^6)*(a^6 - 5*a^4*b^2 + 7*a^2*b^4 - 3*b^6 - a^4*c^2 + 3*a^2*b^2*c^2 + 7*b^4*c^2 - a^2*c^4 - 5*b^2*c^4 + c^6) : :
X(70012) = 2 X[140] - 3 X[3459], 6 X[21975] - 7 X[55856], 5 X[1656] - 6 X[20413], 5 X[1656] - 3 X[58927]

X(70012) lies on the circumconic {{A,B,C,X(4),X(5)}}, the cubics K119 and K618, and these lines: {4, 12175}, {5, 44028}, {53, 68466}, {140, 3459}, {550, 1141}, {1487, 21975}, {1656, 20413}, {3519, 25148}, {7768, 60034}, {15619, 62036}, {17703, 43893}, {21357, 25043}, {38305, 61976}

X(70012) = reflection of X(58927) in X(20413)
X(70012) = X(21230)-cross conjugate of X(5)
X(70012) = X(13152)-isoconjugate of X(36134)
X(70012) = X(i)-Dao conjugate of X(j) for these (i,j): {137, 13152}, {6592, 27090}
X(70012) = barycentric product X(18314)*X(33639)
X(70012) = barycentric quotient X(i)/X(j) for these {i,j}: {12077, 13152}, {33639, 18315}, {68466, 27090}

X(70013) = X(2)X(1487)∩X(4)X(539)

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

X(70013) lies on the circumconic {{A,B,C,X(4),X(5)}}, the cubics K120 and K617, and these lines: {2, 1487}, {4, 539}, {5, 63645}, {20, 1141}, {137, 60824}, {315, 60034}, {382, 15619}, {627, 19713}, {628, 19712}, {631, 3459}, {1154, 32535}, {2165, 7749}, {3843, 38305}, {5562, 63960}, {8797, 45799}, {11082, 42152}, {11087, 42149}, {25043, 57811}

X(70013) = anticomplement of X(39171)
X(70013) = isotomic conjugate of the anticomplement of X(68465)
X(70013) = X(68465)-cross conjugate of X(2)
X(70013) = X(i)-isoconjugate of X(j) for these (i,j): {2148, 41628}, {2190, 41597}, {20184, 36134}
X(70013) = X(i)-Dao conjugate of X(j) for these (i,j): {5, 41597}, {137, 20184}, {140, 13431}, {216, 41628}
X(70013) = cevapoint of X(i) and X(j) for these (i,j): {137, 6368}, {35441, 41221}
X(70013) = barycentric product X(18314)*X(20185)
X(70013) = barycentric quotient X(i)/X(j) for these {i,j}: {5, 41628}, {216, 41597}, {233, 13431}, {12077, 20184}, {20185, 18315}, {68465, 39171}

X(70014) = X(2)X(9475)∩X(4)X(32)

Barycentrics   (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^8 + a^6*b^2 - 2*a^4*b^4 + a^2*b^6 - b^8 + a^6*c^2 - 3*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(70014) lies on the cubics K128 and K780 and these lines: {2, 9475}, {4, 32}, {6, 5117}, {19, 1423}, {69, 648}, {76, 8863}, {147, 57262}, {230, 419}, {232, 420}, {297, 385}, {340, 50249}, {393, 694}, {458, 7806}, {800, 51988}, {1075, 12251}, {1352, 56867}, {1715, 45991}, {1987, 19222}, {1990, 15993}, {2781, 45280}, {3172, 9863}, {3183, 46730}, {3269, 5286}, {3314, 11331}, {3462, 8743}, {3569, 53345}, {5095, 5702}, {5191, 6620}, {5254, 5894}, {5523, 5667}, {6353, 38867}, {8744, 45938}, {9412, 53419}, {9476, 46097}, {14580, 41203}, {15639, 47105}, {16089, 60516}, {16984, 52289}, {33314, 52058}, {35142, 62955}, {35235, 64213}, {37174, 63048}, {68572, 69645}

X(70014) = reflection of X(66880) in X(23976)
X(70014) = polar conjugate of X(9473)
X(70014) = antitomic image of X(69652)
X(70014) = isotomic conjugate of the isogonal conjugate of X(57262)
X(70014) = polar conjugate of the isotomic conjugate of X(147)
X(70014) = polar conjugate of the isogonal conjugate of X(52162)
X(70014) = X(i)-Ceva conjugate of X(j) for these (i,j): {297, 4}, {385, 3186}, {16318, 1249}, {67006, 8863}
X(70014) = X(52162)-cross conjugate of X(147)
X(70014) = X(i)-isoconjugate of X(j) for these (i,j): {48, 9473}, {63, 34130}
X(70014) = X(i)-Dao conjugate of X(j) for these (i,j): {98, 287}, {1249, 9473}, {3162, 34130}, {62595, 63894}
X(70014) = cevapoint of X(52162) and X(57262)
X(70014) = barycentric product X(i)*X(j) for these {i,j}: {4, 147}, {76, 57262}, {92, 16559}, {264, 52162}, {297, 36899}, {2967, 61496}, {39931, 69652}
X(70014) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 9473}, {25, 34130}, {147, 69}, {297, 63894}, {16559, 63}, {36899, 287}, {52162, 3}, {57262, 6}, {69652, 69780}, {69996, 15391}
X(70014) = {X(132),X(45031)}-harmonic conjugate of X(4)

X(70015) = X(1)X(69921)∩X(42)X(57)

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

X(70015) lies on the cubics K135 and K294 and these lines: {1, 69921}, {9, 56716}, {42, 57}, {292, 1279}, {518, 37138}, {672, 2116}, {894, 40739}, {1757, 9499}, {2279, 16469}, {3685, 32041}, {14189, 43736}, {62784, 62785}
on K135, K294

X(70015) = X(1001)-isoconjugate of X(43751)
X(70015) = barycentric product X(i)*X(j) for these {i,j}: {1, 67143}, {292, 56659}, {18789, 67140}
X(70015) = barycentric quotient X(i)/X(j) for these {i,j}: {2279, 43751}, {18789, 56658}, {56659, 1921}, {56895, 63229}, {67143, 75}

X(70016) = X(42)X(2162)∩X(55)X(43077)

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

X(70016) lies on the cubics K135 and K577 and these lines: {42, 2162}, {55, 43077}, {57, 1463}, {239, 63882}, {291, 63884}, {292, 16515}, {17754, 67142}, {26102, 40780}, {40756, 68769}
on K135, K577

X(70016) = X(63884)-Ceva conjugate of X(60665)
X(70016) = X(19586)-cross conjugate of X(21010)
X(70016) = X(i)-isoconjugate of X(j) for these (i,j): {6, 56664}, {3795, 47647}, {4393, 69938}, {16468, 41527}, {40733, 63902}
X(70016) = X(9)-Dao conjugate of X(56664)
X(70016) = barycentric product X(i)*X(j) for these {i,j}: {1, 67142}, {292, 56653}, {17754, 52654}, {19584, 63884}, {20917, 40735}, {21010, 27494}, {21101, 51449}, {24349, 60665}, {24720, 43077}, {53648, 54251}
X(70016) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 56664}, {17754, 30963}, {19586, 27481}, {19587, 3795}, {21010, 4393}, {24349, 10009}, {40735, 69938}, {54251, 4785}, {54275, 4782}, {56653, 1921}, {60665, 41527}, {63884, 63902}, {67142, 75}

X(70017) = X(1)X(69920)∩X(6)X(51838)

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

X(70017) lies on the cubics K135 and K983 and these lines: {1, 69920}, {6, 51838}, {42, 24479}, {291, 294}, {292, 9472}, {894, 33676}, {1376, 9503}, {1475, 51866}, {4518, 31637}, {27945, 62599}

X(70017) = X(291)-Ceva conjugate of X(52030)
X(70017) = X(i)-isoconjugate of X(j) for these (i,j): {238, 63880}, {2115, 39775}, {8299, 9499}, {9500, 17755}, {51329, 69998}
X(70017) = X(i)-Dao conjugate of X(j) for these (i,j): {673, 350}, {9470, 63880}, {63489, 40704}
X(70017) = barycentric product X(i)*X(j) for these {i,j}: {291, 62599}, {1282, 52209}, {2114, 33676}, {20533, 52030}, {20672, 67197}, {52160, 69920}
X(70017) = barycentric quotient X(i)/X(j) for these {i,j}: {292, 63880}, {1282, 17755}, {2114, 39775}, {20533, 64223}, {20672, 8299}, {51866, 9499}, {52030, 69945}, {62599, 350}, {69920, 69998}

X(70018) = X(1)X(40155)∩X(239)X(291)

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

X(70018) lies on the cubics K135 and K997 and these lines: {1, 40155}, {42, 63874}, {239, 291}, {244, 52209}, {292, 672}, {660, 1757}, {813, 3747}, {869, 40730}, {894, 24576}, {1580, 30664}, {1911, 2223}, {1922, 2210}, {1967, 16365}, {2111, 52030}, {7077, 30657}, {16826, 40796}, {18266, 18267}, {22116, 25800}, {30669, 56802}

X(70018) = isogonal conjugate of X(39044)
X(70018) = isotomic conjugate of X(64222)
X(70018) = isogonal conjugate of the complement of X(30669)
X(70018) = isotomic conjugate of the isogonal conjugate of X(18267)
X(70018) = isogonal conjugate of the isotomic conjugate of X(30663)
X(70018) = X(i)-cross conjugate of X(j) for these (i,j): {6, 1967}, {798, 813}, {1964, 741}, {3248, 875}, {40730, 1911}, {58862, 30664}
X(70018) = X(i)-isoconjugate of X(j) for these (i,j): {1, 39044}, {2, 4366}, {6, 56660}, {31, 64222}, {75, 8300}, {76, 51328}, {86, 4368}, {100, 27855}, {190, 4375}, {238, 350}, {257, 53681}, {261, 3027}, {335, 6652}, {385, 17493}, {659, 874}, {673, 27919}, {740, 33295}, {812, 3570}, {870, 3802}, {873, 4094}, {1016, 35119}, {1428, 4087}, {1429, 3975}, and others X(70018) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 64222}, {3, 39044}, {9, 56660}, {206, 8300}, {8054, 27855}, {9467, 18786}, {9470, 350}, {32664, 4366}, {36906, 1921}, {40600, 4368}, {55053, 4375}, {62557, 18891}
X(70018) = cevapoint of X(i) and X(j) for these (i,j): {6, 66973}, {875, 3248}
X(70018) = crosspoint of X(51866) and X(63881)
X(70018) = crosssum of X(i) and X(j) for these (i,j): {238, 27916}, {17755, 17793}
X(70018) = trilinear pole of line {875, 58864}
X(70018) = crossdifference of every pair of points on line {4375, 27855}
X(70018) = barycentric product X(i)*X(j) for these {i,j}: {1, 52205}, {6, 30663}, {31, 40098}, {75, 51856}, {76, 18267}, {256, 30657}, {291, 292}, {334, 1922}, {335, 1911}, {660, 3572}, {694, 18787}, {813, 876}, {872, 57554}, {875, 4562}, {1581, 66973}, {1967, 30669}, {2171, 62714}, {3248, 57566}, {3252, 52030}, {4444, 34067}, {7104, 30642}, {7233, 51858}, {9506, 40794}, {14598, 18895}, {18268, 43534}, {18893, 44170}, {18897, 44172}, {22116, 51866}, {30664, 30671}, {40730, 52209}, {40796, 63874}, {52085, 66999}, {52656, 63881}
X(70018) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 56660}, {2, 64222}, {6, 39044}, {31, 4366}, {32, 8300}, {213, 4368}, {291, 1921}, {292, 350}, {334, 44169}, {335, 18891}, {560, 51328}, {649, 27855}, {660, 27853}, {667, 4375}, {741, 30940}, {813, 874}, {872, 35068}, {875, 812}, {876, 65101}, {1911, 239}, {1922, 238}, {1967, 17493}, {2210, 6652}, {2223, 27919}, {3248, 35119}, {3252, 64223}, {3572, 3766}, {4876, 4087}, {7077, 3975}, {7109, 4094}, {7122, 53681}, {8789, 61385}, {9468, 18786}, {14598, 1914}, {18263, 40767}, {18265, 3684}, {18266, 27926}, {18267, 6}, {18268, 33295}, {18787, 3978}, {18893, 14599}, {18895, 44171}, {18897, 2210}, {30648, 64231}, {30657, 1909}, {30663, 76}, {30669, 1926}, {34067, 3570}, {40098, 561}, {40155, 62553}, {40728, 3802}, {40730, 17755}, {40794, 18035}, {51856, 1}, {51858, 3685}, {52205, 75}, {57129, 68156}, {57554, 57992}, {62714, 52379}, {66973, 1966}, {69826, 68153}

X(70019) = X(1)X(644)∩X(2)X(35111)

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

X(70019) lies on the cubics K137 and K982 and these lines: {1, 644}, {2, 35111}, {6, 56314}, {9, 19604}, {145, 30720}, {241, 56721}, {294, 39272}, {1420, 57192}, {1477, 2137}, {4422, 4648}, {6078, 8686}, {9309, 56715}, {9502, 56722}, {35355, 48032}, {36125, 60355}, {56718, 56720}

X(70019) = isogonal conjugate of X(51839)
X(70019) = X(i)-Ceva conjugate of X(j) for these (i,j): {9, 56721}, {39272, 4162}, {43760, 1280}
X(70019) = X(i)-isoconjugate of X(j) for these (i,j): {1, 51839}, {105, 56719}, {1279, 8056}, {1293, 6084}, {2348, 19604}, {3008, 3445}, {5853, 40151}, {8647, 27818}, {8659, 53647}, {27834, 48032}, {38828, 53523}, {58794, 68768}
X(70019) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 51839}, {39046, 56719}, {45036, 3008}
X(70019) = trilinear pole of line {3158, 4394}
X(70019) = X(35355)-line conjugate of X(48032)
X(70019) = barycentric product X(i)*X(j) for these {i,j}: {145, 1280}, {1477, 44720}, {1743, 36807}, {3158, 35160}, {3161, 43760}, {4462, 6078}, {4925, 39272}, {30720, 37626}, {35355, 43290}
X(70019) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 51839}, {672, 56719}, {1280, 4373}, {1477, 19604}, {1743, 3008}, {2976, 68121}, {3052, 1279}, {3158, 5853}, {4162, 53523}, {4394, 6084}, {4462, 65869}, {4729, 53558}, {6078, 27834}, {8643, 48032}, {35160, 62528}, {36807, 40014}, {43760, 27818}, {57192, 53337}

X(70020) = X(2)X(1975)∩X(4)X(57688)

Barycentrics   (a^2 + b^2 - 3*c^2)*(a^2 - 3*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(70020) lies on the cubics K185 and K777 and these lines: {2, 1975}, {4, 57688}, {6, 34208}, {193, 57857}, {230, 35067}, {524, 35136}, {2501, 3566}, {3815, 40809}, {6391, 53420}, {7745, 9777}, {23291, 44518}, {27364, 53059}, {41932, 66880}, {44377, 65277}, {47286, 47389}, {52454, 53418}

X(70020) = reflection of X(i) in X(j) for these {i,j}: {230, 55152}, {65277, 44377}
X(70020) = isogonal conjugate of X(69778)
X(70020) = polar conjugate of X(63613)
X(70020) = antitomic image of X(230)
X(70020) = isotomic conjugate of the isogonal conjugate of X(67168)
X(70020) = X(i)-cross conjugate of X(j) for these (i,j): {3564, 230}, {51613, 55122}
X(70020) = X(i)-isoconjugate of X(j) for these (i,j): {1, 69778}, {48, 63613}, {193, 36051}, {1707, 2987}, {3053, 8773}, {18156, 32654}
X(70020) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 69778}, {114, 193}, {230, 51374}, {1249, 63613}, {15261, 32654}, {35067, 6337}, {39069, 1707}, {39072, 3053}, {55122, 51613}, {55152, 3566}, {64614, 2987}
X(70020) = cevapoint of X(51613) and X(55122)
X(70020) = crosssum of X(i) and X(j) for these (i,j): {1692, 8780}, {3053, 59707}
X(70020) = crossdifference of every pair of points on line {3167, 8651}
X(70020) = barycentric product X(i)*X(j) for these {i,j}: {76, 67168}, {230, 2996}, {460, 6340}, {1733, 8769}, {3564, 34208}, {6391, 44145}, {8770, 51481}, {35136, 55122}
X(70020) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 63613}, {6, 69778}, {114, 51374}, {230, 193}, {460, 6353}, {1692, 3053}, {1733, 18156}, {2996, 8781}, {3564, 6337}, {3565, 10425}, {4226, 57216}, {5477, 32459}, {6340, 57872}, {6391, 43705}, {8769, 8773}, {8770, 2987}, {8772, 1707}, {14248, 3563}, {34208, 35142}, {35136, 65277}, {38252, 36051}, {40319, 42065}, {42663, 8651}, {44099, 19118}, {44145, 54412}, {51335, 59707}, {51481, 57518}, {51613, 15525}, {52144, 3167}, {53059, 32654}, {55122, 3566}, {55152, 51613}, {65484, 58766}, {67168, 6}, {68175, 65484}

X(70021) = X(2)X(895)∩X(23)X(13493)

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

X(70021) lies on the cubics K273 and K394 and these lines: {2, 895}, {23, 13493}, {69, 32133}, {111, 55029}, {524, 39157}, {671, 14262}, {1992, 13608}, {5095, 30247}, {5523, 10630}, {9084, 15638}, {51224, 53764}

X(70021) = antigonal image of X(55848)
X(70021) = isogonal conjugate of the complement of X(39157)
X(70021) = X(i)-cross conjugate of X(j) for these (i,j): {2444, 35188}, {9125, 30247}
X(70021) = X(i)-isoconjugate of X(j) for these (i,j): {896, 14262}, {14210, 52174}, {53777, 55923}
X(70021) = X(i)-Dao conjugate of X(j) for these (i,j): {15477, 52174}, {15899, 14262}, {35133, 55135}
X(70021) = cevapoint of X(i) and X(j) for these (i,j): {6, 51239}, {2444, 15638}
X(70021) = trilinear pole of line {1499, 13608}
X(70021) = barycentric product X(i)*X(j) for these {i,j}: {671, 13608}, {1992, 60317}, {2408, 65324}, {5486, 52141}
X(70021) = barycentric quotient X(i)/X(j) for these {i,j}: {111, 14262}, {1384, 53777}, {1499, 55135}, {2444, 68778}, {4232, 37855}, {5486, 69944}, {13608, 524}, {15638, 5512}, {32740, 52174}, {35188, 1296}, {51239, 10354}, {52141, 11185}, {60317, 5485}, {65324, 2418}

X(70022) = X(1)X(56196)∩X(2)X(7033)

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

X(70022) lies on the cubics K286 and K1014 and these lines: {1, 56196}, {2, 7033}, {6, 17743}, {76, 1423}, {983, 4279}, {1966, 17350}, {3114, 63902}, {40834, 51314}, {52652, 60737}

X(70022) = isotomic conjugate of X(67174)
X(70022) = X(3114)-Ceva conjugate of X(7033)
X(70022) = X(i)-isoconjugate of X(j) for these (i,j): {31, 67174}, {3117, 47647}, {7032, 69938}
X(70022) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 67174}, {984, 3094}
X(70022) = barycentric product X(i)*X(j) for these {i,j}: {3114, 19584}, {7033, 24349}, {7034, 21010}, {17743, 20917}, {19586, 46281}, {21101, 38810}
X(70022) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 67174}, {3113, 47647}, {3114, 63902}, {4334, 7248}, {7033, 41527}, {17743, 69938}, {17754, 2275}, {19584, 3094}, {19586, 3116}, {19587, 3117}, {20917, 3662}, {21010, 7032}, {21101, 3721}, {24349, 982}, {24720, 3777}, {54251, 50514}, {56180, 7220}

X(70023) = X(4)X(39)∩X(67)X(51943)

Barycentrics   (a^2*b^2 - b^4 + 2*a^2*c^2 + b^2*c^2)*(2*a^2*b^2 + a^2*c^2 + b^2*c^2 - c^4)*(a^10 - 2*a^6*b^4 + a^2*b^8 - 5*a^6*b^2*c^2 + 4*a^4*b^4*c^2 - a^2*b^6*c^2 + 2*b^8*c^2 - 2*a^6*c^4 + 4*a^4*b^2*c^4 - 2*b^6*c^4 - a^2*b^2*c^6 - 2*b^4*c^6 + a^2*c^8 + 2*b^2*c^8) : :

X(70023) lies on the cubics K288 and K481 and these lines: {4, 39}, {67, 51943}, {858, 65310}, {1503, 26714}, {5189, 46807}, {7391, 67175}, {16063, 42313}, {34507, 54032}, {38227, 53827}, {51939, 65349}

X(70023) = circumcircle-of-anticomplementary-triangle-inverse of X(7710)
X(70023) = antigonal image of X(41377)
X(70023) = barycentric product X(41377)*X(42313)
X(70023) = barycentric quotient X(41377)/X(458)

X(70024) = X(2)X(43087)∩X(186)X(6103)

Barycentrics   (a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10 + 2*a^6*b^2*c^2 + 2*a^4*b^4*c^2 - a^2*b^6*c^2 - 3*b^8*c^2 - a^6*c^4 - 4*a^4*b^2*c^4 + 2*a^2*b^4*c^4 + 2*b^6*c^4 - a^4*c^6 + 2*a^2*b^2*c^6 + 2*b^4*c^6 - 3*b^2*c^8 + c^10)*(a^10 - a^6*b^4 - a^4*b^6 + b^10 - 3*a^8*c^2 + 2*a^6*b^2*c^2 - 4*a^4*b^4*c^2 + 2*a^2*b^6*c^2 - 3*b^8*c^2 + 2*a^6*c^4 + 2*a^4*b^2*c^4 + 2*a^2*b^4*c^4 + 2*b^6*c^4 + 2*a^4*c^6 - a^2*b^2*c^6 + 2*b^4*c^6 - 3*a^2*c^8 - 3*b^2*c^8 + c^10) : :

X(70024) lies on the cubics K292 and K524 and these lines: {2, 43087}, {186, 6103}, {249, 64182}, {323, 542}, {427, 17986}, {549, 16092}, {842, 1989}, {868, 52192}, {14165, 47223}, {14355, 34369}

X(70024) = isogonal conjugate of X(19140)
X(70024) = X(1)-isoconjugate of X(19140)
X(70024) = X(3)-Dao conjugate of X(19140)
X(70024) = trilinear pole of line {526, 1640}
X(70024) = barycentric quotient X(6)/X(19140)

X(70025) = X(2)X(56706)∩X(75)X(56897)

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

X(70025) lies on the cubics K323 and K984 and these lines: {2, 56706}, {75, 56897}, {239, 9436}, {518, 910}, {1861, 1886}, {2115, 3693}, {3717, 40869}, {4712, 9501}, {10025, 33888}, {24578, 40873}

X(70025) = isogonal conjugate of X(2114)
X(70025) = X(69945)-Ceva conjugate of X(9499)
X(70025) = X(i)-cross conjugate of X(j) for these (i,j): {291, 2319}, {294, 9}, {2115, 9499}
X(70025) = X(i)-isoconjugate of X(j) for these (i,j): {1, 2114}, {6, 52160}, {7, 20672}, {56, 20533}, {57, 1282}, {278, 20761}, {1014, 20692}, {1458, 62599}
X(70025) = X(i)-Dao conjugate of X(j) for these (i,j): {1, 20533}, {3, 2114}, {9, 52160}, {5452, 1282}
X(70025) = crosspoint of X(69945) and X(69998)
X(70025) = trilinear pole of line {65664, 68813}
X(70025) = barycentric product X(i)*X(j) for these {i,j}: {1, 69998}, {8, 9499}, {9, 69945}, {75, 2115}, {312, 9500}, {14942, 63880}
X(70025) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 52160}, {6, 2114}, {9, 20533}, {41, 20672}, {55, 1282}, {212, 20761}, {294, 62599}, {1334, 20692}, {2115, 1}, {3684, 27945}, {9499, 7}, {9500, 57}, {63880, 9436}, {69945, 85}, {69998, 75}

X(70026) = X(2)X(66974)∩X(4)X(39)

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

X(70026) lies on the cubics K354 and K780 and these lines: {2, 66974}, {4, 39}, {6, 65005}, {230, 694}, {263, 5304}, {325, 65271}, {327, 7868}, {1432, 2186}, {3289, 26714}, {3498, 13357}, {5999, 57259}, {6037, 36899}, {6330, 16089}, {7735, 51338}, {7774, 67175}, {7779, 9473}, {16318, 65349}, {16990, 42313}, {61101, 63741}

X(70026) = isotomic conjugate of the isogonal conjugate of X(57259)
X(70026) = X(1916)-Ceva conjugate of X(65005)
X(70026) = X(43702)-isoconjugate of X(52134)
X(70026) = crosssum of X(3288) and X(62596)
X(70026) = barycentric product X(i)*X(j) for these {i,j}: {76, 57259}, {262, 5999}, {46807, 47737}, {54267, 65271}
X(70026) = barycentric quotient X(i)/X(j) for these {i,j}: {263, 43702}, {5999, 183}, {47737, 46806}, {54267, 23878}, {57259, 6}
X(70026) = {X(2),X(66974)}-harmonic conjugate of X(67187)

X(70027) = X(2)X(6795)∩X(4)X(4846)

Barycentrics   a^12 - a^10*b^2 - a^8*b^4 + a^4*b^8 + a^2*b^10 - b^12 - a^10*c^2 - a^8*b^2*c^2 + 4*a^6*b^4*c^2 + 10*a^4*b^6*c^2 - 11*a^2*b^8*c^2 - b^10*c^2 - a^8*c^4 + 4*a^6*b^2*c^4 - 26*a^4*b^4*c^4 + 10*a^2*b^6*c^4 + 13*b^8*c^4 + 10*a^4*b^2*c^6 + 10*a^2*b^4*c^6 - 22*b^6*c^6 + a^4*c^8 - 11*a^2*b^2*c^8 + 13*b^4*c^8 + a^2*c^10 - b^2*c^10 - c^12 : :

X(70027) lies on the Hutson-Parry circle, the cubics K479 and K884 and these lines: {2, 6795}, {4, 4846}, {30, 46339}, {69, 850}, {125, 52125}, {376, 476}, {1300, 6699}, {2697, 7493}, {4240, 67640}, {5071, 11639}, {5466, 36163}, {6032, 7736}, {6792, 43448}, {9140, 12243}, {9159, 35922}, {9214, 34320}, {9979, 30227}, {11640, 31105}, {14846, 56403}, {14932, 65870}, {14982, 36789}, {16051, 46436}, {48906, 68701}

X(70027) = anticomplement of X(14685)
X(70027) = polar-circle-inverse of X(44084)
X(70027) = antigonal image of X(46341)
X(70027) = psi-transform of X(113)
X(70027) = barycentric product X(3260)*X(46341)
X(70027) = barycentric quotient X(46341)/X(74)

X(70028) = X(5)X(39)∩X(54)X(83)

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

X(70028) lies on the cubics K589 and K1068 and these lines: {2, 34157}, {4, 47049}, {5, 39}, {54, 83}, {140, 47079}, {826, 1209}, {868, 23098}, {1235, 62274}, {1352, 56687}, {6328, 10627}, {7794, 35088}, {21243, 40804}, {24206, 40810}, {25555, 36213}, {33330, 52042}, {38939, 40107}, {51371, 62431}

X(70028) = X(59805)-cross conjugate of X(2799)
X(70028) = X(i)-isoconjugate of X(j) for these (i,j): {293, 19128}, {36084, 53263}
X(70028) = X(i)-Dao conjugate of X(j) for these (i,j): {132, 19128}, {35088, 53331}, {38987, 53263}, {60596, 60518}
X(70028) = cevapoint of X(i) and X(j) for these (i,j): {868, 41167}, {44114, 55267}
X(70028) = crosssum of X(38987) and X(53263)
X(70028) = barycentric product X(i)*X(j) for these {i,j}: {32458, 60523}, {60526, 69963}
X(70028) = barycentric quotient X(i)/X(j) for these {i,j}: {232, 19128}, {2799, 53331}, {3569, 53263}, {59805, 38987}, {60523, 41932}, {60524, 60518}, {60526, 1976}
X(70028) = {X(5),X(52006)}-harmonic conjugate of X(114)

X(70029) = X(2)X(46235)∩X(147)X(325)

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

X(70029) lies on the cubics K699 and K777 and these lines: {2, 46235}, {147, 325}, {287, 1916}, {290, 61496}, {401, 8782}, {4027, 39931}, {5976, 8784}, {36849, 66880}

X(70029) = X(i)-cross conjugate of X(j) for these (i,j): {4, 39927}, {9469, 63898}, {40820, 385}
X(70029) = X(i)-isoconjugate of X(j) for these (i,j): {147, 1967}, {694, 16559}, {1581, 52162}, {1755, 69652}, {1959, 69996}, {57262, 66933}
X(70029) = X(i)-Dao conjugate of X(j) for these (i,j): {8290, 147}, {19576, 52162}, {36899, 69652}, {39043, 16559}
X(70029) = barycentric product X(i)*X(j) for these {i,j}: {385, 9473}, {3978, 34130}, {40820, 63894}
X(70029) = barycentric quotient X(i)/X(j) for these {i,j}: {98, 69652}, {385, 147}, {1580, 16559}, {1691, 52162}, {1976, 69996}, {9473, 1916}, {34130, 694}, {40820, 36899}, {44089, 57262}

X(70030) = X(8)X(6625)∩X(274)X(350)

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

X(70030) lies on the cubics K702 and K767 and these lines: {8, 6625}, {10, 65288}, {79, 17746}, {239, 56658}, {256, 56653}, {274, 350}, {291, 30570}, {740, 56703}, {1698, 60676}, {6650, 17755}, {40845, 56659}, {49452, 59272}

X(70030) = X(i)-Ceva conjugate of X(j) for these (i,j): {75, 56658}, {65288, 54256}
X(70030) = X(40776)-isoconjugate of X(60697)
X(70030) = barycentric product X(i)*X(j) for these {i,j}: {24342, 27483}, {40750, 60678}, {54265, 65288}
X(70030) = barycentric quotient X(i)/X(j) for these {i,j}: {24342, 16826}, {30571, 40776}, {40750, 4649}, {54253, 4784}, {54256, 4824}, {54265, 28840}

X(70031) = X(2)X(7167)∩X(6)X(39940)

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

X(70031) lies on the cubics K739 and K1305 and these lines: {2, 7167}, {6, 39940}, {239, 1821}, {732, 40846}, {894, 38382}, {4027, 39929}, {19590, 39936}, {28358, 65289}, {39914, 39935}, {39928, 39931}

X(70031) = reflection of X(65289) in X(28358)
X(70031) = antitomic image of X(17787)
X(70031) = X(3978)-cross conjugate of X(39936)
X(70031) = X(i)-isoconjugate of X(j) for these (i,j): {694, 51935}, {1431, 3508}, {1432, 51928}, {1967, 39940}, {52664, 67144}, {56802, 66996}
X(70031) = X(i)-Dao conjugate of X(j) for these (i,j): {8290, 39940}, {39043, 51935}
X(70031) = barycentric product X(i)*X(j) for these {i,j}: {7167, 17787}, {27958, 43686}
X(70031) = barycentric quotient X(i)/X(j) for these {i,j}: {385, 39940}, {1580, 51935}, {2329, 3508}, {2330, 51928}, {7081, 56802}, {7167, 1432}, {17787, 52664}, {43686, 60245}

X(70032) = X(3)X(194)∩X(6)X(69771)

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

X(70032) lies on the cubics K739 and K776 and these lines: {3, 194}, {6, 69771}, {76, 59804}, {83, 64621}, {287, 14382}, {12203, 67751}, {14937, 69139}, {17752, 39930}, {67179, 69992}

X(70032) = isogonal conjugate of X(51997)
X(70032) = isotomic conjugate of X(67179)
X(70032) = X(52658)-cross conjugate of X(183)
X(70032) = X(i)-isoconjugate of X(j) for these (i,j): {1, 51997}, {31, 67179}, {263, 19591}, {694, 56678}, {2186, 11328}, {3402, 18906}, {26714, 54252}, {45907, 65252}
X(70032) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 67179}, {3, 51997}, {3117, 19602}, {38997, 45907}, {39043, 56678}, {51580, 18906}
X(70032) = cevapoint of X(23878) and X(59804)
X(70032) = barycentric product X(i)*X(j) for these {i,j}: {183, 19222}, {20023, 47643}
X(70032) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 67179}, {6, 51997}, {182, 11328}, {183, 18906}, {1580, 56678}, {3288, 45907}, {19222, 262}, {23878, 54262}, {47643, 263}, {52134, 19591}, {52658, 19602}

X(70033) = X(2)X(51)∩X(327)X(524)

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

X(70033) lies on the cubics K757 and K1359 and these lines: {2, 51}, {6, 43664}, {287, 10796}, {327, 524}, {381, 66879}, {458, 65349}, {597, 51543}, {598, 60869}, {3329, 67187}, {3618, 51338}, {6037, 60862}, {7787, 60601}, {11179, 39682}, {11328, 65310}, {37765, 68572}, {43718, 59373}, {45329, 66291}, {51171, 66974}, {53196, 64621}

X(70033) = X(67187)-Dao conjugate of X(60126)
X(70033) = barycentric product X(327)*X(11842)
X(70033) = barycentric quotient X(i)/X(j) for these {i,j}: {262, 60126}, {11842, 182}
X(70033) = {X(2),X(65005)}-harmonic conjugate of X(67175)

X(70034) = X(6)X(67073)∩X(31)X(19580)

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

X(70034) lies on the cubics K773 and K789 and these lines: {6, 67073}, {31, 19580}, {237, 67005}, {932, 1258}, {1691, 14598}, {2176, 18756}, {3747, 62421}, {7168, 20663}, {24294, 39933}, {34248, 57264}, {41526, 56836}, {51328, 66931}

X(70034) = isogonal conjugate of X(19567)
X(70034) = isogonal conjugate of the isotomic conjugate of X(7168)
X(70034) = X(238)-cross conjugate of X(31)
X(70034) = X(i)-isoconjugate of X(j) for these (i,j): {1, 19567}, {2, 19565}, {6, 18275}, {75, 3510}, {76, 18278}, {171, 69956}, {238, 51868}, {239, 64233}, {264, 23186}, {291, 19581}, {292, 18277}, {334, 19580}, {335, 19579}, {894, 40849}, {1909, 69935}, {1920, 51979}, {8875, 17789}, {18274, 18895}, {30634, 44172}, {40755, 52043}
X(70034) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 19567}, {9, 18275}, {206, 3510}, {9470, 51868}, {19557, 18277}, {32664, 19565}, {39029, 19581}
X(70034) = trilinear pole of line {1197, 8640}
X(70034) = barycentric product X(i)*X(j) for these {i,j}: {1, 51919}, {6, 7168}, {31, 69954}, {238, 63893}, {256, 67073}, {727, 40782}, {893, 51920}, {904, 39933}, {1914, 24576}, {7104, 52175}, {8852, 8868}, {14599, 30633}
X(70034) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 18275}, {6, 19567}, {31, 19565}, {32, 3510}, {238, 18277}, {292, 51868}, {560, 18278}, {893, 69956}, {904, 40849}, {1911, 64233}, {1914, 19581}, {2210, 19579}, {7104, 69935}, {7168, 76}, {9247, 23186}, {14599, 19580}, {18892, 18274}, {18894, 30634}, {24576, 18895}, {30633, 44170}, {40782, 35538}, {51919, 75}, {51920, 1920}, {63893, 334}, {66931, 51979}, {67073, 1909}, {69954, 561}

X(70035) = X(4)X(67073)∩X(31)X(19580)

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

X(70035) lies on the cubics K777 and K1325 and these lines: {4, 57553}, {6, 47736}, {98, 325}, {401, 2987}, {1503, 35142}, {5967, 55266}, {12215, 65277}, {47389, 62348}

X(70035) = X(i)-isoconjugate of X(j) for these (i,j): {114, 38252}, {1959, 67168}, {8769, 51335}, {8770, 17462}
X(70035) = X(i)-Dao conjugate of X(j) for these (i,j): {69, 62590}, {15525, 55267}, {51579, 114}
X(70035) = barycentric product X(i)*X(j) for these {i,j}: {193, 40428}, {287, 63613}, {290, 69778}, {2065, 57518}, {3566, 55266}
X(70035) = barycentric quotient X(i)/X(j) for these {i,j}: {193, 114}, {1707, 17462}, {1976, 67168}, {2065, 8770}, {3053, 51335}, {3167, 47406}, {3566, 55267}, {6337, 62590}, {40428, 2996}, {55266, 35136}, {56891, 60595}, {63613, 297}, {69778, 511}

X(70036) = X(2)X(9289)∩X(20)X(64)

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

X(70036) lies on the cubics K780 and K824 and these lines: {2, 9289}, {20, 64}, {98, 53886}, {193, 37199}, {297, 459}, {1073, 37188}, {3926, 52566}, {4176, 69425}, {6339, 41489}, {6526, 35142}, {12111, 32840}, {14572, 26958}, {14642, 39141}, {16089, 52581}, {20023, 41530}, {26204, 67118}, {32605, 32831}, {40813, 53415}, {41909, 46639}

X(70036) = isotomic conjugate of X(69924)
X(70036) = X(459)-Ceva conjugate of X(253)
X(70036) = X(6353)-cross conjugate of X(193)
X(70036) = X(i)-isoconjugate of X(j) for these (i,j): {20, 38252}, {31, 69924}, {154, 8769}, {204, 6391}, {610, 8770}, {1895, 40319}, {17898, 65178}, {18750, 53059}
X(70036) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 69924}, {69, 37669}, {3343, 6391}, {6388, 8057}, {14092, 8770}, {15525, 6587}, {40839, 34208}, {51579, 20}
X(70036) = barycentric product X(i)*X(j) for these {i,j}: {64, 57518}, {193, 253}, {459, 6337}, {1073, 54412}, {1707, 57921}, {2184, 18156}, {3053, 41530}, {3167, 52581}, {3566, 44326}, {6353, 34403}, {15394, 21447}, {57216, 58759}
X(70036) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 69924}, {64, 8770}, {193, 20}, {253, 2996}, {459, 34208}, {1073, 6391}, {1707, 610}, {2155, 38252}, {2184, 8769}, {3053, 154}, {3167, 15905}, {3566, 6587}, {3798, 21172}, {4028, 8804}, {6337, 37669}, {6353, 1249}, {8651, 62176}, {10607, 35602}, {13157, 27364}, {14642, 40319}, {15394, 60839}, {17081, 18623}, {18156, 18750}, {19118, 3172}, {21447, 14249}, {21874, 3198}, {33581, 53059}, {33632, 51508}, {34403, 6340}, {41489, 14248}, {41588, 42459}, {44326, 35136}, {46639, 3565}, {54412, 15466}, {57071, 44705}, {57216, 36841}, {57518, 14615}
X(70036) = {X(64),X(34403)}-harmonic conjugate of X(253)

X(70037) = X(1)X(4602)∩X(31)X(799)

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

X(70037) lies on the cubics K985 and K992 and these lines: {1, 4602}, {31, 799}, {42, 1978}, {213, 668}, {561, 3223}, {699, 789}, {811, 1973}, {875, 40017}, {1042, 46406}, {1096, 57973}, {1402, 4554}, {1909, 23493}, {1966, 1967}, {3112, 18273}, {3212, 66935}, {4583, 19565}, {4593, 46289}, {9239, 23478}, {18056, 38275}, {18075, 37132}, {31002, 69480}, {39914, 39933}, {40718, 52611}, {46277, 69475}, {46404, 57652}

X(70037) = isogonal conjugate of X(51907)
X(70037) = isotomic conjugate of X(2227)
X(70037) = isotomic conjugate of the isogonal conjugate of X(43761)
X(70037) = X(i)-cross conjugate of X(j) for these (i,j): {1581, 1821}, {1926, 3112}, {69957, 75}
X(70037) = X(i)-isoconjugate of X(j) for these (i,j): {1, 51907}, {2, 32748}, {3, 52460}, {6, 3229}, {31, 2227}, {32, 698}, {99, 9429}, {187, 36821}, {194, 67002}, {385, 69947}, {511, 32540}, {512, 41337}, {560, 69957}, {694, 51322}, {699, 59802}, {805, 62649}, {1501, 35524}, {1691, 47648}, {1967, 51912}, {1974, 59567}, {2076, 51248}, {9468, 39080}, {17970, 52462}, {61098, 66906}
X(70037) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 2227}, {3, 51907}, {9, 3229}, {6374, 69957}, {6376, 698}, {8290, 51912}, {32664, 32748}, {36103, 52460}, {38986, 9429}, {39043, 51322}, {39044, 39080}, {39054, 41337}
X(70037) = cevapoint of X(i) and X(j) for these (i,j): {1, 1966}, {75, 69957}, {740, 6376}, {812, 38986}
X(70037) = trilinear pole of line {75, 798}
X(70037) = barycentric product X(i)*X(j) for these {i,j}: {1, 66842}, {75, 3225}, {76, 43761}, {92, 8858}, {561, 699}, {1821, 69910}, {1926, 51992}, {1934, 32544}
X(70037) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 3229}, {2, 2227}, {6, 51907}, {19, 52460}, {31, 32748}, {75, 698}, {76, 69957}, {304, 59567}, {385, 51912}, {561, 35524}, {662, 41337}, {699, 31}, {798, 9429}, {897, 36821}, {1580, 51322}, {1581, 47648}, {1910, 32540}, {1966, 39080}, {1967, 69947}, {2227, 59802}, {3225, 1}, {8858, 63}, {8864, 17799}, {32544, 1580}, {34248, 67002}, {43761, 6}, {51992, 1967}, {66842, 75}, {69910, 1959}, {69957, 65925}
X(70037) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {51912, 51914, 799}, {51914, 52138, 51912}

X(70038) = X(3)X(8694)∩X(84)X(165)

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

X(70038) lies on the cubics K297, K654, and K760, and these lines: {3, 8694}, {6, 1334}, {8, 4606}, {84, 165}, {183, 53658}, {220, 34074}, {5687, 35339}, {6766, 61121}, {32636, 56237}

X(70038) = isogonal conjugate of X(34244)
X(70038) = X(i)-isoconjugate of X(j) for these (i,j): {1, 34244}, {4801, 58946}
X(70038) = X(3)-Dao conjugate of X(34244)
X(70038) = barycentric product X(i)*X(j) for these {i,j}: {2334, 34255}, {5936, 54322}, {25430, 57279}, {34046, 56086}
X(70038) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 34244}, {34046, 21454}, {54322, 3616}, {57279, 19804}

X(70039) = X(4)X(5913)∩X(6)X(5505)

Barycentrics   a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^6 - 3*a^4*b^2 - a^2*b^4 + 3*b^6 - 3*a^4*c^2 + 14*a^2*b^2*c^2 - 11*b^4*c^2 - a^2*c^4 - 11*b^2*c^4 + 3*c^6) : :

X(70039) lies on the Moses-Parry circle and these lines: {2, 5523}, {3, 56922}, {4, 5913}, {6, 5505}, {24, 39576}, {25, 187}, {111, 378}, {112, 1995}, {115, 5094}, {154, 67303}, {186, 20481}, {232, 8585}, {381, 1560}, {427, 5203}, {468, 2453}, {1344, 8106}, {1345, 8105}, {3066, 35325}, {3162, 5020}, {3172, 30734}, {3291, 10311}, {3569, 11472}, {5013, 52293}, {5064, 68498}, {5158, 11284}, {5210, 37969}, {6644, 8428}, {7577, 9745}, {8430, 14687}, {8541, 67553}, {8743, 16042}, {9209, 9756}, {10249, 35901}, {13854, 69286}, {15922, 64213}, {21213, 62369}, {22111, 44102}, {35259, 61207}, {50718, 66376}

X(70039) = circumcircle-inverse of X(56922)
X(70039) = orthocentroidal-circle-inverse of X(1560)
X(70039) = polar-circle-inverse of X(5913)
X(70039) = orthoptic-circle-of-the-Steiner-inellipse-inverse of X(5523)
X(70039) = psi-transform of X(10766)

X(70040) = X(3)X(46970)∩X(4)X(5984)

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

X(70040) lies on the cubics K028 and K1013 and these lines: {3, 46970}, {4, 5984}, {32, 14370}, {76, 65278}, {182, 34130}, {3407, 9477}, {7785, 39938}, {18898, 46286}, {40820, 60860}

X(70040) = X(i)-Ceva conjugate of X(j) for these (i,j): {9477, 46286}, {65278, 14316}
X(70040) = X(19576)-cross conjugate of X(6660)
X(70040) = X(17799)-isoconjugate of X(43696)
X(70040) = X(i)-Dao conjugate of X(j) for these (i,j): {1691, 8290}, {46669, 9479}
X(70040) = barycentric product X(i)*X(j) for these {i,j}: {5207, 46286}, {6660, 11606}, {9477, 19576}, {14316, 46970}
X(70040) = barycentric quotient X(i)/X(j) for these {i,j}: {6660, 7779}, {19558, 2076}, {19559, 17799}, {19576, 8290}, {46286, 43696}

X(70041) = X(3)X(22456)∩X(4)X(290)

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

X(70041) lies on the cubics K028 and K1319 and these lines: {3, 22456}, {4, 290}, {76, 53200}, {264, 57541}, {276, 15412}, {458, 34536}, {9291, 16083}, {14382, 37124}, {16081, 40815}, {16089, 39682}, {41204, 64227}, {44144, 46271}, {54114, 57799}

X(70041) = polar conjugate of X(57500)
X(70041) = X(57541)-Ceva conjugate of X(60199)
X(70041) = X(62595)-cross conjugate of X(16089)
X(70041) = X(i)-isoconjugate of X(j) for these (i,j): {48, 57500}, {1755, 52177}, {9247, 40804}, {9417, 14941}
X(70041) = X(i)-Dao conjugate of X(j) for these (i,j): {297, 11672}, {1249, 57500}, {14382, 3}, {36899, 52177}, {38974, 39469}, {39058, 14941}, {39081, 3289}, {62576, 40804}
X(70041) = cevapoint of X(16089) and X(62595)
X(70041) = trilinear pole of line {6130, 16089}
X(70041) = barycentric product X(i)*X(j) for these {i,j}: {290, 16089}, {401, 60199}, {6130, 65272}, {16081, 44137}, {18022, 32545}, {18024, 41204}, {57541, 62595}, {57844, 64227}
X(70041) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 57500}, {98, 52177}, {264, 40804}, {290, 14941}, {401, 3289}, {879, 53175}, {6130, 39469}, {16081, 1987}, {16089, 511}, {22456, 65305}, {32545, 184}, {41204, 237}, {44137, 36212}, {58311, 9418}, {60199, 1972}, {62595, 11672}, {64227, 418}
X(70041) = {X(18027),X(51257)}-harmonic conjugate of X(60199)

X(70042) = X(3)X(65271)∩X(5)X(76)

Barycentrics   (a^2*b^2 - b^4 + 2*a^2*c^2 + b^2*c^2)*(2*a^2*b^2 + a^2*c^2 + b^2*c^2 - c^4)*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6 + a^6*c^2 - 3*a^4*b^2*c^2 + 3*a^2*b^4*c^2 - b^6*c^2 - 2*a^4*c^4 + 3*a^2*b^2*c^4 + 2*b^4*c^4 + a^2*c^6 - b^2*c^6) : :
X(70042) = 4 X[5] - 3 X[64621], 3 X[262] - 2 X[69771], X[20] - 3 X[57450]

X(70042) lies on the cubics K071 and K778 and these lines: {3, 65271}, {5, 76}, {20, 39682}, {69, 40803}, {98, 70032}, {376, 67084}, {511, 67179}, {576, 70033}, {631, 43718}, {1972, 15595}, {10519, 66974}, {11672, 14252}, {12110, 34386}, {12251, 51997}, {15069, 66879}, {15318, 56866}, {26714, 60601}, {51338, 63428}, {52247, 67175}

X(70042) = X(i)-Ceva conjugate of X(j) for these (i,j): {40803, 262}, {65271, 54257}
X(70042) = X(67187)-Dao conjugate of X(40815)
X(70042) = barycentric product X(i)*X(j) for these {i,j}: {327, 40805}, {47739, 59257}
X(70042) = barycentric quotient X(i)/X(j) for these {i,j}: {262, 40815}, {40805, 182}, {42313, 43711}, {47739, 33971}, {54269, 3288}

X(70043) = X(1)X(20596)∩X(6)X(20462)

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

X(70043) lies on the cubics K1021 and K1029 and these lines: {1, 20596}, {6, 20462}, {32, 66931}, {182, 8927}, {184, 69912}, {560, 40736}, {1397, 2210}, {1501, 45217}, {1974, 18262}, {1980, 68125}, {2053, 2194}, {2162, 20986}, {2175, 16283}, {3955, 17105}, {9454, 18269}, {18759, 51974}, {44120, 45209}, {51321, 60722}

X(70043) = isogonal conjugate of X(69913)
X(70043) = isogonal conjugate of the isotomic conjugate of X(2053)
X(70043) = X(i)-cross conjugate of X(j) for these (i,j): {41, 2175}, {23550, 6}
X(70043) = X(i)-isoconjugate of X(j) for these (i,j): {1, 69913}, {2, 30545}, {7, 6376}, {43, 6063}, {57, 6382}, {75, 3212}, {76, 1423}, {85, 192}, {226, 31008}, {279, 4110}, {331, 22370}, {349, 27644}, {350, 63489}, {514, 66991}, {561, 1403}, {604, 40367}, {664, 20906}, {1088, 27538}, {1441, 33296}, {1447, 70000}, {1463, 64226}, {1502, 41526}, {1978, 43051}, {2176, 20567}, {2209, 41283}, {3208, 57792}, {3596, 62791}, {3676, 36863}, {3835, 4554}, {3971, 57785}, {4077, 62530}, {4083, 4572}, {4147, 4569}, {4595, 24002}, {4625, 21051}, {6358, 7304}, {7178, 36860}, {7179, 69911}, {7196, 63486}, {7209, 53675}, {7249, 41318}, {10030, 40848}, {18033, 41531}, {20760, 57787}, {21138, 67038}, {25098, 46404}, {30097, 63243}, {40844, 43040}, {50491, 55213}, {52136, 69662}, {52621, 52923}
X(70043) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 69913}, {206, 3212}, {3161, 40367}, {5452, 6382}, {20547, 20635}, {32664, 30545}, {39025, 20906}, {40368, 1403}, {57264, 20649}, {62574, 41283}
X(70043) = cevapoint of X(41) and X(57264)
X(70043) = crosspoint of X(7121) and X(57264)
X(70043) = crosssum of X(i) and X(j) for these (i,j): {1, 20608}, {2, 20350}, {6376, 30545}
X(70043) = barycentric product X(i)*X(j) for these {i,j}: {1, 57264}, {6, 2053}, {9, 7121}, {21, 21759}, {31, 2319}, {32, 7155}, {33, 15373}, {41, 87}, {55, 2162}, {60, 6378}, {284, 23493}, {330, 2175}, {560, 27424}, {607, 23086}, {663, 34071}, {932, 3063}, {1172, 22381}, {1253, 7153}, {2150, 7148}, {2194, 16606}, {2330, 51974}, {2344, 69912}, {6383, 9448}, {6384, 9447}, {7077, 51321}, {7252, 65163}, {8851, 51864}, {18265, 39914}, {18269, 39924}, {34252, 51858}, {40736, 52133}, {42027, 57657}
X(70043) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 69913}, {8, 40367}, {31, 30545}, {32, 3212}, {41, 6376}, {55, 6382}, {87, 20567}, {330, 41283}, {560, 1423}, {692, 66991}, {1253, 4110}, {1501, 1403}, {1917, 41526}, {1922, 63489}, {1980, 43051}, {2053, 76}, {2162, 6063}, {2175, 192}, {2194, 31008}, {2319, 561}, {3063, 20906}, {6378, 34388}, {6383, 41287}, {7121, 85}, {7155, 1502}, {9447, 43}, {9448, 2176}, {14827, 27538}, {15373, 7182}, {18265, 40848}, {21759, 1441}, {22381, 1231}, {23086, 57918}, {23493, 349}, {23550, 20338}, {27424, 1928}, {34071, 4572}, {40736, 7179}, {51321, 18033}, {51858, 70000}, {57264, 75}, {57657, 33296}, {65375, 36860}, {69912, 69662}
X(70043) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 20608, 20596}, {6, 20473, 20462}

X(70044) = X(3)X(95)∩X(14)X(275)

Barycentrics   (Sqrt[3]*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2) - 2*(a^2 - b^2 - c^2)*S)/((a^2 - b^2 - c^2)*(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)) : :

X(70044) lies on the cubics K112 and K1133a and these lines: {3, 95}, {4, 19713}, {14, 275}, {54, 41897}, {470, 51275}, {472, 8175}, {19169, 44667}, {36760, 51220}, {39286, 54306}

X(70044) = isogonal conjugate of X(51242)
X(70044) = X(i)-isoconjugate of X(j) for these (i,j): {1, 51242}, {1953, 64246}, {2992, 62266}, {3438, 44706}
X(70044) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 51242}, {15, 44711}, {46666, 15451}
X(70044) = barycentric product X(i)*X(j) for these {i,j}: {275, 621}, {276, 3129}, {11093, 51268}, {14368, 65360}, {46138, 64250}, {51275, 65579}
X(70044) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 51242}, {54, 64246}, {275, 2992}, {621, 343}, {3129, 216}, {8882, 3438}, {11093, 33530}, {40580, 44711}, {51270, 44713}, {64250, 1154}, {65579, 33529}
X(70044) = {X(6117),X(33497)}-harmonic conjugate of X(473)

X(70045) = X(3)X(95)∩X(13)X(275)

Barycentrics   (Sqrt[3]*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2) + 2*(a^2 - b^2 - c^2)*S)/((a^2 - b^2 - c^2)*(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)) : :

X(70045) lies on the cubics K112 and K1133b and these lines: {3, 95}, {4, 19712}, {13, 275}, {54, 41898}, {471, 51268}, {473, 8174}, {19169, 44666}, {36759, 51219}, {39286, 54307}

X(70045) = isogonal conjugate of X(51243)
X(70045) = X(i)-isoconjugate of X(j) for these (i,j): {1, 51243}, {1953, 64245}, {2993, 62266}, {3439, 44706}
X(70045) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 51243}, {16, 44712}, {46667, 15451}
X(70045) = barycentric product X(i)*X(j) for these {i,j}: {275, 622}, {276, 3130}, {11094, 51275}, {14369, 65360}, {46138, 64251}, {51268, 65580}
X(70045) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 51243}, {54, 64245}, {275, 2993}, {622, 343}, {3130, 216}, {8882, 3439}, {11094, 33529}, {40581, 44712}, {51277, 44714}, {64251, 1154}, {65580, 33530}
X(70045) = {X(6116),X(33496)}-harmonic conjugate of X(472)

X(70046) = X(6)X(15369)∩X(69)X(1368)

Barycentrics   a^2*(a^2 + b^2 - 3*c^2)*(a^2 - b^2 - c^2)*(a^2 - 3*b^2 + c^2)*(a^6 - 5*a^4*b^2 - 5*a^2*b^4 + b^6 - 5*a^4*c^2 + 18*a^2*b^2*c^2 - b^4*c^2 - 5*a^2*c^4 - b^2*c^4 + c^6) : :

X(70046) lies on the cubics K1165 and K1314 and these lines: {6, 15369}, {69, 1368}, {3565, 40318}, {5254, 14248}, {6467, 8770}, {19118, 65178}, {19459, 53059}, {19588, 65311}, {52545, 60839}

X(70046) = reflection of X(15369) in X(6)
X(70046) = orthic-isogonal conjugate of X(8770)
X(70046) = X(4)-Ceva conjugate of X(8770)
X(70046) = X(18156)-isoconjugate of X(40324)
X(70046) = X(i)-Dao conjugate of X(j) for these (i,j): {6391, 69}, {15261, 40324}
X(70046) = barycentric product X(2996)*X(40321)
X(70046) = barycentric quotient X(i)/X(j) for these {i,j}: {40321, 193}, {53059, 40324}

X(70047) = X(2)X(36823)∩X(6)X(36183)

Barycentrics   a^2*(a - b)*(a + b)*(a - c)*(a + c)*(a^8*b^2 - 2*a^6*b^4 + 2*a^2*b^8 - b^10 + a^8*c^2 - a^6*b^2*c^2 - a^4*b^4*c^2 - a^2*b^6*c^2 + 2*b^8*c^2 - a^6*c^4 + 4*a^4*b^2*c^4 - a^2*b^4*c^4 - a^4*c^6 - a^2*b^2*c^6 - 2*b^4*c^6 + a^2*c^8 + b^2*c^8)*(a^8*b^2 - a^6*b^4 - a^4*b^6 + a^2*b^8 + a^8*c^2 - a^6*b^2*c^2 + 4*a^4*b^4*c^2 - a^2*b^6*c^2 + b^8*c^2 - 2*a^6*c^4 - a^4*b^2*c^4 - a^2*b^4*c^4 - 2*b^6*c^4 - a^2*b^2*c^6 + 2*a^2*c^8 + 2*b^2*c^8 - c^10) : :

X(70047) lies on the cubics K1352 and K1353 and these lines: {2, 36823}, {6, 36183}, {39, 14264}, {51, 51980}, {110, 61216}, {512, 46592}, {525, 2421}, {647, 14966}, {648, 43665}, {878, 1576}, {1625, 10097}, {2433, 35325}, {2493, 2781}, {2501, 58070}, {2623, 61207}, {3016, 39985}, {3049, 60505}, {6103, 65733}, {14582, 41512}, {56395, 60589}, {60496, 60587}, {60507, 60509}

X(70047) = isogonal conjugate of X(62307)
X(70047) = isogonal conjugate of the anticomplement of X(18312)
X(70047) = X(1640)-cross conjugate of X(6)
X(70047) = X(i)-isoconjugate of X(j) for these (i,j): {1, 62307}, {656, 41253}, {662, 36189}, {1577, 15462}, {32679, 53768}
X(70047) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 62307}, {1084, 36189}, {40596, 41253}, {42426, 60513}, {65728, 65732}
X(70047) = cevapoint of X(3049) and X(5191)
X(70047) = trilinear pole of line {237, 2393}
X(70047) = barycentric product X(i)*X(j) for these {i,j}: {110, 65618}, {648, 65736}
X(70047) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 62307}, {112, 41253}, {512, 36189}, {1576, 15462}, {1640, 65732}, {6103, 60513}, {14560, 53768}, {65618, 850}, {65736, 525}

X(70048) = X(6)X(888)∩X(99)X(187)

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

X(70048) lies on the cubics K150 and K222 and these lines: {6, 888}, {99, 187}, {111, 1645}, {729, 46303}, {887, 14609}, {5106, 9149}, {5118, 52067}, {9147, 41309}, {23342, 35073}, {31128, 63747}, {43765, 64479}

X(70048) = X(i)-isoconjugate of X(j) for these (i,j): {5969, 37132}, {11182, 36133}
X(70048) = X(i)-Dao conjugate of X(j) for these (i,j): {38998, 5969}, {39010, 11182}
X(70048) = trilinear pole of line {3231, 38366}
X(70048) = barycentric product X(i)*X(j) for these {i,j}: {538, 5970}, {3231, 35146}, {5118, 60226}, {14606, 23342}, {14609, 69948}, {47646, 67007}
X(70048) = barycentric quotient X(i)/X(j) for these {i,j}: {888, 11182}, {3231, 5969}, {5118, 14607}, {5970, 3228}, {14606, 60028}, {33875, 5106}, {35146, 34087}, {46522, 56390}, {60226, 66278}
X(70048) = {X(99),X(47646)}-harmonic conjugate of X(69948)

X(70049) = X(2)X(2987)∩X(69)X(8754)

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

X(70049) lies on the cubics K185 and K778 and these lines: {2, 2987}, {69, 8754}, {76, 42298}, {193, 15525}, {287, 55266}, {297, 57553}, {524, 65277}, {2374, 10425}, {3563, 55023}, {6337, 40819}, {6353, 57216}, {9307, 52091}, {17040, 43705}, {32654, 40405}, {51374, 70035}, {55122, 62645}

X(70049) = reflection of X(i) in X(j) for these {i,j}: {193, 15525}, {35136, 69}
X(70049) = isogonal conjugate of X(67168)
X(70049) = isotomic conjugate of X(70020)
X(70049) = antitomic image of X(193)
X(70049) = isotomic conjugate of the isogonal conjugate of X(69778)
X(70049) = isotomic conjugate of the polar conjugate of X(63613)
X(70049) = X(35142)-Ceva conjugate of X(8781)
X(70049) = X(i)-cross conjugate of X(j) for these (i,j): {193, 70035}, {51613, 3566}, {69778, 63613}
X(70049) = X(i)-isoconjugate of X(j) for these (i,j): {1, 67168}, {31, 70020}, {230, 38252}, {1692, 8769}, {1733, 53059}, {8770, 8772}
X(70049) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 70020}, {3, 67168}, {69, 3564}, {3566, 51613}, {15525, 55122}, {51579, 230}
X(70049) = cevapoint of X(i) and X(j) for these (i,j): {193, 51374}, {3566, 51613}
X(70049) = crosspoint of X(35142) and X(63613)
X(70049) = trilinear pole of line {3566, 6337}
X(70049) = barycentric product X(i)*X(j) for these {i,j}: {69, 63613}, {76, 69778}, {193, 8781}, {325, 70035}, {2987, 57518}, {3566, 65277}, {6337, 35142}, {6353, 57872}, {8773, 18156}, {40428, 51374}, {43705, 54412}, {57216, 62645}
X(70049) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 70020}, {6, 67168}, {193, 230}, {1707, 8772}, {2987, 8770}, {3053, 1692}, {3167, 52144}, {3563, 14248}, {3566, 55122}, {6337, 3564}, {6353, 460}, {8651, 42663}, {8773, 8769}, {8781, 2996}, {10425, 3565}, {15525, 51613}, {18156, 1733}, {19118, 44099}, {32459, 5477}, {32654, 53059}, {35142, 34208}, {36051, 38252}, {42065, 40319}, {43705, 6391}, {51374, 114}, {51613, 55152}, {54412, 44145}, {57216, 4226}, {57518, 51481}, {57872, 6340}, {58766, 65484}, {59707, 51335}, {63613, 4}, {65277, 35136}, {65484, 68175}, {69778, 6}, {70035, 98}
X(70049) = {X(2987),X(57872)}-harmonic conjugate of X(8781)

X(70050) = X(2)X(1429)∩X(6)X(983)

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

X(70050) lies on the cubics K285 and K1013 and these lines: {2, 1429}, {6, 983}, {31, 19589}, {32, 2319}, {1376, 1580}, {2344, 60726}, {2345, 56196}, {40415, 60721}, {43265, 48864}

X(70050) = isogonal conjugate of X(67174)
X(70050) = isogonal conjugate of the isotomic conjugate of X(70022)
X(70050) = X(3407)-Ceva conjugate of X(983)
X(70050) = X(i)-isoconjugate of X(j) for these (i,j): {1, 67174}, {982, 69938}, {2275, 41527}, {3094, 47647}, {3116, 63902}, {7220, 41777}
X(70050) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 67174}, {984, 3314}
X(70050) = barycentric product X(i)*X(j) for these {i,j}: {6, 70022}, {983, 24349}, {3113, 19586}, {3114, 19587}, {3407, 19584}, {4334, 56180}, {4621, 54249}, {7033, 21010}, {17743, 17754}, {54271, 65291}
X(70050) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 67174}, {983, 41527}, {3407, 63902}, {4334, 7185}, {17754, 3662}, {19584, 3314}, {19586, 51836}, {19587, 3094}, {21010, 982}, {21101, 20234}, {24349, 33930}, {54249, 3776}, {54251, 3777}, {54271, 3810}, {70022, 76}

X(70051) = X(69)X(694)∩X(76)X(115)

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

X(70051) lies on the cubics K322 and K778 and these lines: {2, 19222}, {69, 694}, {76, 115}, {141, 9229}, {194, 47642}, {248, 39291}, {257, 66933}, {297, 67078}, {335, 1581}, {384, 3491}, {385, 3225}, {805, 5167}, {1975, 30496}, {3186, 53147}, {6234, 12251}, {7791, 46735}, {7806, 18872}, {8789, 33786}, {9227, 15993}, {9307, 15595}, {9983, 42486}, {14970, 65287}, {15391, 31635}, {37890, 46226}

X(70051) = isogonal conjugate of X(67069)
X(70051) = isotomic conjugate of X(39927)
X(70051) = antitomic image of X(51843)
X(70051) = isotomic conjugate of the isogonal conjugate of X(47642)
X(70051) = X(i)-Ceva conjugate of X(j) for these (i,j): {694, 1916}, {39291, 2524}
X(70051) = X(i)-isoconjugate of X(j) for these (i,j): {1, 67069}, {31, 39927}, {385, 34248}, {1580, 3224}, {1691, 3223}, {1933, 2998}, {1966, 51951}, {3504, 56828}, {14602, 18832}
X(70051) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 39927}, {3, 67069}, {76, 3978}, {9467, 51951}, {32746, 385}, {39092, 3224}, {47648, 67170}
X(70051) = cevapoint of X(3229) and X(3491)
X(70051) = crosspoint of X(694) and X(47642)
X(70051) = crosssum of X(385) and X(39927)
X(70051) = barycentric product X(i)*X(j) for these {i,j}: {76, 47642}, {194, 1916}, {694, 6374}, {1581, 17149}, {1613, 18896}, {1740, 1934}, {1967, 18837}, {3186, 40708}, {18829, 23301}, {20910, 37134}, {36214, 51843}, {57150, 66267}
X(70051) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 39927}, {6, 67069}, {194, 385}, {694, 3224}, {1581, 3223}, {1613, 1691}, {1740, 1580}, {1916, 2998}, {1934, 18832}, {1967, 34248}, {3186, 419}, {3221, 5027}, {6374, 3978}, {9468, 51951}, {11325, 44089}, {17149, 1966}, {17970, 15389}, {18829, 3222}, {18837, 1926}, {18896, 40162}, {21056, 69579}, {21080, 4039}, {21191, 4107}, {23301, 804}, {23807, 14296}, {36214, 3504}, {38834, 56975}, {40708, 43714}, {40810, 67170}, {46161, 65172}, {47642, 6}, {50516, 4164}, {51427, 36213}, {51843, 17984}, {51913, 56828}, {56836, 1933}, {56977, 42551}, {57150, 17941}, {69947, 67002}
X(70051) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {76, 42061, 1916}, {18896, 56978, 1916}

X(70052) = X(335)X(1926)∩X(350)X(694)

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

X(70052) lies on the cubics K322 and K994 and these lines: {335, 1926}, {350, 694}, {384, 8868}, {385, 1911}, {698, 3862}, {1575, 2669}, {1909, 52205}, {2227, 17759}, {36906, 63489}, {41535, 52043}, {54117, 63892}

X(70052) = isogonal conjugate of X(18274)
X(70052) = isotomic conjugate of X(19579)
X(70052) = isotomic conjugate of the isogonal conjugate of X(63893)
X(70052) = X(76)-cross conjugate of X(335)
X(70052) = X(i)-isoconjugate of X(j) for these (i,j): {1, 18274}, {2, 30634}, {6, 19580}, {31, 19579}, {32, 19581}, {238, 18278}, {385, 57265}, {560, 18277}, {1580, 51979}, {1691, 69935}, {1914, 3510}, {1933, 40849}, {2201, 23186}, {2210, 19565}, {8875, 19561}, {14599, 19567}, {14602, 69956}, {18275, 18892}, {20663, 40755}
X(70052) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 19579}, {3, 18274}, {9, 19580}, {6374, 18277}, {6376, 19581}, {9470, 18278}, {32664, 30634}, {36906, 3510}, {39092, 51979}, {62557, 19565}
X(70052) = cevapoint of X(7168) and X(8868)
X(70052) = barycentric product X(i)*X(j) for these {i,j}: {1, 30633}, {75, 24576}, {76, 63893}, {334, 7168}, {335, 69954}, {1581, 52175}, {1916, 39933}, {1934, 51920}, {8868, 63895}, {18895, 51919}, {18896, 67073}, {44172, 70034}
X(70052) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 19580}, {2, 19579}, {6, 18274}, {31, 30634}, {75, 19581}, {76, 18277}, {291, 3510}, {292, 18278}, {295, 23186}, {334, 19567}, {335, 19565}, {694, 51979}, {1581, 69935}, {1916, 40849}, {1934, 69956}, {1967, 57265}, {7168, 238}, {8868, 19557}, {18895, 18275}, {24479, 8875}, {24576, 1}, {30633, 75}, {39933, 385}, {40098, 64233}, {40782, 17475}, {51919, 1914}, {51920, 1580}, {52175, 1966}, {63893, 6}, {67073, 1691}, {69954, 239}, {70034, 2210}

X(70053) = X(3)X(57487)∩X(74)X(186)

Barycentrics   a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^4 - 2*a^2*b^2 + b^4 + a^2*c^2 + b^2*c^2 - 2*c^4)*(a^4 + a^2*b^2 - 2*b^4 - 2*a^2*c^2 + b^2*c^2 + c^4)*(5*a^8 - 11*a^6*b^2 + 3*a^4*b^4 + 7*a^2*b^6 - 4*b^8 - 11*a^6*c^2 + 23*a^4*b^2*c^2 - 13*a^2*b^4*c^2 + b^6*c^2 + 3*a^4*c^4 - 13*a^2*b^2*c^4 + 6*b^4*c^4 + 7*a^2*c^6 + b^2*c^6 - 4*c^8) : :

X(70053) lies on the cubics K523 and K639 and these lines: {3, 57487}, {25, 38937}, {30, 16080}, {74, 186}, {250, 15055}, {1494, 44280}, {1552, 37942}, {2071, 3284}, {2693, 8431}, {3470, 17506}, {5627, 13619}, {5667, 43911}, {6623, 59434}, {7480, 15021}, {10151, 10152}, {10295, 10421}, {10419, 22455}, {10990, 57587}, {11410, 35908}, {14264, 35472}, {14919, 37941}, {17986, 37931}, {21844, 52130}, {37487, 57488}, {52646, 55572}, {56369, 57471}, {57584, 68642}

X(70053) = X(250)-Ceva conjugate of X(1304)
X(70053) = X(656)-isoconjugate of X(43941)
X(70053) = X(i)-Dao conjugate of X(j) for these (i,j): {2394, 339}, {40596, 43941}
X(70053) = crossdifference of every pair of points on line {14401, 57295}
X(70053) = barycentric product X(i)*X(j) for these {i,j}: {648, 57147}, {1304, 63248}, {15051, 16080}
X(70053) = barycentric quotient X(i)/X(j) for these {i,j}: {112, 43941}, {15051, 11064}, {57147, 525}, {63248, 66073}
X(70053) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {74, 186, 68546}, {186, 68546, 1304}, {10295, 40630, 10421}

X(70054) = X(2)X(36891)∩X(30)X(115)

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

X(70054) lies on the cubics K599 and K1367 and these lines: {2, 36891}, {4, 54495}, {6, 9214}, {30, 115}, {249, 671}, {338, 524}, {460, 1990}, {512, 61675}, {523, 6128}, {843, 34169}, {1640, 65610}, {1989, 31644}, {3163, 61339}, {3815, 35606}, {5254, 15454}, {5306, 35906}, {5641, 41254}, {6034, 34175}, {7468, 44533}, {7745, 14254}, {8370, 14608}, {9300, 18872}, {18314, 65611}, {21043, 69545}, {30452, 36299}, {30453, 36298}, {34294, 53416}, {36889, 67531}, {52661, 60428}

X(70054) = midpoint of X(51441) and X(57598)
X(70054) = isogonal conjugate of X(54439)
X(70054) = polar conjugate of the isotomic conjugate of X(65729)
X(70054) = X(51428)-cross conjugate of X(523)
X(70054) = X(i)-isoconjugate of X(j) for these (i,j): {1, 54439}, {163, 65710}, {662, 34291}, {1101, 65608}
X(70054) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 54439}, {115, 65710}, {523, 65608}, {1084, 34291}
X(70054) = cevapoint of X(i) and X(j) for these (i,j): {6, 44533}, {115, 1640}
X(70054) = crosssum of X(47079) and X(66354)
X(70054) = trilinear pole of line {351, 1637}
X(70054) = barycentric product X(i)*X(j) for these {i,j}: {4, 65729}, {30, 54495}, {523, 65716}
X(70054) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 54439}, {115, 65608}, {512, 34291}, {523, 65710}, {51428, 65728}, {54495, 1494}, {65716, 99}, {65729, 69}
X(70054) = {X(115),X(48721)}-harmonic conjugate of X(230)

X(70055) = X(30)X(69)∩X(66)X(56576)

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

X(70055) lies on the cubics K611 and K1315 and these lines: {30, 69}, {66, 56576}, {193, 2986}, {340, 59430}, {1494, 69985}, {3580, 69877}, {18554, 20423}, {37644, 40386}, {55848, 56571}, {56580, 69922}, {65715, 67736}

X(70055) = isotomic conjugate of X(59430)
X(70055) = polar conjugate of X(56710)
X(70055) = anticomplement of the isogonal conjugate of X(69877)
X(70055) = isotomic conjugate of the anticomplement of X(51471)
X(70055) = isotomic conjugate of the isogonal conjugate of X(52168)
X(70055) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {92, 59429}, {47649, 192}, {69877, 8}, {70001, 6360}
X(70055) = X(i)-cross conjugate of X(j) for these (i,j): {40909, 37645}, {51471, 2}
X(70055) = X(i)-isoconjugate of X(j) for these (i,j): {31, 59430}, {48, 56710}
X(70055) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 59430}, {1249, 56710}
X(70055) = barycentric product X(i)*X(j) for these {i,j}: {76, 52168}, {36889, 37645}
X(70055) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 59430}, {4, 56710}, {18533, 40138}, {36889, 60256}, {37645, 376}, {40387, 40385}, {52165, 69942}, {52168, 6}, {56270, 52487}, {65322, 53958}, {67080, 40348}, {69877, 58081}

X(70056) = X(4)X(160)∩X(39)X(51)

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

X(70056) lies on the cubics K622 and K1065 and these lines: {3, 36952}, {4, 160}, {39, 51}, {217, 4173}, {1298, 1614}, {3926, 51252}, {5562, 42487}, {7668, 43679}, {11257, 60520}, {23198, 56743}, {23208, 54003}, {37121, 60514}, {48259, 53701}

X(70056) = isogonal conjugate of X(54100)
X(70056) = isogonal conjugate of the anticomplement of X(46394)
X(70056) = isogonal conjugate of the isotomic conjugate of X(42487)
X(70056) = X(3269)-cross conjugate of X(39201)
X(70056) = X(i)-isoconjugate of X(j) for these (i,j): {1, 54100}, {75, 1629}, {92, 36794}, {158, 1078}, {393, 33764}, {823, 31296}, {1096, 33769}, {1969, 10312}, {2052, 18042}, {2207, 33778}, {3050, 57973}, {5012, 57806}, {7668, 23999}, {24000, 36901}, {24019, 57082}, {30506, 40440}=
X(70056) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 54100}, {206, 1629}, {1147, 1078}, {6503, 33769}, {22391, 36794}, {35071, 57082}
X(70056) = crosssum of X(1629) and X(36794)
X(70056) = barycentric product X(i)*X(j) for these {i,j}: {6, 42487}, {184, 36952}, {394, 27375}, {577, 3613}, {3269, 27867}, {11794, 39201}, {54032, 60497}
X(70056) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 54100}, {32, 1629}, {184, 36794}, {217, 30506}, {255, 33764}, {326, 33778}, {394, 33769}, {520, 57082}, {577, 1078}, {3269, 36901}, {3613, 18027}, {14575, 10312}, {14585, 5012}, {20775, 37125}, {27375, 2052}, {36952, 18022}, {39201, 31296}, {42487, 76}, {44088, 41334}, {52430, 18042}, {58310, 3050}, {61054, 27010}

X(70057) = X(2)X(14363)∩X(4)X(3527)

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

X(70057) lies on the cubics K813 and K917 and these lines: {2, 14363}, {4, 3527}, {253, 5056}, {1294, 3522}, {1990, 34818}, {2883, 52452}, {3346, 3523}, {3542, 18349}, {5068, 15319}, {6525, 38808}, {13464, 39130}, {16251, 49135}, {31361, 50691}, {35140, 69410}, {41372, 54211}, {51348, 62067}, {52301, 64815}

X(70057) = X(8797)-Ceva conjugate of X(8796)
X(70057) = X(i)-isoconjugate of X(j) for these (i,j): {631, 19614}, {2184, 36748}, {11402, 19611}
X(70057) = X(4)-Dao conjugate of X(631)
X(70057) = barycentric product X(i)*X(j) for these {i,j}: {20, 8796}, {1249, 8797}, {1895, 56033}, {3527, 15466}, {14249, 63154}, {14615, 34818}
X(70057) = barycentric quotient X(i)/X(j) for these {i,j}: {154, 36748}, {1249, 631}, {3172, 11402}, {3527, 1073}, {6525, 3087}, {8796, 253}, {8797, 34403}, {15466, 44149}, {34818, 64}, {44705, 47122}, {56033, 19611}, {57219, 65177}, {58950, 46639}, {63154, 15394}
X(70057) = {X(3527),X(8796)}-harmonic conjugate of X(11282)

X(70058) = X(335)X(40849)∩X(904)X(66999)

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

X(70058) lies on the cubics K863 and K991 and these lines: {335, 40849}, {904, 66999}, {1581, 1959}, {1755, 1967}, {1911, 41882}, {1926, 1934}, {1927, 1933}, {2236, 37134}, {3862, 41517}, {18272, 19555}, {52205, 59480}

X(70058) = X(i)-cross conjugate of X(j) for these (i,j): {2084, 37134}, {2085, 43763}
X(70058) = X(i)-isoconjugate of X(j) for these (i,j): {2, 4027}, {75, 51903}, {76, 51318}, {99, 68155}, {239, 27982}, {419, 12215}, {523, 46294}, {661, 46295}, {732, 56976}, {804, 17941}, {880, 5027}, {894, 53681}, {1580, 1966}, {1691, 3978}, {1926, 1933}, {4154, 17103}, {4366, 6645}, {4590, 35078}, {5026, 60863}, {5976, 40820}, {8623, 56979}, {9865, 64981}, {14295, 56980}, {14382, 36213}, {14602, 14603}, {16985, 54129}, {18901, 18902}, {19571, 51244}, {32544, 39080}, {35540, 56975}, {39291, 58850}, {52395, 61063}, {56971, 67160}
X(70058) = X(i)-Dao conjugate of X(j) for these (i,j): {206, 51903}, {9467, 1580}, {32664, 4027}, {36830, 46295}, {38986, 68155}, {39092, 1966}
X(70058) = cevapoint of X(694) and X(59480)
X(70058) = barycentric product X(i)*X(j) for these {i,j}: {1, 41517}, {561, 66998}, {694, 1581}, {882, 37134}, {1916, 1967}, {1927, 18896}, {1934, 9468}, {17980, 66933}, {30663, 59480}, {40099, 70018}, {43763, 56978}, {56977, 67149}, {66942, 68575}
X(70058) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 4027}, {32, 51903}, {110, 46295}, {163, 46294}, {560, 51318}, {694, 1966}, {798, 68155}, {904, 53681}, {1581, 3978}, {1911, 27982}, {1916, 1926}, {1927, 1691}, {1934, 14603}, {1967, 385}, {3493, 19574}, {8789, 1933}, {8871, 18270}, {9468, 1580}, {17938, 56982}, {37134, 880}, {40099, 64222}, {40729, 4154}, {41517, 75}, {43763, 56979}, {51954, 19572}, {56978, 67160}, {59480, 39044}, {66942, 12215}, {66998, 31}, {67149, 56976}, {69947, 51912}, {70018, 6645}

X(70059) = X(38)X(9285)∩X(257)X(40847)

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

X(70059) lies on the cubics K863 and K991 and these lines: {38, 9285}, {257, 40847}, {695, 59480}, {711, 817}, {745, 783}, {904, 67000}, {1925, 1934}, {1927, 1932}, {1964, 9288}, {14946, 21814}, {18272, 19555}, {18828, 57938}, {21035, 51982}, {57937, 57961}

X(70059) = X(i)-isoconjugate of X(j) for these (i,j): {2, 16985}, {75, 51904}, {76, 51320}, {384, 385}, {419, 37894}, {710, 40416}, {782, 4577}, {827, 35558}, {1580, 1965}, {1582, 1966}, {1691, 9230}, {1915, 3978}, {1925, 1933}, {1926, 1932}, {4027, 54130}, {4074, 56976}, {8623, 69953}, {16101, 19576}, {17941, 68787}, {17984, 37893}, {19585, 22252}, {35530, 38826}, {36432, 54129}
X(70059) = X(i)-Dao conjugate of X(j) for these (i,j): {206, 51904}, {9467, 1582}, {32664, 16985}, {39092, 1965}, {55043, 35558}
X(70059) = crosssum of X(18272) and X(19555)
X(70059) = trilinear pole of line {2084, 2085}
X(70059) = barycentric product X(i)*X(j) for these {i,j}: {1, 51982}, {31, 40847}, {75, 14946}, {561, 67000}, {694, 9285}, {695, 1581}, {711, 4118}, {783, 8061}, {1916, 9288}, {1934, 51948}, {1967, 9229}, {2084, 18828}, {2085, 57937}, {9236, 18896}, {9239, 9468}, {37892, 66942}, {43763, 67165}, {69928, 69999}
X(70059) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 16985}, {32, 51904}, {560, 51320}, {694, 1965}, {695, 1966}, {711, 38847}, {783, 4593}, {1581, 9230}, {1916, 1925}, {1927, 1915}, {1967, 384}, {2084, 782}, {2085, 710}, {3505, 19574}, {4118, 35530}, {8061, 35558}, {8789, 1932}, {9229, 1926}, {9236, 1691}, {9239, 14603}, {9285, 3978}, {9288, 385}, {9468, 1582}, {14946, 1}, {18828, 37204}, {40847, 561}, {43763, 69953}, {51948, 1580}, {51982, 75}, {66942, 37894}, {67000, 31}, {67165, 67160}, {69928, 2236}

X(70060) = X(75)X(18036)∩X(290)X(18033)

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

X(70060) lies on the cubics K865 and K1020 and these lines: {75, 18036}, {290, 18033}, {304, 27424}, {561, 4388}, {1920, 19574}, {1921, 18896}, {3263, 63875}, {17787, 40846}, {18836, 24211}

X(70060) = isogonal conjugate of X(67145)
X(70060) = isotomic conjugate of X(41532)
X(70060) = isotomic conjugate of the isogonal conjugate of X(7061)
X(70060) = X(1966)-cross conjugate of X(1920)
X(70060) = X(i)-isoconjugate of X(j) for these (i,j): {1, 67145}, {6, 41882}, {31, 41532}, {32, 40873}, {256, 18262}, {560, 52135}, {694, 18038}, {893, 19554}, {904, 17798}, {1281, 1927}, {1501, 69914}, {1967, 19561}, {3509, 7104}, {4645, 66931}, {8789, 18037}, {9468, 19557}
X(70060) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 41532}, {3, 67145}, {9, 41882}, {6374, 52135}, {6376, 40873}, {8290, 19561}, {39030, 18037}, {39043, 18038}, {39044, 19557}, {40597, 19554}, {62610, 1281}, {62650, 17798}
X(70060) = crosssum of X(23868) and X(51931)
X(70060) = barycentric product X(i)*X(j) for these {i,j}: {75, 40846}, {76, 7061}, {561, 41534}, {894, 18036}, {1909, 40845}, {1920, 7261}, {1926, 24479}, {1928, 70009}, {1966, 63895}, {3978, 63875}, {14603, 30648}
X(70060) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 41882}, {2, 41532}, {6, 67145}, {75, 40873}, {76, 52135}, {171, 19554}, {172, 18262}, {385, 19561}, {561, 69914}, {894, 17798}, {1237, 4071}, {1580, 18038}, {1909, 3509}, {1920, 4645}, {1926, 18037}, {1966, 19557}, {3512, 904}, {3963, 20715}, {3978, 1281}, {7061, 6}, {7196, 5018}, {7261, 893}, {8852, 7104}, {8875, 57265}, {18036, 257}, {24479, 1967}, {30648, 9468}, {40845, 256}, {40846, 1}, {41534, 31}, {52175, 8868}, {63875, 694}, {63895, 1581}, {64231, 18786}, {65237, 29055}, {65293, 37137}, {66999, 1927}, {70009, 560}

X(70061) = X(105)X(43751)∩X(291)X(294)

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

X(70061) lies on the cubics K961 and K983 and these lines: {105, 43751}, {171, 63891}, {291, 294}, {518, 910}, {1281, 8932}, {2108, 2115}, {6654, 63878}, {8299, 8853}, {8300, 34253}, {8849, 8936}, {8852, 43747}

X(70061) = X(i)-cross conjugate of X(j) for these (i,j): {57, 34252}, {9472, 63872}
X(70061) = X(i)-isoconjugate of X(j) for these (i,j): {291, 1282}, {292, 20533}, {335, 20672}, {518, 70017}, {2114, 4876}, {3252, 62599}, {7077, 52160}, {8934, 40796}, {20692, 37128}, {27945, 52205}
X(70061) = X(i)-Dao conjugate of X(j) for these (i,j): {19557, 20533}, {39029, 1282}
X(70061) = barycentric product X(i)*X(j) for these {i,j}: {238, 69945}, {239, 9499}, {350, 9500}, {1429, 69998}, {1447, 70025}, {2115, 10030}, {6654, 63880}
X(70061) = barycentric quotient X(i)/X(j) for these {i,j}: {238, 20533}, {1428, 2114}, {1429, 52160}, {1438, 70017}, {1914, 1282}, {2115, 4876}, {2210, 20672}, {3747, 20692}, {8300, 27945}, {9499, 335}, {9500, 291}, {63880, 40217}, {69945, 334}, {69998, 66882}, {70025, 4518}

X(70062) = X(1)X(3329)∩X(6)X(292)

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

X(70062) lies on the cubics K991 and K997 and these lines: {1, 3329}, {6, 292}, {31, 18265}, {41, 1922}, {42, 4876}, {43, 40848}, {100, 19580}, {213, 904}, {291, 1193}, {334, 37678}, {385, 2664}, {386, 3864}, {741, 29199}, {875, 8660}, {1927, 2330}, {2176, 38986}, {2209, 21762}, {2210, 14598}, {2340, 20464}, {3009, 33854}, {3226, 5378}, {3747, 51928}, {4281, 56154}, {18268, 59192}, {19606, 34248}, {21803, 66882}, {27644, 41531}, {32748, 70034}, {33296, 70000}, {44090, 57653}, {51907, 51921}, {51992, 57265}, {52635, 70018}

X(70062) = isogonal conjugate of X(69955)
X(70062) = isogonal conjugate of the isotomic conjugate of X(41531)
X(70062) = X(1922)-Ceva conjugate of X(1911)
X(70062) = X(51973)-cross conjugate of X(1911)
X(70062) = X(i)-isoconjugate of X(j) for these (i,j): {1, 69955}, {2, 39914}, {75, 34252}, {76, 51321}, {87, 350}, {238, 6384}, {239, 330}, {385, 27447}, {659, 18830}, {812, 4598}, {874, 43931}, {932, 3766}, {1429, 27424}, {1447, 7155}, {1914, 6383}, {1921, 2162}, {2053, 18033}, {2319, 10030}, {3226, 56663}, {3253, 67196}, {3684, 7209}, {3975, 7153}, {3978, 51974}, {4010, 56053}, {5383, 27918}, {7121, 18891}, {8843, 18032}, {14199, 54128}, {16606, 30940}, {20332, 64225}, {23086, 40717}, {27450, 56042}, {33295, 42027}, {34071, 65101}, {45782, 63230}, {51837, 63237}, {52655, 63242}, {60244, 69887}
X(70062) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 69955}, {75, 44169}, {206, 34252}, {798, 27918}, {9470, 6384}, {32664, 39914}, {36906, 6383}, {40598, 18891}, {40610, 65101}
X(70062) = cevapoint of X(21762) and X(65498)
X(70062) = crosspoint of X(5378) and X(34067)
X(70062) = crosssum of X(3766) and X(27846)
X(70062) = crossdifference of every pair of points on line {812, 14296}
X(70062) = barycentric product X(i)*X(j) for these {i,j}: {1, 51973}, {6, 41531}, {31, 40848}, {32, 70000}, {41, 63489}, {43, 292}, {192, 1911}, {291, 2176}, {334, 62420}, {335, 2209}, {660, 20979}, {694, 51902}, {741, 20691}, {813, 4083}, {875, 4595}, {876, 69085}, {1403, 4876}, {1423, 7077}, {1581, 51319}, {1922, 6376}, {1967, 17752}, {3212, 51858}, {3572, 52923}, {3835, 34067}, {3971, 18268}, {4518, 41526}, {4562, 8640}, {4584, 50491}, {5378, 6377}, {6382, 14598}, {9468, 41318}, {18265, 30545}, {18893, 40367}, {21760, 33680}, {32937, 67005}, {40155, 62421}, {43534, 69068}
X(70062) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 69955}, {31, 39914}, {32, 34252}, {43, 1921}, {192, 18891}, {291, 6383}, {292, 6384}, {560, 51321}, {813, 18830}, {1403, 10030}, {1423, 18033}, {1911, 330}, {1922, 87}, {1927, 51974}, {1967, 27447}, {2176, 350}, {2209, 239}, {3009, 64225}, {3208, 4087}, {4083, 65101}, {6376, 44169}, {6382, 44171}, {7077, 27424}, {8640, 812}, {14598, 2162}, {17752, 1926}, {18265, 2319}, {18758, 56657}, {18897, 7121}, {20691, 35544}, {20979, 3766}, {21760, 56663}, {21762, 27846}, {34067, 4598}, {38832, 30940}, {38986, 27918}, {40848, 561}, {41318, 14603}, {41526, 1447}, {41531, 76}, {51319, 1966}, {51858, 7155}, {51902, 3978}, {51949, 14199}, {51973, 75}, {52923, 27853}, {56806, 33891}, {62420, 238}, {63489, 20567}, {65498, 62558}, {67005, 54128}, {69068, 33295}, {69085, 874}, {70000, 1502}

X(70063) = X(4)X(512)∩X(237)X(511)

Barycentrics   a^2*(a^2*b^2 - b^4 + a^2*c^2 - c^4)*(a^12*b^4 - 4*a^10*b^6 + 6*a^8*b^8 - 4*a^6*b^10 + a^4*b^12 + a^10*b^4*c^2 - 5*a^8*b^6*c^2 + 9*a^6*b^8*c^2 - 7*a^4*b^10*c^2 + 2*a^2*b^12*c^2 + a^12*c^4 + a^10*b^2*c^4 + 4*a^8*b^4*c^4 - 6*a^6*b^6*c^4 + 12*a^4*b^8*c^4 - 5*a^2*b^10*c^4 + b^12*c^4 - 4*a^10*c^6 - 5*a^8*b^2*c^6 - 6*a^6*b^4*c^6 - 12*a^4*b^6*c^6 + 3*a^2*b^8*c^6 - 4*b^10*c^6 + 6*a^8*c^8 + 9*a^6*b^2*c^8 + 12*a^4*b^4*c^8 + 3*a^2*b^6*c^8 + 6*b^8*c^8 - 4*a^6*c^10 - 7*a^4*b^2*c^10 - 5*a^2*b^4*c^10 - 4*b^6*c^10 + a^4*c^12 + 2*a^2*b^2*c^12 + b^4*c^12) : :
X(70063) = 3 X[6785] - X[34175]

X(70063) lies on the cubics K591 and these lines: {4, 512}, {113, 2679}, {237, 511}, {32444, 41330}, {35060, 47620}, {37114, 67352}, {37988, 67220}, {54003, 67349}

X(70063) = reflection of X(i) in X(j) for these {i,j}: {5167, 44227}, {47620, 35060}
X(70063) = polar-circle-inverse of X(68624)
X(70063) = crossdifference of every pair of points on line {2395, 3289}

X(70064) = X(4)X(14570)∩X(99)X(51843)

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

X(70064) lies on the cubic K591 and these lines: {4, 14570}, {99, 51843}, {1899, 2549}, {2782, 18474}, {5186, 67286}, {5254, 7668}, {6146, 34980}

X(70064) = orthic-isogonal conjugate of X(5167)
X(70064) = X(4)-Ceva conjugate of X(5167)
X(70064) = barycentric quotient X(5167)/X(60039)

X(70065) = X(4)X(54)∩X(5)X(52122)

Barycentrics   (a^2 - b^2 - c^2)*(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)*(2*a^16 - 7*a^14*b^2 + 8*a^12*b^4 - 4*a^10*b^6 + 5*a^8*b^8 - 7*a^6*b^10 + 2*a^4*b^12 + 2*a^2*b^14 - b^16 - 7*a^14*c^2 + 14*a^12*b^2*c^2 - 5*a^10*b^4*c^2 - 7*a^8*b^6*c^2 + 11*a^6*b^8*c^2 - 4*a^4*b^10*c^2 - 7*a^2*b^12*c^2 + 5*b^14*c^2 + 8*a^12*c^4 - 5*a^10*b^2*c^4 + 4*a^8*b^4*c^4 - 4*a^6*b^6*c^4 - 2*a^4*b^8*c^4 + 9*a^2*b^10*c^4 - 10*b^12*c^4 - 4*a^10*c^6 - 7*a^8*b^2*c^6 - 4*a^6*b^4*c^6 + 8*a^4*b^6*c^6 - 4*a^2*b^8*c^6 + 11*b^10*c^6 + 5*a^8*c^8 + 11*a^6*b^2*c^8 - 2*a^4*b^4*c^8 - 4*a^2*b^6*c^8 - 10*b^8*c^8 - 7*a^6*c^10 - 4*a^4*b^2*c^10 + 9*a^2*b^4*c^10 + 11*b^6*c^10 + 2*a^4*c^12 - 7*a^2*b^2*c^12 - 10*b^4*c^12 + 2*a^2*c^14 + 5*b^2*c^14 - c^16) : :

X(70065) lies on the cubic K591 and these lines: {4, 54}, {5, 52122}, {113, 35592}, {125, 16337}, {130, 5167}, {137, 13851}, {1568, 6368}, {6000, 18402}, {34304, 46966}

X(70065) = midpoint of X(4) and X(3484)
X(70065) = reflection of X(i) in X(j) for these {i,j}: {52122, 5}, {61440, 16810}
X(70065) = polar-circle-inverse of X(8884)
X(70065) = crossdifference of every pair of points on line {8882, 17434}

X(70066) = X(4)X(51)∩X(113)X(35579)

Barycentrics   a^2*(a^2 - b^2 - c^2)^2*(a^12*b^4 - 5*a^10*b^6 + 10*a^8*b^8 - 10*a^6*b^10 + 5*a^4*b^12 - a^2*b^14 + 4*a^10*b^4*c^2 - 15*a^8*b^6*c^2 + 20*a^6*b^8*c^2 - 10*a^4*b^10*c^2 + b^14*c^2 + a^12*c^4 + 4*a^10*b^2*c^4 + 10*a^8*b^4*c^4 - 10*a^6*b^6*c^4 - 5*a^4*b^8*c^4 + 6*a^2*b^10*c^4 - 6*b^12*c^4 - 5*a^10*c^6 - 15*a^8*b^2*c^6 - 10*a^6*b^4*c^6 + 20*a^4*b^6*c^6 - 5*a^2*b^8*c^6 + 15*b^10*c^6 + 10*a^8*c^8 + 20*a^6*b^2*c^8 - 5*a^4*b^4*c^8 - 5*a^2*b^6*c^8 - 20*b^8*c^8 - 10*a^6*c^10 - 10*a^4*b^2*c^10 + 6*a^2*b^4*c^10 + 15*b^6*c^10 + 5*a^4*c^12 - 6*b^4*c^12 - a^2*c^14 + b^2*c^14) : :

X(70066) lies on the cubic K591 and these lines: {4, 51}, {113, 35579}, {520, 4091}, {1147, 6760}, {10745, 13754}, {18445, 38283}, {34147, 43844}

X(70066) = reflection of X(34170) in X(63920)
X(70066) = polar-circle-inverse of X(1093)
X(70066) = crossdifference of every pair of points on line {393, 32320}

X(70067) = X(4)X(74)∩X(113)X(402)

Barycentrics   (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)*(2*a^16 - 3*a^14*b^2 - 8*a^12*b^4 + 16*a^10*b^6 + 5*a^8*b^8 - 27*a^6*b^10 + 18*a^4*b^12 - 2*a^2*b^14 - b^16 - 3*a^14*c^2 + 22*a^12*b^2*c^2 - 17*a^10*b^4*c^2 - 55*a^8*b^6*c^2 + 87*a^6*b^8*c^2 - 28*a^4*b^10*c^2 - 11*a^2*b^12*c^2 + 5*b^14*c^2 - 8*a^12*c^4 - 17*a^10*b^2*c^4 + 100*a^8*b^4*c^4 - 60*a^6*b^6*c^4 - 50*a^4*b^8*c^4 + 45*a^2*b^10*c^4 - 10*b^12*c^4 + 16*a^10*c^6 - 55*a^8*b^2*c^6 - 60*a^6*b^4*c^6 + 120*a^4*b^6*c^6 - 32*a^2*b^8*c^6 + 11*b^10*c^6 + 5*a^8*c^8 + 87*a^6*b^2*c^8 - 50*a^4*b^4*c^8 - 32*a^2*b^6*c^8 - 10*b^8*c^8 - 27*a^6*c^10 - 28*a^4*b^2*c^10 + 45*a^2*b^4*c^10 + 11*b^6*c^10 + 18*a^4*c^12 - 11*a^2*b^2*c^12 - 10*b^4*c^12 - 2*a^2*c^14 + 5*b^2*c^14 - c^16) : :
X(70067) = 2 X[133] - 3 X[14847], X[10990] + 2 X[52057], X[13202] - 3 X[14847], 5 X[15081] - 3 X[57472], 2 X[122] - 3 X[38727], 2 X[5972] - 3 X[23239], 4 X[6716] - 3 X[36518], 3 X[15055] - X[34186], 3 X[23515] - 2 X[49117], X[38591] - 3 X[38788], 2 X[46686] - 3 X[57301]

X(70067) lies on the cubic K591 and these lines: {4, 74}, {30, 57424}, {113, 402}, {122, 38727}, {974, 34980}, {1112, 45960}, {1294, 37853}, {1539, 61569}, {2816, 11709}, {2935, 52604}, {3184, 9033}, {3258, 21663}, {5642, 11845}, {5972, 23239}, {6699, 10745}, {6716, 36518}, {9530, 53719}, {11587, 25564}, {15055, 34186}, {15063, 53757}, {15311, 57448}, {16111, 53803}, {16278, 53723}, {17702, 23240}, {18400, 65107}, {20127, 38577}, {23515, 49117}, {32417, 61462}, {38591, 38788}, {46686, 57301}, {65749, 66463}

X(70067) = midpoint of X(i) and X(j) for these {i,j}: {74, 5667}, {20127, 38577}
X(70067) = reflection of X(i) in X(j) for these {i,j}: {4, 24930}, {113, 38605}, {125, 53716}, {1294, 37853}, {1539, 61569}, {10152, 7687}, {10745, 6699}, {13202, 133}, {15063, 53757}, {16163, 3184}, {16278, 53723}
X(70067) = polar-circle-inverse of X(68642)
X(70067) = crossdifference of every pair of points on line {1636, 8749}
X(70067) = {X(13202),X(14847)}-harmonic conjugate of X(133)

X(70068) = X(4)X(542)∩X(113)X(22566)

Barycentrics   (2*a^2 - b^2 - c^2)*(2*a^8 - 3*a^6*b^2 + 8*a^4*b^4 - 6*a^2*b^6 - b^8 - 3*a^6*c^2 - 10*a^4*b^2*c^2 + 5*a^2*b^4*c^2 + 9*b^6*c^2 + 8*a^4*c^4 + 5*a^2*b^2*c^4 - 16*b^4*c^4 - 6*a^2*c^6 + 9*b^2*c^6 - c^8) : :
X(70068) = X[671] - 3 X[9144], X[671] + 3 X[15342], 2 X[671] - 3 X[16278], X[15063] + 2 X[31854], 2 X[15342] + X[16278], 3 X[110] - X[8591], 3 X[113] - 2 X[22566], 3 X[125] - 4 X[5461], 2 X[5461] - 3 X[5465], 2 X[2482] - 3 X[5642], X[14830] - 3 X[18332], 3 X[5655] - X[48657], 6 X[5972] - 5 X[64019], 3 X[11006] - 5 X[64019], X[8596] + 3 X[9143], 2 X[8787] - 3 X[15303], X[10488] - 3 X[34319], 3 X[11693] - 2 X[33813], 2 X[20379] - 3 X[66093], 3 X[36518] - 2 X[67221]

X(70068) lies on the cubic K591 and these lines: {4, 542}, {110, 8591}, {113, 22566}, {125, 5461}, {148, 10552}, {351, 690}, {524, 2682}, {541, 14830}, {543, 51431}, {2777, 67641}, {2782, 56567}, {5655, 48657}, {5663, 6784}, {5972, 11006}, {8596, 9143}, {8724, 16534}, {8787, 15303}, {9830, 56565}, {10488, 34319}, {10553, 16093}, {11005, 68317}, {11693, 33813}, {12355, 23236}, {14832, 64092}, {16003, 49102}, {20126, 33511}, {20379, 66093}, {24981, 56566}, {36518, 67221}, {39846, 41911}, {41672, 67224}, {53725, 69874}, {58348, 68087}, {59793, 68318}

X(70068) = midpoint of X(i) and X(j) for these {i,j}: {9144, 15342}, {11061, 14833}, {12243, 14094}, {12355, 23236}
X(70068) = reflection of X(i) in X(j) for these {i,j}: {125, 5465}, {8724, 16534}, {11005, 68317}, {11006, 5972}, {16003, 49102}, {16278, 9144}, {20126, 33511}, {24981, 56566}, {59793, 68318}, {69874, 53725}
X(70068) = reflection of X(5642) in the Fermat line
X(70068) = polar-circle-inverse of X(17983)

X(70069) = X(4)X(94)∩X(113)X(35581)

Barycentrics   a^2*(a^2 - b^2 - b*c - c^2)*(a^2 - b^2 + b*c - c^2)*(a^12*b^4 - 5*a^10*b^6 + 10*a^8*b^8 - 10*a^6*b^10 + 5*a^4*b^12 - a^2*b^14 + 2*a^10*b^4*c^2 - 9*a^8*b^6*c^2 + 14*a^6*b^8*c^2 - 8*a^4*b^10*c^2 + b^14*c^2 + a^12*c^4 + 2*a^10*b^2*c^4 + 4*a^8*b^4*c^4 - 5*a^6*b^6*c^4 - 2*a^4*b^8*c^4 + 6*a^2*b^10*c^4 - 6*b^12*c^4 - 5*a^10*c^6 - 9*a^8*b^2*c^6 - 5*a^6*b^4*c^6 + 10*a^4*b^6*c^6 - 5*a^2*b^8*c^6 + 15*b^10*c^6 + 10*a^8*c^8 + 14*a^6*b^2*c^8 - 2*a^4*b^4*c^8 - 5*a^2*b^6*c^8 - 20*b^8*c^8 - 10*a^6*c^10 - 8*a^4*b^2*c^10 + 6*a^2*b^4*c^10 + 15*b^6*c^10 + 5*a^4*c^12 - 6*b^4*c^12 - a^2*c^14 + b^2*c^14) : :

X(70069) lies on the cubic K591 and these lines: {4, 94}, {113, 35581}, {526, 1511}, {924, 38609}, {7668, 10264}, {13754, 66795}, {16221, 63839}

X(70069) = polar-circle-inverse of X(6344)

X(70070) = X(4)X(804)∩X(263)X(351)

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

X(70070) lies on the cubics K027 and K978 and these lines: {4, 804}, {263, 351}, {511, 58262}, {512, 58260}, {878, 881}, {2395, 60523}, {9420, 51980}, {14251, 39469}, {27375, 45911}, {46142, 53197}, {51229, 52765}

X(70070) = midpoint of X(46039) and X(46040)
X(70070) = X(i)-isoconjugate of X(j) for these (i,j): {799, 48452}, {2782, 36036}, {43187, 69609}
X(70070) = X(i)-Dao conjugate of X(j) for these (i,j): {2679, 2782}, {38996, 48452}
X(70070) = trilinear pole of line {2491, 47418}
X(70070) = crossdifference of every pair of points on line {48452, 61070}
X(70070) = barycentric product X(i)*X(j) for these {i,j}: {237, 46040}, {512, 51229}, {2491, 46142}, {2698, 3569}
X(70070) = barycentric quotient X(i)/X(j) for these {i,j}: {669, 48452}, {2491, 2782}, {2698, 43187}, {46040, 18024}, {51229, 670}

X(70071) = X(1)X(53560)∩X(125)X(226)

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

X(70071) lies on the cubics K040 and K683 and these lines: {1, 53560}, {63, 53847}, {72, 43694}, {92, 1836}, {125, 226}, {306, 7068}, {1155, 2349}, {1214, 2632}, {1367, 56382}, {1754, 2629}, {2167, 17660}, {8558, 26702}, {10538, 35145}

X(70071) = isogonal conjugate of X(14192)
X(70071) = X(i)-isoconjugate of X(j) for these (i,j): {1, 14192}, {6, 44331}, {110, 47210}, {162, 69587}, {1474, 69588}, {2299, 16091}
X(70071) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 14192}, {9, 44331}, {125, 69587}, {226, 16091}, {244, 47210}, {51574, 69588}
X(70071) = trilinear pole of line {656, 18675}
X(70071) = barycentric product X(i)*X(j) for these {i,j}: {75, 43694}, {656, 53206}
X(70071) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 44331}, {6, 14192}, {72, 69588}, {647, 69587}, {661, 47210}, {1214, 16091}, {43694, 1}, {53206, 811}

X(70072) = X(3)X(5672)∩X(48)X(10638)

Barycentrics   a^2/(Sqrt[3]*(c*(a^2 + b^2 - c^2) + b*(a^2 - b^2 + c^2) - a*(2*b*c + (-a^2 + b^2 + c^2))) - 2*(-a + b + c)*S) : :

X(70072) lies on the cubics K1042 and K1054a and these lines: {3, 5672}, {48, 10638}, {1444, 15771}, {2151, 11243}, {2173, 3129}, {11142, 19302}, {18735, 37773}, {19297, 51891}

X(70072) = isogonal conjugate of the anticomplement of X(37773)
X(70072) = X(i)-isoconjugate of X(j) for these (i,j): {2, 1277}, {10, 15772}, {75, 19305}
X(70072) = X(i)-Dao conjugate of X(j) for these (i,j): {206, 19305}, {32664, 1277}
X(70072) = barycentric product X(1)*X(7059)
X(70072) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 1277}, {32, 19305}, {1333, 15772}, {7059, 75}
X(70072) = {X(2173),X(3129)}-harmonic conjugate of X(19305)

X(70073) = X(3)X(5673)∩X(48)X(1250)

Barycentrics   a^2/(Sqrt[3]*(c*(a^2 + b^2 - c^2) + b*(a^2 - b^2 + c^2) - a*(2*b*c + (-a^2 + b^2 + c^2))) + 2*(-a + b + c)*S) : :

X(70073) lies on the cubics K1042 and K1054b and these lines: {3, 5673}, {48, 1250}, {603, 2307}, {1444, 15772}, {2152, 11244}, {2173, 3130}, {11141, 19302}, {18735, 37772}, {19297, 51890}

X(70073) = isogonal conjugate of the anticomplement of X(37772)
X(70073) = X(i)-isoconjugate of X(j) for these (i,j): {2, 1276}, {10, 15771}, {75, 19304}
X(70073) = X(i)-Dao conjugate of X(j) for these (i,j): {206, 19304}, {32664, 1276}
X(70073) = barycentric product X(1)*X(7060)
X(70073) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 1276}, {32, 19304}, {1333, 15771}, {7060, 75}
X(70073) = {X(2173),X(3130)}-harmonic conjugate of X(19304)

X(70074) = X(3)X(52677)∩X(4)X(64256)

Barycentrics   b^2*c^2*(-a^12 + 4*a^10*b^2 - 5*a^8*b^4 + 5*a^4*b^8 - 4*a^2*b^10 + b^12 + 2*a^10*c^2 - 3*a^8*b^2*c^2 + a^6*b^4*c^2 - 5*a^4*b^6*c^2 + 9*a^2*b^8*c^2 - 4*b^10*c^2 - a^8*c^4 - a^6*b^2*c^4 + 2*a^4*b^4*c^4 - 5*a^2*b^6*c^4 + 5*b^8*c^4 - a^4*b^2*c^6 + a^2*b^4*c^6 - a^4*c^8 - 3*a^2*b^2*c^8 - 5*b^4*c^8 + 2*a^2*c^10 + 4*b^2*c^10 - c^12)*(a^12 - 2*a^10*b^2 + a^8*b^4 + a^4*b^8 - 2*a^2*b^10 + b^12 - 4*a^10*c^2 + 3*a^8*b^2*c^2 + a^6*b^4*c^2 + a^4*b^6*c^2 + 3*a^2*b^8*c^2 - 4*b^10*c^2 + 5*a^8*c^4 - a^6*b^2*c^4 - 2*a^4*b^4*c^4 - a^2*b^6*c^4 + 5*b^8*c^4 + 5*a^4*b^2*c^6 + 5*a^2*b^4*c^6 - 5*a^4*c^8 - 9*a^2*b^2*c^8 - 5*b^4*c^8 + 4*a^2*c^10 + 4*b^2*c^10 - c^12) : :

X(70074) lies on the cubics K1338 and K1342 and these lines: {3, 52677}, {4, 64256}, {2888, 3153}, {3432, 39431}, {10224, 34900}, {32345, 53959}, {58730, 58731}, {58927, 69997}

X(70074) = isogonal conjugate of X(10274)
X(70074) = isogonal conjugate of the anticomplement of X(14076)
X(70074) = X(i)-cross conjugate of X(j) for these (i,j): {14533, 5392}, {32351, 4}
X(70074) = X(i)-isoconjugate of X(j) for these (i,j): {1, 10274}, {2964, 21394}
X(70074) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 10274}, {21975, 21394}
X(70074) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 10274}, {2963, 21394}

X(70075) = X(3)X(8872)∩X(6)X(43)

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

X(70075) lies on the cubics K225 and K252 and these lines: {2, 20547}, {3, 8872}, {6, 43}, {419, 2201}, {932, 1055}, {2238, 51321}, {13588, 67001}, {34071, 67196}, {40597, 63618}, {40881, 52127}

X(70075) = X(i)-isoconjugate of X(j) for these (i,j): {75, 67005}, {335, 57505}, {1423, 43748}, {3212, 51995}, {3500, 41531}, {51973, 54128}
X(70075) = X(206)-Dao conjugate of X(67005)
X(70075) = barycentric product X(i)*X(j) for these {i,j}: {1, 14199}, {2053, 56930}, {2319, 39930}, {3501, 39914}, {3978, 67001}, {7155, 56413}, {17786, 51321}, {27424, 51956}, {32937, 34252}, {34247, 69955}
X(70075) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 67005}, {2053, 43748}, {2210, 57505}, {3501, 40848}, {14199, 75}, {32937, 70000}, {34247, 41531}, {34252, 54128}, {39930, 30545}, {51321, 3500}, {51949, 51973}, {51956, 1423}, {56413, 3212}, {56930, 69913}, {57264, 51995}, {67001, 694}

X(70076) = X(2)X(69922)∩X(6)X(66)

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

X(70076) lies on the cubics K260 and K836 and these lines: {2, 69922}, {6, 66}, {39, 14376}, {69, 44766}, {159, 455}, {574, 52973}, {577, 23976}, {1370, 40357}, {3763, 46829}, {3767, 34138}, {5286, 43678}, {6697, 53851}, {7803, 40421}, {8743, 59432}, {8879, 46767}, {14907, 53657}, {15388, 35902}, {17907, 65266}, {31670, 41382}, {41361, 58075}, {53059, 65712}

X(70076) = isogonal conjugate of X(40358)
X(70076) = complement of X(69922)
X(70076) = complement of the isogonal conjugate of X(3162)
X(70076) = complement of the isotomic conjugate of X(41361)
X(70076) = isotomic conjugate of the polar conjugate of X(17407)
X(70076) = isogonal conjugate of the polar conjugate of X(58075)
X(70076) = X(i)-complementary conjugate of X(j) for these (i,j): {19, 23300}, {25, 36907}, {31, 14376}, {159, 18589}, {1973, 25}, {3162, 10}, {17407, 16607}, {18596, 1368}, {41361, 2887}, {41766, 20305}, {52588, 34846}, {57086, 4369}
X(70076) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 14376}, {58075, 17407}
X(70076) = X(55069)-cross conjugate of X(47125)
X(70076) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40358}, {75, 46767}, {92, 39172}, {206, 39733}, {1760, 34207}, {2172, 13575}, {17453, 40009}
X(70076) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 40358}, {25, 8743}, {206, 46767}, {14376, 2}, {22391, 39172}, {52588, 62573}, {53822, 33294}, {55069, 2485}
X(70076) = crosspoint of X(2) and X(41361)
X(70076) = crosssum of X(i) and X(j) for these (i,j): {6, 52041}, {34207, 46769}, {39172, 46767}
X(70076) = barycentric product X(i)*X(j) for these {i,j}: {3, 58075}, {66, 1370}, {69, 17407}, {141, 40357}, {159, 18018}, {2156, 21582}, {8024, 46766}, {13854, 28419}, {14376, 41361}, {23115, 43678}, {44766, 47125}
X(70076) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 40358}, {32, 46767}, {66, 13575}, {159, 22}, {184, 39172}, {1370, 315}, {2353, 34207}, {3162, 8743}, {13854, 52583}, {14376, 69922}, {17407, 4}, {18018, 40009}, {18596, 1760}, {18629, 17076}, {21582, 20641}, {23115, 20806}, {28419, 34254}, {40357, 83}, {41361, 17907}, {41766, 52448}, {46766, 251}, {47125, 33294}, {52588, 2485}, {55069, 62573}, {57086, 52915}, {58075, 264}, {60495, 52041}

X(70077) = X(2)X(154)∩X(3)X(8779)

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

X(70077) lies on the cubics K280 and K804 and these lines: {2, 154}, {3, 8779}, {6, 1297}, {182, 40801}, {184, 1073}, {276, 38808}, {394, 53852}, {1181, 52041}, {1217, 37476}, {3167, 36609}, {3346, 11425}, {3926, 35602}, {5481, 53094}, {7757, 54973}, {10605, 18876}, {10606, 38699}, {12017, 14489}, {14376, 19357}, {14919, 33924}, {20208, 65749}, {34129, 37074}, {34225, 36752}, {34579, 64509}, {34897, 47391}, {37072, 67192}, {37514, 66552}, {58354, 60839}

X(70077) = isogonal conjugate of X(10002)
X(70077) = isotomic conjugate of the polar conjugate of X(60674)
X(70077) = isogonal conjugate of the polar conjugate of X(42287)
X(70077) = X(42287)-Ceva conjugate of X(60674)
X(70077) = X(i)-isoconjugate of X(j) for these (i,j): {1, 10002}, {4, 23052}, {19, 52283}, {92, 45141}, {158, 1350}, {240, 45031}, {393, 51304}, {1096, 37668}, {1529, 8767}, {51315, 66974}
X(70077) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 10002}, {6, 52283}, {1147, 1350}, {6503, 37668}, {14390, 40813}, {17434, 12037}, {22391, 45141}, {36033, 23052}, {39071, 1529}, {39085, 45031}
X(70077) = crosssum of X(4) and X(45864)
X(70077) = barycentric product X(i)*X(j) for these {i,j}: {3, 42287}, {69, 60674}, {394, 3424}, {520, 65276}, {577, 59256}, {3265, 58963}, {35571, 58796}
X(70077) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 52283}, {6, 10002}, {48, 23052}, {184, 45141}, {248, 45031}, {255, 51304}, {394, 37668}, {577, 1350}, {2972, 12037}, {3424, 2052}, {8779, 1529}, {14379, 40813}, {42287, 264}, {58796, 14343}, {58963, 107}, {59256, 18027}, {60674, 4}, {65276, 6528}

X(70078) = X(30)X(6699)∩X(74)X(54512)

Barycentrics   (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)*(4*a^8 - a^6*b^2 - 6*a^4*b^4 - a^2*b^6 + 4*b^8 - 7*a^6*c^2 + 13*a^4*b^2*c^2 + 13*a^2*b^4*c^2 - 7*b^6*c^2 - 3*a^4*c^4 - 23*a^2*b^2*c^4 - 3*b^4*c^4 + 11*a^2*c^6 + 11*b^2*c^6 - 5*c^8)*(4*a^8 - 7*a^6*b^2 - 3*a^4*b^4 + 11*a^2*b^6 - 5*b^8 - a^6*c^2 + 13*a^4*b^2*c^2 - 23*a^2*b^4*c^2 + 11*b^6*c^2 - 6*a^4*c^4 + 13*a^2*b^2*c^4 - 3*b^4*c^4 - a^2*c^6 - 7*b^2*c^6 + 4*c^8) : :
X(70078) = 3 X[7687] - 2 X[38246]

X(70078) lies on the Euler asymptotic hyperbola (see X(1650)), the cubics K313 and K638, and these lines: {30, 6699}, {74, 54512}, {146, 16075}, {1294, 57472}, {1494, 10733}, {2777, 34297}, {3163, 13202}, {5667, 47111}, {14847, 38956}, {17702, 20123}

X(70078) = isogonal conjugate of X(70053)
X(70078) = X(125)-cross conjugate of X(9033)
X(70078) = X(i)-isoconjugate of X(j) for these (i,j): {1, 70053}, {162, 57147}, {15051, 36119}, {36131, 63248}
X(70078) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 70053}, {125, 57147}, {1511, 15051}, {39008, 63248}
X(70078) = trilinear pole of line {14401, 57295}
X(70078) = barycentric product X(525)*X(43941)
X(70078) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 70053}, {647, 57147}, {3284, 15051}, {9033, 63248}, {43941, 648}

X(70079) = X(2)X(330)∩X(76)X(2319)

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

X(70079) lies on the cubics K356 and K1304 and these lines: {2, 330}, {76, 2319}, {87, 34283}, {239, 64225}, {385, 51321}, {527, 18830}, {732, 39934}, {3948, 39914}, {4083, 26148}, {17984, 18037}, {27436, 44139}, {32937, 56931}

X(70079) = isogonal conjugate of X(67005)
X(70079) = antitomic image of X(39930)
X(70079) = X(i)-isoconjugate of X(j) for these (i,j): {1, 67005}, {292, 57505}, {1403, 51995}, {3500, 70062}, {41526, 43748}
X(70079) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 67005}, {19557, 57505}
X(70079) = barycentric product X(i)*X(j) for these {i,j}: {75, 14199}, {7155, 56930}, {14603, 67001}, {17786, 39914}, {27424, 39930}, {32937, 69955}
X(70079) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 67005}, {238, 57505}, {2319, 51995}, {3501, 51973}, {7155, 43748}, {14199, 1}, {17786, 40848}, {32937, 41531}, {34247, 70062}, {39914, 3500}, {39930, 1423}, {51956, 41526}, {56413, 1403}, {56930, 3212}, {67001, 9468}, {69955, 54128}

X(70080) = X(2)X(10030)∩X(75)X(56654)

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

X(70080) lies on the cubics K767 and K973 and these lines: {2, 10030}, {75, 56654}, {239, 56664}, {256, 56662}, {740, 7220}, {2481, 56663}, {40845, 56655}, {56705, 62697}

X(70080) = X(75)-Ceva conjugate of X(56664)
X(70080) = X(1922)-isoconjugate of X(56654)
X(70080) = X(39028)-Dao conjugate of X(56654)
X(70080) = barycentric quotient X(i)/X(j) for these {i,j}: {350, 56654}, {41354, 4334}

X(70081) = X(3)X(5888)∩X(23)X(53890)

Barycentrics   a^2*(a^10 + 6*a^8*b^2 - 22*a^6*b^4 + 20*a^4*b^6 - 3*a^2*b^8 - 2*b^10 + 6*a^8*c^2 + 86*a^6*b^2*c^2 - 10*a^4*b^4*c^2 - 67*a^2*b^6*c^2 - 15*b^8*c^2 - 22*a^6*c^4 - 10*a^4*b^2*c^4 + 65*a^2*b^4*c^4 + 17*b^6*c^4 + 20*a^4*c^6 - 67*a^2*b^2*c^6 + 17*b^4*c^6 - 3*a^2*c^8 - 15*b^2*c^8 - 2*c^10) : :

X(70081) lies on the cubics K728, K834, K903, and K905, and these lines: {3, 5888}, {23, 53890}, {30, 69879}

X(70081) = reflection of X(69882) in X(23)
X(70081) = circumcircle-inverse of X(5888)
X(70081) = Stammler-circle-inverse of X(18551)

X(70082) = X(2)X(24356)∩X(11)X(244)

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

X(70082) lies on these lines: {2, 24356}, {11, 244}, {649, 17204}, {768, 3261}, {812, 30095}, {4025, 21206}, {21053, 30639}, {21056, 21263}, {21123, 48101}, {21351, 21964}, {42327, 45882}, {50451, 50454}

X(70082) = X(i)-isoconjugate of X(j) for these (i,j): {100, 699}, {101, 43761}, {692, 3225}, {32739, 70037}
X(70082) = X(i)-Dao conjugate of X(j) for these (i,j): {1015, 43761}, {1086, 3225}, {8054, 699}, {39080, 101}, {40618, 8858}, {40619, 70037}, {65925, 190}
X(70082) = crossdifference of every pair of points on line {101, 699}
X(70082) = barycentric product X(i)*X(j) for these {i,j}: {513, 69957}, {514, 698}, {649, 35524}, {693, 2227}, {3229, 3261}, {7649, 59567}, {21207, 41337}, {40495, 51907}
X(70082) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 43761}, {514, 3225}, {649, 699}, {693, 70037}, {698, 190}, {2227, 100}, {3229, 101}, {3261, 66842}, {4025, 8858}, {4107, 32544}, {9429, 1918}, {32748, 32739}, {35524, 1978}, {41337, 4570}, {51907, 692}, {52460, 8750}, {59567, 4561}, {69394, 69910}, {69957, 668}

X(70083) = X(42)X(192)∩X(523)X(661)

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

X(70083) lies on these lines: {10, 33890}, {42, 192}, {190, 53231}, {306, 21095}, {313, 561}, {523, 661}, {698, 2227}, {756, 27697}, {3263, 20590}, {4039, 33889}, {4568, 52894}, {6664, 21035}, {17760, 27880}, {20684, 22039}, {22231, 49774}, {24943, 24958}, {35524, 69957}, {63234, 69594}, {69956, 70000}

X(70083) = X(70000)-Ceva conjugate of X(321)
X(70083) = X(i)-isoconjugate of X(j) for these (i,j): {58, 43761}, {81, 699}, {1333, 3225}, {2203, 8858}, {2206, 70037}
X(70083) = X(i)-Dao conjugate of X(j) for these (i,j): {10, 43761}, {37, 3225}, {39080, 58}, {40586, 699}, {40603, 70037}, {62564, 8858}, {65925, 86}
X(70083) = crosspoint of X(i) and X(j) for these (i,j): {334, 42027}, {698, 69957}
X(70083) = crosssum of X(2210) and X(38832)
X(70083) = crossdifference of every pair of points on line {58, 23572}
X(70083) = barycentric product X(i)*X(j) for these {i,j}: {10, 698}, {37, 69957}, {42, 35524}, {313, 3229}, {321, 2227}, {1826, 59567}, {27801, 51907}, {40071, 52460}, {41337, 52623}
X(70083) = barycentric quotient X(i)/X(j) for these {i,j}: {10, 3225}, {37, 43761}, {42, 699}, {306, 8858}, {313, 66842}, {321, 70037}, {698, 86}, {2227, 81}, {3229, 58}, {4039, 32544}, {9429, 1919}, {32748, 2206}, {35524, 310}, {41337, 4556}, {51907, 1333}, {52460, 1474}, {59567, 17206}, {69594, 69910}, {69957, 274}

X(70084) = X(2)X(5027)∩X(115)X(125)

Barycentrics   (b - c)*(b + c)*(-(a^2*b^4) + b^4*c^2 - a^2*c^4 + b^2*c^4) : :
X(70084) = 2 X[5027] - 3 X[45680], X[3569] + 3 X[9148], X[3569] - 3 X[11182], X[24284] - 3 X[45689], X[5113] - 3 X[45692], X[6333] + 3 X[9134], X[3288] - 5 X[31279], 5 X[3763] - X[53272], 3 X[9979] - X[50542], 3 X[10278] - X[14316], 3 X[11183] - X[42663], 3 X[34290] + X[53331]

X(70084) lies on these lines: {2, 5027}, {115, 125}, {126, 62611}, {141, 888}, {512, 625}, {525, 59568}, {782, 2507}, {804, 5113}, {808, 2485}, {826, 850}, {882, 14295}, {2780, 20304}, {2793, 24206}, {2799, 23596}, {3005, 7927}, {3221, 56739}, {3288, 31279}, {3763, 53272}, {5466, 10290}, {5996, 12073}, {6697, 55121}, {7703, 32121}, {9208, 53365}, {9429, 39080}, {9979, 50542}, {10278, 14316}, {11183, 42663}, {14318, 44445}, {18911, 39499}, {22260, 35522}, {30094, 69306}, {30217, 44451}, {34290, 53331}, {45693, 61575}, {67152, 67488}

X(70084) = midpoint of X(i) and X(j) for these {i,j}: {850, 50549}, {882, 14295}, {9148, 11182}, {9208, 53365}, {14318, 44445}, {22260, 35522}, {23301, 54262}
X(70084) = reflection of X(45680) in X(2)
X(70084) = complement of X(5027)
X(70084) = complement of the isogonal conjugate of X(18829)
X(70084) = medial-isogonal conjugate of X(35078)
X(70084) = tripolar centroid of X(43688)
X(70084) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 35078}, {38, 39079}, {75, 2679}, {99, 19563}, {662, 5976}, {694, 16592}, {799, 39080}, {805, 37}, {1581, 115}, {1916, 8287}, {1934, 125}, {1967, 1084}, {3903, 35068}, {4584, 59509}, {4589, 51575}, {4594, 17793}, {4603, 17755}, {7260, 20333}, {8773, 56788}, {17938, 16584}, {18827, 40608}, {18829, 10}, {18896, 21253}, {27805, 46842}, {32010, 38989}, {36214, 16573}, {37134, 2}, {39291, 16609}, {39292, 4369}, {40432, 35119}, {40708, 34846}, {41209, 1215}, {43763, 3124}, {46161, 16587}, {56241, 45162}, {65289, 50440}, {65327, 1214}, {65351, 226}, {66267, 24040}, {66933, 15526}, {67149, 64650}, {69999, 7668}, {70058, 41178}
X(70084) = X(i)-Ceva conjugate of X(j) for these (i,j): {882, 826}, {14295, 2799}, {18896, 115}
X(70084) = X(i)-isoconjugate of X(j) for these (i,j): {110, 43761}, {163, 3225}, {662, 699}, {1576, 70037}, {8858, 32676}, {51992, 56982}
X(70084) = X(i)-Dao conjugate of X(j) for these (i,j): {115, 3225}, {244, 43761}, {1084, 699}, {2086, 1691}, {3229, 17941}, {4858, 70037}, {15526, 8858}, {35078, 32544}, {35088, 69910}, {35540, 880}, {36901, 66842}, {39080, 110}, {40810, 805}, {65925, 99}
X(70084) = crosspoint of X(850) and X(66267)
X(70084) = crosssum of X(i) and X(j) for these (i,j): {110, 41337}, {1576, 56980}
X(70084) = crossdifference of every pair of points on line {110, 699}
X(70084) = barycentric product X(i)*X(j) for these {i,j}: {338, 41337}, {512, 35524}, {523, 698}, {661, 69957}, {850, 3229}, {1502, 9429}, {1577, 2227}, {2501, 59567}, {3267, 52460}, {14295, 47648}, {18896, 62649}, {20948, 51907}, {32748, 44173}, {35522, 36821}, {39080, 66267}, {51322, 56981}
X(70084) = barycentric quotient X(i)/X(j) for these {i,j}: {512, 699}, {523, 3225}, {525, 8858}, {661, 43761}, {698, 99}, {804, 32544}, {850, 66842}, {882, 51992}, {1577, 70037}, {2227, 662}, {2799, 69910}, {3229, 110}, {9429, 32}, {9479, 8864}, {32540, 2715}, {32748, 1576}, {35524, 670}, {36821, 691}, {39080, 17941}, {41337, 249}, {47648, 805}, {51248, 46970}, {51322, 56980}, {51907, 163}, {51912, 56982}, {52460, 112}, {59567, 4563}, {59802, 41337}, {62649, 1691}, {69947, 17938}, {69957, 799}

X(70085) = X(39)X(4074)∩X(99)X(16985)

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

X(70085) lies on these lines: {39, 4074}, {99, 16985}, {115, 69963}, {305, 32452}, {698, 3229}, {826, 2474}, {2979, 7826}, {2998, 69781}, {3118, 6292}, {4576, 8623}, {6379, 66143}, {7794, 8024}, {19568, 41756}, {35524, 65925}, {35540, 56978}, {37004, 37190}, {51371, 56977}

X(70085) = reflection of X(3229) in X(59567)
X(70085) = X(i)-Ceva conjugate of X(j) for these (i,j): {35540, 51371}, {47648, 65925}, {56978, 7794}
X(70085) = X(i)-isoconjugate of X(j) for these (i,j): {82, 699}, {251, 43761}, {3225, 46289}, {32544, 67149}, {46288, 70037}, {51992, 56971}
X(70085) = X(i)-Dao conjugate of X(j) for these (i,j): {39, 3225}, {141, 699}, {3229, 56976}, {35540, 56979}, {39080, 251}, {40585, 43761}, {40810, 733}, {61063, 32544}, {65925, 83}
X(70085) = crosspoint of X(i) and X(j) for these (i,j): {698, 35524}, {8024, 56977}, {47648, 56978}
X(70085) = crosssum of X(i) and X(j) for these (i,j): {32544, 56976}, {46288, 56975}
X(70085) = barycentric product X(i)*X(j) for these {i,j}: {38, 69957}, {39, 35524}, {141, 698}, {427, 59567}, {1930, 2227}, {3229, 8024}, {23285, 41337}, {32748, 52568}, {35540, 47648}, {39080, 56977}
X(70085) = barycentric quotient X(i)/X(j) for these {i,j}: {38, 43761}, {39, 699}, {141, 3225}, {698, 83}, {732, 32544}, {1930, 70037}, {2227, 82}, {3229, 251}, {3933, 8858}, {8024, 66842}, {32748, 46288}, {35524, 308}, {39080, 56976}, {41337, 827}, {47648, 733}, {51322, 56975}, {51371, 69910}, {51907, 46289}, {51912, 56971}, {56978, 51992}, {59567, 1799}, {69957, 3112}

X(70086) = X(2)X(18037)∩X(257)X(30966)

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

X(70086) lies on these lines: {2, 18037}, {257, 30966}, {350, 17493}, {659, 812}, {668, 51973}, {698, 2227}, {893, 31008}, {984, 4493}, {1107, 16705}, {1655, 2276}, {1921, 44169}, {3061, 30945}, {3229, 69957}, {3703, 20484}, {7200, 40017}, {17149, 19581}, {17759, 52662}

X(70086) = X(31008)-Ceva conjugate of X(350)
X(70086) = X(i)-isoconjugate of X(j) for these (i,j): {171, 51992}, {291, 699}, {292, 43761}, {1911, 3225}, {1922, 70037}, {14598, 66842}
X(70086) = X(i)-Dao conjugate of X(j) for these (i,j): {2086, 7234}, {3229, 894}, {6651, 3225}, {18277, 66842}, {19557, 43761}, {35540, 1920}, {39028, 70037}, {39029, 699}, {39080, 292}, {65925, 335}
X(70086) = crosspoint of X(i) and X(j) for these (i,j): {257, 1921}, {274, 39914}
X(70086) = crosssum of X(i) and X(j) for these (i,j): {172, 1922}, {213, 51973}
X(70086) = barycentric product X(i)*X(j) for these {i,j}: {238, 69957}, {239, 698}, {242, 59567}, {257, 39080}, {350, 2227}, {1914, 35524}, {1921, 3229}, {7018, 51912}, {7019, 52462}, {18891, 51907}, {32748, 44169}, {44187, 51322}
X(70086) = barycentric quotient X(i)/X(j) for these {i,j}: {238, 43761}, {239, 3225}, {350, 70037}, {698, 335}, {893, 51992}, {1914, 699}, {1921, 66842}, {2227, 291}, {3229, 292}, {32748, 1922}, {35524, 18895}, {39080, 894}, {51322, 172}, {51907, 1911}, {51912, 171}, {52462, 7009}, {53681, 32544}, {59567, 337}, {62649, 7234}, {69957, 334}

X(70087) = X(43)X(213)∩X(76)X(321)

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

X(70087) lies on these lines: {10, 52651}, {37, 19584}, {43, 213}, {72, 30496}, {76, 321}, {100, 53966}, {512, 661}, {698, 69957}, {2227, 3229}, {3864, 41517}, {3912, 20861}, {21085, 21086}, {21802, 21814}, {22202, 29674}, {40848, 40849}

X(70087) = X(40848)-Ceva conjugate of X(10)
X(70087) = X(i)-isoconjugate of X(j) for these (i,j): {58, 3225}, {81, 43761}, {86, 699}, {1333, 70037}, {1474, 8858}, {2206, 66842}
X(70087) = X(i)-Dao conjugate of X(j) for these (i,j): {10, 3225}, {37, 70037}, {2086, 4164}, {39080, 81}, {40586, 43761}, {40600, 699}, {40603, 66842}, {51574, 8858}, {65925, 274}
X(70087) = crosspoint of X(i) and X(j) for these (i,j): {335, 16606}, {698, 2227}
X(70087) = crosssum of X(i) and X(j) for these (i,j): {699, 43761}, {1914, 27644}
X(70087) = crossdifference of every pair of points on line {81, 1980}
X(70087) = barycentric product X(i)*X(j) for these {i,j}: {10, 2227}, {37, 698}, {42, 69957}, {213, 35524}, {313, 51907}, {321, 3229}, {1824, 59567}, {4036, 41337}, {6386, 9429}, {20336, 52460}, {27801, 32748}, {32540, 42703}, {36821, 42713}
X(70087) = barycentric quotient X(i)/X(j) for these {i,j}: {10, 70037}, {37, 3225}, {42, 43761}, {72, 8858}, {213, 699}, {321, 66842}, {698, 274}, {2227, 86}, {3229, 81}, {9429, 667}, {32748, 1333}, {35524, 6385}, {41337, 52935}, {51907, 58}, {52460, 28}, {62649, 4164}, {69593, 69910}, {69957, 310}

X(70088) = X(1)X(1281)∩X(192)X(869)

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

X(70088) lies on these lines: {1, 1281}, {190, 70062}, {192, 869}, {194, 6196}, {239, 18786}, {256, 40773}, {350, 18891}, {659, 4435}, {698, 51907}, {712, 57020}, {904, 7260}, {1193, 4368}, {2227, 3229}, {2309, 54308}, {2664, 33889}, {3747, 8844}, {7155, 24621}, {18827, 53541}, {18906, 69912}, {20704, 33299}, {20862, 64223}, {24578, 25834}, {56185, 61183}

X(70088) = X(i)-Ceva conjugate of X(j) for these (i,j): {7260, 21832}, {33296, 239}
X(70088) = X(i)-isoconjugate of X(j) for these (i,j): {291, 43761}, {292, 3225}, {335, 699}, {894, 51992}, {1911, 70037}, {1922, 66842}
X(70088) = X(i)-Dao conjugate of X(j) for these (i,j): {2086, 57234}, {3229, 1909}, {6651, 70037}, {19557, 3225}, {39028, 66842}, {39029, 43761}, {39080, 291}, {65925, 334}
X(70088) = crosspoint of X(i) and X(j) for these (i,j): {86, 34252}, {256, 350}
X(70088) = crosssum of X(i) and X(j) for these (i,j): {42, 41531}, {171, 1911}
X(70088) = barycentric product X(i)*X(j) for these {i,j}: {238, 698}, {239, 2227}, {256, 39080}, {257, 51912}, {350, 3229}, {1914, 69957}, {1921, 51907}, {2201, 59567}, {2210, 35524}, {7018, 51322}, {7260, 62649}, {18891, 32748}
X(70088) = barycentric quotient X(i)/X(j) for these {i,j}: {238, 3225}, {239, 70037}, {350, 66842}, {698, 334}, {904, 51992}, {1914, 43761}, {2210, 699}, {2227, 335}, {3229, 291}, {20769, 8858}, {32748, 1911}, {35524, 44172}, {39080, 1909}, {41337, 4584}, {51322, 171}, {51907, 292}, {51912, 894}, {62649, 57234}, {69957, 18895}

X(70089) = X(1)X(87)∩X(9)X(25838)

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

X(70089) lies on these lines: {1, 87}, {9, 25838}, {291, 56838}, {698, 51907}, {1909, 27880}, {1911, 4639}, {3009, 25302}, {3287, 3805}, {3510, 8782}, {18906, 56806}, {27954, 27998}

X(70089) = X(4639)-Ceva conjugate of X(57234)
X(70089) = X(i)-isoconjugate of X(j) for these (i,j): {239, 51992}, {256, 43761}, {257, 699}, {893, 3225}, {904, 70037}, {7104, 66842}
X(70089) = X(i)-Dao conjugate of X(j) for these (i,j): {2086, 21832}, {3229, 350}, {35540, 18891}, {39080, 256}, {40597, 3225}, {62650, 70037}, {65925, 7018}
X(70089) = crosspoint of X(291) and X(1909)
X(70089) = crosssum of X(238) and X(904)
X(70089) = crossdifference of every pair of points on line {256, 20979}
X(70089) = barycentric product X(i)*X(j) for these {i,j}: {171, 698}, {172, 69957}, {291, 39080}, {334, 51322}, {335, 51912}, {894, 2227}, {1909, 3229}, {1920, 51907}, {4639, 62649}, {7119, 59567}, {7122, 35524}
X(70089) = barycentric quotient X(i)/X(j) for these {i,j}: {171, 3225}, {172, 43761}, {698, 7018}, {894, 70037}, {1909, 66842}, {1911, 51992}, {2227, 257}, {3229, 256}, {7122, 699}, {32748, 904}, {39080, 350}, {41337, 4603}, {51322, 238}, {51907, 893}, {51912, 239}, {62649, 21832}, {69957, 44187}

X(70090) = X(1)X(25918)∩X(2)X(49516)

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

X(70090) lies on these lines: {1, 25918}, {2, 49516}, {8, 27340}, {9, 24586}, {37, 25349}, {38, 31087}, {43, 49496}, {57, 312}, {65, 17760}, {75, 17026}, {144, 27538}, {171, 385}, {183, 24333}, {190, 3509}, {192, 982}, {210, 4416}, {241, 3693}, {291, 740}, {304, 3501}, {325, 4071}, {333, 36483}, {335, 33889}, {341, 56025}, {354, 49528}, {484, 33952}, {513, 20723}, {518, 40883}, {524, 20693}, {538, 68897}, {664, 52089}, {668, 35102}, {672, 3263}, {712, 69247}, {742, 1575}, {758, 4568}, {985, 4672}, {1015, 68890}, {1018, 14210}, {1111, 69869}, {1212, 30030}, {1423, 21590}, {1654, 33079}, {1909, 4095}, {1920, 4032}, {1930, 16549}, {2170, 69028}, {2292, 25263}, {2295, 16720}, {2319, 62419}, {3061, 21281}, {3208, 18156}, {3252, 3930}, {3701, 56024}, {3706, 4431}, {3718, 44421}, {3730, 33942}, {3971, 49514}, {4009, 4480}, {4070, 32043}, {4087, 40875}, {4253, 33937}, {4369, 4374}, {4376, 69230}, {4488, 4903}, {4518, 4645}, {4595, 49779}, {4695, 17497}, {4754, 21021}, {4766, 33864}, {4858, 20646}, {4865, 7774}, {4986, 45751}, {5205, 10025}, {6168, 40704}, {6327, 31080}, {6363, 47890}, {6645, 17741}, {6647, 18047}, {6656, 24211}, {7182, 40493}, {7187, 17752}, {7227, 44379}, {7264, 29438}, {7278, 29699}, {8680, 17790}, {8682, 52959}, {8924, 29057}, {9451, 68969}, {10453, 49507}, {16600, 24170}, {16601, 29968}, {16609, 17789}, {16887, 28594}, {17048, 33940}, {17063, 26274}, {17137, 33299}, {17152, 39244}, {17248, 33174}, {17319, 17598}, {17333, 42056}, {17353, 30748}, {17379, 17716}, {17489, 24443}, {17735, 24358}, {17744, 29473}, {17751, 25244}, {17768, 20716}, {17770, 59724}, {18134, 36482}, {18157, 39258}, {18193, 55998}, {18743, 51052}, {18830, 56657}, {20446, 69752}, {20553, 24712}, {20924, 21232}, {21216, 24440}, {21872, 59504}, {21888, 35101}, {24036, 30109}, {24241, 26590}, {24326, 24512}, {24514, 59511}, {24691, 49509}, {25066, 29960}, {25068, 29991}, {25082, 29966}, {25264, 63800}, {25353, 37664}, {26685, 30791}, {26690, 30036}, {27697, 27968}, {27798, 28604}, {28595, 31090}, {28968, 60716}, {30962, 51058}, {31993, 35466}, {32117, 66669}, {33169, 48628}, {39959, 49451}, {40859, 68995}, {41318, 56558}, {43037, 69049}, {43065, 49774}, {49502, 62865}, {59515, 69248}

X(70090) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1222, 20554}, {23617, 20345}, {51476, 17794}
X(70090) = X(22116)-Ceva conjugate of X(17755)
X(70090) = X(i)-isoconjugate of X(j) for these (i,j): {105, 893}, {256, 1438}, {257, 64216}, {294, 1431}, {673, 904}, {884, 37137}, {1024, 29055}, {1178, 18785}, {1432, 2195}, {1967, 6654}, {2481, 7104}, {3903, 43929}, {7015, 8751}, {7116, 36124}, {14942, 66996}, {18031, 66931}, {18786, 51866}, {29956, 30670}, {36796, 67144}, {40432, 56853}, {52209, 61385}
X(70090) = X(i)-Dao conjugate of X(j) for these (i,j): {2238, 18786}, {3912, 17493}, {6184, 256}, {8290, 6654}, {16587, 13576}, {16592, 62635}, {17755, 257}, {36905, 7249}, {39046, 893}, {39063, 1432}, {40597, 105}, {52656, 1581}, {62587, 7018}, {62650, 673}
X(70090) = cevapoint of X(17759) and X(56555)
X(70090) = crosspoint of X(i) and X(j) for these (i,j): {894, 30669}, {4562, 67038}
X(70090) = crossdifference of every pair of points on line {884, 904}
X(70090) = barycentric product X(i)*X(j) for these {i,j}: {75, 4447}, {171, 3263}, {241, 17787}, {385, 40217}, {518, 1909}, {668, 53553}, {672, 1920}, {883, 3907}, {894, 3912}, {918, 18047}, {1026, 4374}, {1215, 30941}, {1237, 3286}, {1926, 40730}, {1966, 22116}, {2254, 69896}, {2295, 18157}, {2329, 40704}, {2340, 7205}, {2533, 68998}, {3252, 3978}, {3693, 7196}, {3717, 7176}, {3930, 8033}, {3932, 17103}, {3963, 18206}, {4019, 15149}, {4369, 42720}, {6649, 50333}, {7081, 9436}, {17755, 30669}, {18787, 64223}, {23829, 69897}, {43042, 69898}, {55260, 57234}
X(70090) = barycentric quotient X(i)/X(j) for these {i,j}: {171, 105}, {172, 1438}, {241, 1432}, {385, 6654}, {518, 256}, {672, 893}, {883, 65289}, {894, 673}, {1025, 37137}, {1026, 3903}, {1215, 13576}, {1458, 1431}, {1818, 7015}, {1840, 68565}, {1909, 2481}, {1920, 18031}, {2223, 904}, {2283, 29055}, {2295, 18785}, {2329, 294}, {2330, 2195}, {3252, 694}, {3263, 7018}, {3286, 1178}, {3287, 1024}, {3717, 4451}, {3907, 885}, {3912, 257}, {3930, 52651}, {3955, 36057}, {4032, 66941}, {4367, 1027}, {4369, 62635}, {4447, 1}, {4529, 28132}, {4579, 36086}, {4684, 4835}, {6649, 927}, {7009, 36124}, {7081, 14942}, {7119, 8751}, {7122, 64216}, {7175, 1462}, {7176, 56783}, {7196, 34018}, {8299, 18786}, {9436, 7249}, {9454, 7104}, {9455, 66931}, {17755, 17493}, {17787, 36796}, {18047, 666}, {18206, 40432}, {18787, 52030}, {20683, 66971}, {20752, 7116}, {20964, 56853}, {20981, 43929}, {22116, 1581}, {30669, 52209}, {30941, 32010}, {39258, 40729}, {40217, 1916}, {40730, 1967}, {40790, 52029}, {42720, 27805}, {45882, 29956}, {52635, 66996}, {53541, 43921}, {53553, 513}, {55260, 7260}, {57234, 55261}, {66973, 51866}, {68998, 4594}, {69093, 59191}, {69894, 919}, {69895, 32666}, {69896, 51560}, {69898, 36802}
X(70090) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 17754, 24631}, {190, 20947, 3985}, {672, 3263, 17755}, {2295, 16720, 59509}, {4071, 24318, 325}, {30941, 42720, 3930}

X(70091) = X(2)X(16517)∩X(63)X(69)

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

X(70091) lies on these lines: {2, 16517}, {7, 29641}, {8, 32830}, {9, 45962}, {10, 3761}, {31, 3879}, {38, 3778}, {63, 69}, {72, 3933}, {75, 1233}, {76, 6734}, {77, 1264}, {78, 3926}, {86, 5294}, {144, 10513}, {183, 59491}, {190, 4872}, {304, 3710}, {305, 307}, {312, 69264}, {315, 64002}, {319, 3996}, {325, 908}, {326, 56813}, {329, 37668}, {332, 47487}, {341, 33298}, {344, 14548}, {348, 1265}, {350, 26015}, {516, 20553}, {518, 69093}, {527, 4071}, {656, 4025}, {668, 6735}, {672, 3912}, {902, 49750}, {960, 69094}, {1007, 30852}, {1018, 49773}, {1210, 18135}, {1444, 5314}, {1737, 6381}, {1738, 69015}, {1909, 24987}, {1975, 57287}, {3006, 20347}, {3263, 3717}, {3419, 69380}, {3663, 29673}, {3664, 29653}, {3687, 56509}, {3693, 4437}, {3699, 68926}, {3705, 30946}, {3760, 10916}, {3785, 4652}, {3914, 49518}, {3916, 7767}, {3940, 69437}, {3945, 26065}, {3951, 69409}, {3952, 33864}, {3971, 24241}, {3975, 26001}, {3984, 69414}, {4115, 5074}, {4292, 69670}, {4358, 69083}, {4416, 5282}, {4422, 68929}, {4441, 4847}, {4554, 51364}, {4855, 6337}, {4967, 33162}, {5088, 16086}, {5175, 69379}, {5179, 63817}, {5224, 19804}, {5232, 62300}, {5249, 37664}, {5440, 6390}, {5744, 15589}, {5745, 37670}, {5748, 63098}, {6376, 24982}, {6646, 30179}, {6736, 25278}, {7085, 68653}, {7179, 32937}, {7758, 54406}, {7763, 27385}, {7776, 58798}, {7788, 17781}, {7795, 69283}, {9369, 56928}, {10436, 33163}, {13161, 24995}, {14828, 33116}, {16992, 54357}, {17149, 24997}, {17270, 26034}, {17272, 32778}, {17321, 62833}, {17735, 49752}, {17755, 51400}, {18651, 62564}, {20007, 32840}, {20541, 68870}, {20728, 25083}, {20924, 69080}, {21101, 25353}, {21711, 49777}, {24514, 69276}, {24564, 31997}, {25007, 52043}, {26590, 49514}, {27383, 32831}, {30701, 55337}, {30962, 56507}, {32099, 63140}, {32851, 68928}, {33948, 69967}, {41012, 69254}, {42703, 65196}, {53332, 67267}, {54303, 55912}, {54398, 69433}, {56078, 64702}

X(70091) = isotomic conjugate of X(36124)
X(70091) = isotomic conjugate of the isogonal conjugate of X(1818)
X(70091) = isotomic conjugate of the polar conjugate of X(3912)
X(70091) = X(i)-cross conjugate of X(j) for these (i,j): {1818, 3912}, {20820, 3}
X(70091) = X(i)-isoconjugate of X(j) for these (i,j): {4, 64216}, {6, 8751}, {19, 1438}, {25, 105}, {28, 56853}, {31, 36124}, {32, 54235}, {33, 1416}, {34, 2195}, {108, 884}, {112, 55261}, {294, 608}, {393, 32658}, {607, 1462}, {667, 65333}, {673, 1973}, {919, 6591}, {1024, 32674}, {1027, 8750}, {1096, 36057}, {1333, 68565}, {1395, 14942}, {1398, 28071}, {1474, 18785}, {1783, 43929}, {1814, 2207}, {1974, 2481}, {2201, 51866}, {2203, 13576}, {2204, 66941}, {2212, 56783}, {2356, 51838}, {5089, 41934}, {5377, 42067}, {7649, 32666}, {10099, 32713}, {18344, 32735}, {32703, 68776}, {43923, 52927}, {52030, 57654}, {57655, 66290}
X(70091) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 36124}, {6, 1438}, {9, 8751}, {37, 68565}, {518, 2356}, {2238, 2201}, {3008, 54234}, {3912, 242}, {6184, 19}, {6337, 673}, {6338, 31637}, {6376, 54235}, {6503, 36057}, {6505, 105}, {6631, 65333}, {11517, 2195}, {17060, 40987}, {17755, 4}, {20621, 1096}, {25083, 1738}, {26932, 1027}, {27918, 65106}, {34591, 55261}, {35072, 1024}, {35094, 7649}, {36033, 64216}, {36905, 278}, {38980, 6591}, {38983, 884}, {39006, 43929}, {39046, 25}, {39063, 34}, {40591, 56853}, {40609, 33}, {40618, 62635}, {40626, 885}, {40869, 1886}, {51574, 18785}, {62564, 13576}, {62565, 66941}, {62584, 14942}, {62587, 92}, {62591, 56639}, {62604, 18031}, {62647, 294}
X(70091) = cevapoint of X(3) and X(20807)
X(70091) = crosspoint of X(69) and X(337)
X(70091) = crosssum of X(25) and X(57654)
X(70091) = crossdifference of every pair of points on line {1973, 57047}
X(70091) = barycentric product X(i)*X(j) for these {i,j}: {63, 3263}, {69, 3912}, {72, 18157}, {75, 25083}, {76, 1818}, {78, 40704}, {241, 3718}, {304, 518}, {305, 672}, {306, 30941}, {326, 46108}, {337, 17755}, {345, 9436}, {348, 3717}, {525, 68998}, {561, 20752}, {656, 55260}, {883, 6332}, {918, 4561}, {1025, 35518}, {1026, 15413}, {1264, 5236}, {1265, 62786}, {1458, 57919}, {1861, 3926}, {1978, 53550}, {2223, 40364}, {2340, 57918}, {3267, 54353}, {3286, 40071}, {3693, 7182}, {3932, 17206}, {4025, 42720}, {4088, 4563}, {4437, 31637}, {9454, 40050}, {10029, 44722}, {15149, 52396}, {15416, 41353}, {18031, 65744}, {18206, 20336}, {18895, 20778}, {23151, 63231}, {23829, 52609}, {24290, 55202}, {34855, 52406}, {50333, 65164}, {53551, 55207}
X(70091) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 8751}, {2, 36124}, {3, 1438}, {10, 68565}, {48, 64216}, {63, 105}, {69, 673}, {71, 56853}, {72, 18785}, {75, 54235}, {77, 1462}, {78, 294}, {190, 65333}, {219, 2195}, {222, 1416}, {241, 34}, {255, 32658}, {295, 51866}, {304, 2481}, {305, 18031}, {306, 13576}, {307, 66941}, {326, 1814}, {337, 52209}, {345, 14942}, {348, 56783}, {394, 36057}, {518, 19}, {521, 1024}, {652, 884}, {656, 55261}, {672, 25}, {883, 653}, {905, 1027}, {906, 32666}, {914, 52456}, {918, 7649}, {1025, 108}, {1026, 1783}, {1265, 6559}, {1331, 919}, {1332, 36086}, {1458, 608}, {1459, 43929}, {1813, 32735}, {1814, 51838}, {1818, 6}, {1861, 393}, {2223, 1973}, {2254, 6591}, {2283, 32674}, {2284, 8750}, {2340, 607}, {2356, 2207}, {3263, 92}, {3286, 1474}, {3692, 28071}, {3693, 33}, {3717, 281}, {3718, 36796}, {3912, 4}, {3926, 31637}, {3930, 1824}, {3932, 1826}, {3942, 43921}, {4025, 62635}, {4064, 66282}, {4088, 2501}, {4101, 14625}, {4238, 24019}, {4437, 1861}, {4447, 7119}, {4561, 666}, {4587, 52927}, {4712, 5089}, {4966, 1839}, {5089, 1096}, {5236, 1118}, {6184, 2356}, {6332, 885}, {6516, 36146}, {7182, 34018}, {8299, 2201}, {9436, 278}, {9454, 1974}, {15149, 8747}, {16593, 54234}, {16728, 54407}, {17755, 242}, {18157, 286}, {18206, 28}, {20683, 2333}, {20752, 31}, {20776, 9454}, {20778, 1914}, {20902, 66290}, {22350, 51987}, {23225, 1919}, {23829, 17925}, {24018, 10099}, {25083, 1}, {26006, 56639}, {30941, 27}, {31637, 6185}, {34230, 8752}, {34855, 1435}, {36057, 41934}, {40704, 273}, {41353, 32714}, {42720, 1897}, {46108, 158}, {50333, 3064}, {50441, 1886}, {51390, 1785}, {51400, 1851}, {52635, 1395}, {53544, 43923}, {53550, 649}, {53551, 55208}, {53583, 68783}, {54353, 112}, {54407, 5317}, {55260, 811}, {56753, 36123}, {62552, 65106}, {62786, 1119}, {65164, 927}, {65744, 672}, {68743, 40983}, {68813, 18344}, {68998, 648}, {69093, 1848}
X(70091) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 60729, 4001}, {668, 69038, 6735}, {1975, 69737, 57287}, {3717, 9436, 3263}

X(70092) = X(9)X(26234)∩X(38)X(17353)

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

X(70092) lies on these lines: {9, 26234}, {38, 17353}, {72, 27109}, {344, 3873}, {672, 3263}, {2225, 20610}, {2275, 26689}, {3008, 69015}, {3210, 37681}, {3218, 69263}, {3219, 4359}, {3618, 28606}, {3726, 4422}, {3759, 3896}, {4358, 37686}, {4487, 4595}, {4687, 7226}, {4899, 53552}, {4981, 17289}, {7792, 56520}, {16552, 20911}, {16601, 17141}, {24631, 59207}, {25248, 41015}, {26242, 26685}, {26562, 69246}, {33819, 69283}, {33950, 69858}, {43065, 53332}

X(70092) = X(i)-isoconjugate of X(j) for these (i,j): {105, 65027}, {1438, 7241}
X(70092) = X(i)-Dao conjugate of X(j) for these (i,j): {6184, 7241}, {39046, 65027}, {62587, 30636}
X(70092) = barycentric product X(i)*X(j) for these {i,j}: {3263, 17127}, {3759, 3912}, {3896, 30941}, {4170, 68998}, {4380, 42720}
X(70092) = barycentric quotient X(i)/X(j) for these {i,j}: {518, 7241}, {672, 65027}, {3263, 30636}, {3759, 673}, {3896, 13576}, {4380, 62635}, {4401, 1027}, {7031, 1438}, {17127, 105}
X(70092) = {X(672),X(17755)}-harmonic conjugate of X(3263)

X(70093) = X(9)X(24602)∩X(190)X(3218)

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

X(70093) lies on these lines: {9, 24602}, {190, 3218}, {518, 42720}, {672, 3263}, {742, 20331}, {894, 37670}, {1025, 40704}, {3693, 16728}, {3758, 17126}, {3912, 14439}, {4392, 4664}, {4406, 47762}, {4766, 24318}, {5205, 60960}, {9318, 26239}, {16549, 20911}, {17137, 25066}, {17256, 33086}, {17754, 24629}, {17756, 49496}, {21281, 26690}, {25350, 46907}, {32931, 50127}, {43065, 69028}, {54280, 63961}

X(70093) = X(i)-isoconjugate of X(j) for these (i,j): {105, 65026}, {1438, 4492}, {57725, 64216}
X(70093) = X(i)-Dao conjugate of X(j) for these (i,j): {6184, 4492}, {17755, 57725}, {39046, 65026}, {62587, 30635}
X(70093) = crosspoint of X(3758) and X(43262)
X(70093) = barycentric product X(i)*X(j) for these {i,j}: {518, 64133}, {883, 47729}, {1026, 4406}, {3263, 17126}, {3758, 3912}, {3997, 18157}, {4761, 68998}, {17755, 43262}, {30941, 46897}, {42720, 47762}, {62627, 64612}
X(70093) = barycentric quotient X(i)/X(j) for these {i,j}: {518, 4492}, {609, 1438}, {672, 65026}, {3263, 30635}, {3758, 673}, {3809, 52029}, {3912, 57725}, {3997, 18785}, {17126, 105}, {43262, 52209}, {46897, 13576}, {47729, 885}, {47762, 62635}, {64133, 2481}

X(70094) = X(10)X(50155)∩X(38)X(3122)

Barycentrics   (2*a^2 - b^2 - c^2)*(a*b - b^2 + a*c - c^2) : :
X(70094) = 3 X[3120] - 4 X[25383]

X(70094) lies on these lines: {10, 50155}, {38, 3122}, {63, 2895}, {190, 24712}, {325, 69727}, {524, 896}, {527, 3006}, {545, 57035}, {668, 21013}, {672, 3912}, {918, 2254}, {1025, 52502}, {1647, 4465}, {2642, 4750}, {3120, 25383}, {3770, 21014}, {3952, 24318}, {3985, 69083}, {4126, 25355}, {4419, 33120}, {4437, 14439}, {4470, 33163}, {4643, 36263}, {4644, 29643}, {4697, 50261}, {4754, 21674}, {4758, 5294}, {5282, 54280}, {7200, 21711}, {7813, 21839}, {8013, 49717}, {15523, 24690}, {17163, 63147}, {17165, 25353}, {20072, 69576}, {21029, 56024}, {21085, 50278}, {22110, 30868}, {23827, 48571}, {24330, 29690}, {24685, 51583}, {24691, 29687}, {24694, 32933}, {29576, 39367}, {31129, 31349}, {32781, 42439}, {50274, 59624}

X(70094) = X(i)-isoconjugate of X(j) for these (i,j): {105, 111}, {294, 7316}, {671, 64216}, {673, 923}, {691, 55261}, {895, 8751}, {897, 1438}, {919, 69473}, {1462, 5547}, {1814, 8753}, {2481, 32740}, {5380, 43929}, {14908, 54235}, {17983, 32658}, {32666, 62626}, {32735, 69476}, {36057, 36128}, {36060, 36124}, {36086, 66945}
X(70094) = X(i)-Dao conjugate of X(j) for these (i,j): {1560, 36124}, {2482, 673}, {6184, 897}, {6593, 1438}, {17755, 671}, {20621, 36128}, {35094, 62626}, {38980, 69473}, {38989, 66945}, {39046, 111}, {52881, 31637}, {62587, 46277}
X(70094) = crossdifference of every pair of points on line {923, 1438}
X(70094) = barycentric product X(i)*X(j) for these {i,j}: {518, 14210}, {524, 3912}, {672, 3266}, {690, 68998}, {883, 14432}, {896, 3263}, {1818, 44146}, {1861, 6390}, {2254, 42721}, {2642, 55260}, {3712, 9436}, {3717, 7181}, {3930, 16741}, {3932, 6629}, {4062, 30941}, {4088, 5468}, {4750, 42720}, {4760, 40217}, {4966, 31013}, {18157, 21839}, {18206, 42713}, {24039, 24290}, {35522, 54353}
X(70094) = barycentric quotient X(i)/X(j) for these {i,j}: {187, 1438}, {468, 36124}, {518, 897}, {524, 673}, {665, 66945}, {672, 111}, {896, 105}, {918, 62626}, {922, 64216}, {1026, 5380}, {1458, 7316}, {1818, 895}, {1861, 17983}, {2223, 923}, {2254, 69473}, {2340, 5547}, {2356, 8753}, {2642, 55261}, {3263, 46277}, {3266, 18031}, {3292, 36057}, {3712, 14942}, {3912, 671}, {4062, 13576}, {4088, 5466}, {4750, 62635}, {4760, 6654}, {5089, 36128}, {6390, 31637}, {7181, 56783}, {9454, 32740}, {14210, 2481}, {14419, 1027}, {14432, 885}, {14439, 69474}, {20752, 36060}, {21839, 18785}, {24290, 23894}, {42721, 51560}, {51653, 1462}, {54353, 691}, {68813, 69476}, {68998, 892}, {69572, 66282}

X(70095) = X(2)X(21101)∩X(9)X(31130)

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

X(70095) lies on these lines: {2, 21101}, {9, 31130}, {38, 30748}, {75, 59207}, {141, 4126}, {142, 17165}, {672, 3263}, {748, 4361}, {756, 3739}, {1334, 33937}, {1475, 33942}, {1930, 3691}, {3305, 28605}, {3717, 51400}, {3718, 28351}, {3720, 49481}, {3946, 3995}, {3952, 20335}, {4000, 32925}, {4357, 31077}, {4382, 4408}, {4661, 17296}, {4723, 21232}, {14439, 40883}, {17050, 56318}, {17141, 29968}, {17353, 31087}, {20257, 25253}, {24068, 24790}, {24592, 33931}, {24786, 59666}, {30821, 49509}, {30949, 32937}, {33933, 56024}, {49774, 53332}

X(70095) = X(i)-isoconjugate of X(j) for these (i,j): {105, 30651}, {749, 1438}
X(70095) = X(i)-Dao conjugate of X(j) for these (i,j): {6184, 749}, {39046, 30651}, {62587, 57947}
X(70095) = barycentric product X(i)*X(j) for these {i,j}: {518, 3760}, {748, 3263}, {1026, 4408}, {3693, 7243}, {3912, 4361}, {4365, 30941}, {4382, 42720}, {4387, 9436}
X(70095) = barycentric quotient X(i)/X(j) for these {i,j}: {518, 749}, {672, 30651}, {748, 105}, {2241, 1438}, {3263, 57947}, {3760, 2481}, {4361, 673}, {4365, 13576}, {4382, 62635}, {4387, 14942}, {4501, 1024}, {7225, 1462}, {7243, 34018}
X(70095) = {X(3263),X(17755)}-harmonic conjugate of X(672)

X(70096) = X(75)X(24629)∩X(244)X(536)

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

X(70096) lies on these lines: {75, 24629}, {190, 24602}, {192, 30967}, {244, 536}, {320, 3807}, {527, 3952}, {545, 4937}, {672, 3263}, {742, 899}, {750, 4363}, {902, 24358}, {1149, 68890}, {1334, 33942}, {1475, 33937}, {1978, 40875}, {3006, 24318}, {3306, 4659}, {3703, 25355}, {3720, 24326}, {3912, 42720}, {3930, 40883}, {3989, 25349}, {4070, 24582}, {4071, 33864}, {4119, 69083}, {4379, 4411}, {4419, 64178}, {4667, 62668}, {4723, 35102}, {4871, 24403}, {5205, 9318}, {8682, 49984}, {9055, 17449}, {10436, 26247}, {10459, 16720}, {17754, 31130}, {20893, 69869}, {23891, 49780}, {24357, 30950}, {24712, 32850}, {25342, 37762}, {25353, 69250}, {25384, 30970}, {28301, 42026}, {30758, 59207}, {31063, 50116}, {33932, 56024}, {42713, 61163}

X(70096) = reflection of X(24403) in X(4871)
X(70096) = X(i)-isoconjugate of X(j) for these (i,j): {105, 30650}, {751, 1438}, {1027, 65832}
X(70096) = X(i)-Dao conjugate of X(j) for these (i,j): {6184, 751}, {39046, 30650}, {62587, 57948}
X(70096) = crosspoint of X(4363) and X(7245)
X(70096) = barycentric product X(i)*X(j) for these {i,j}: {241, 4494}, {518, 3761}, {750, 3263}, {883, 4474}, {918, 4482}, {1026, 4411}, {3717, 7223}, {3912, 4363}, {4377, 18206}, {4379, 42720}, {4390, 40704}, {4396, 40217}, {4495, 22116}, {7245, 17755}
X(70096) = barycentric quotient X(i)/X(j) for these {i,j}: {518, 751}, {672, 30650}, {750, 105}, {2242, 1438}, {2284, 65832}, {3263, 57948}, {3761, 2481}, {4363, 673}, {4378, 1027}, {4379, 62635}, {4390, 294}, {4396, 6654}, {4474, 885}, {4482, 666}, {4494, 36796}, {7223, 56783}, {7245, 52209}

X(70097) = X(10)X(23407)∩X(35)X(404)

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

X(70097) lies on these lines: {10, 23407}, {21, 19868}, {35, 404}, {36, 49768}, {39, 3744}, {55, 17023}, {69, 16688}, {100, 3008}, {386, 62834}, {978, 62875}, {1001, 16412}, {1266, 4436}, {1279, 69016}, {1324, 11344}, {1429, 54440}, {2078, 43054}, {2223, 3912}, {3286, 4684}, {3662, 41430}, {3722, 20456}, {3759, 4097}, {3870, 4253}, {3879, 3941}, {3920, 25092}, {4170, 4380}, {4184, 16887}, {4203, 13405}, {4238, 5236}, {4314, 37030}, {4357, 8053}, {4416, 20992}, {4433, 49770}, {4480, 21320}, {4967, 16684}, {5010, 29660}, {5144, 19308}, {5248, 19310}, {6745, 35992}, {7031, 17127}, {8618, 20878}, {11329, 52015}, {15624, 17353}, {15953, 37610}, {16834, 67331}, {17397, 61155}, {20888, 26237}, {21010, 29574}, {21495, 40910}, {24598, 62806}, {25101, 34247}, {25440, 26241}, {35270, 62817}, {37590, 49476}, {48696, 50022}, {58327, 69735}, {59301, 62807}

X(70097) = X(i)-isoconjugate of X(j) for these (i,j): {105, 7241}, {673, 65027}, {30636, 64216}
X(70097) = X(i)-Dao conjugate of X(j) for these (i,j): {17755, 30636}, {39046, 7241}
X(70097) = crossdifference of every pair of points on line {29956, 65027}
X(70097) = barycentric product X(i)*X(j) for these {i,j}: {518, 3759}, {1026, 4380}, {3263, 7031}, {3896, 18206}, {3912, 17127}, {4401, 42720}, {4447, 43263}
X(70097) = barycentric quotient X(i)/X(j) for these {i,j}: {672, 7241}, {2223, 65027}, {3759, 2481}, {3912, 30636}, {4401, 62635}, {7031, 105}, {17127, 673}
X(70097) = {X(2223),X(8299)}-harmonic conjugate of X(3912)

X(70098) = X(3)X(49476)∩X(36)X(100)

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

X(70098) lies on these lines: {3, 49476}, {36, 100}, {55, 16436}, {56, 49466}, {63, 41276}, {171, 11364}, {192, 41430}, {344, 16688}, {538, 15447}, {609, 3809}, {672, 1026}, {730, 4434}, {760, 67428}, {993, 50291}, {1155, 14839}, {1376, 50095}, {2223, 3912}, {2283, 9436}, {2340, 18206}, {3218, 67417}, {3286, 3717}, {3879, 15624}, {3941, 17353}, {4097, 17377}, {4357, 20990}, {4416, 34247}, {4433, 49761}, {4480, 69723}, {4761, 4844}, {9024, 67501}, {9441, 69735}, {17023, 21010}, {20992, 25101}, {23407, 29571}, {50573, 65573}, {54440, 56530}, {61156, 66441}, {63145, 69903}

X(70098) = X(43262)-Ceva conjugate of X(3997)
X(70098) = X(i)-isoconjugate of X(j) for these (i,j): {105, 4492}, {673, 65026}, {1438, 57725}, {30635, 64216}
X(70098) = X(i)-Dao conjugate of X(j) for these (i,j): {6184, 57725}, {17755, 30635}, {39046, 4492}, {62587, 57920}
X(70098) = crossdifference of every pair of points on line {29956, 65026}
X(70098) = barycentric product X(i)*X(j) for these {i,j}: {518, 3758}, {609, 3263}, {672, 64133}, {1025, 47729}, {1026, 47762}, {2284, 4406}, {3912, 17126}, {3997, 30941}, {8299, 43262}, {18206, 46897}
X(70098) = barycentric quotient X(i)/X(j) for these {i,j}: {518, 57725}, {609, 105}, {672, 4492}, {2223, 65026}, {3263, 57920}, {3758, 2481}, {3912, 30635}, {3997, 13576}, {17126, 673}, {43262, 67197}, {64133, 18031}
X(70098) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2223, 4447, 3912}, {3809, 17126, 3997}

X(70099) = X(2)X(2795)∩X(3)X(191)

Barycentrics   a*(2*a^2 - b^2 - c^2)*(a*b - b^2 + a*c - c^2) : :
X(70099) = X[2223] + 2 X[25083], 2 X[4436] + X[4516], X[4433] + 2 X[69084], X[4459] + 2 X[22003], X[7202] + 2 X[69842]

X(70099) lies on these lines: {2, 2795}, {3, 191}, {39, 3121}, {100, 53180}, {187, 896}, {351, 690}, {392, 37575}, {513, 40988}, {518, 2223}, {574, 4414}, {665, 1642}, {1009, 5883}, {1018, 67428}, {1155, 57015}, {1580, 38221}, {2805, 4436}, {2826, 6174}, {3647, 37023}, {3675, 8299}, {3712, 6390}, {3793, 4831}, {4062, 7813}, {4427, 9978}, {4433, 69084}, {4459, 22003}, {4933, 39785}, {5467, 41606}, {7202, 69842}, {7801, 33156}, {8369, 46899}, {25066, 46196}, {30799, 30862}, {35258, 37586}, {37592, 58401}

X(70099) = complement of X(53373)
X(70099) = psi-transform of X(67629)
X(i)-isoconjugate of X(j) for these (i,j): {105, 897}, {111, 673}, {666, 66945}, {671, 1438}, {895, 36124}, {919, 62626}, {923, 2481}, {1027, 5380}, {1814, 36128}, {5547, 56783}, {7316, 14942}, {8753, 31637}, {17983, 36057}, {18031, 32740}, {36060, 54235}, {36085, 55261}, {36086, 69473}, {36146, 69476}, {46277, 64216}
X(70099) = X(i)-Dao conjugate of X(j) for these (i,j): {1560, 54235}, {1649, 66290}, {2482, 2481}, {6184, 671}, {6593, 105}, {17755, 46277}, {20621, 17983}, {38980, 62626}, {38988, 55261}, {38989, 69473}, {39014, 69476}, {39046, 897}, {62587, 18023}
X(70099) = crosssum of X(6) and X(53310)
X(70099) = crossdifference of every pair of points on line {105, 111}
X(70099) = barycentric product X(i)*X(j) for these {i,j}: {187, 3263}, {241, 3712}, {351, 55260}, {468, 25083}, {518, 524}, {665, 42721}, {672, 14210}, {896, 3912}, {1025, 14432}, {1026, 4750}, {2223, 3266}, {2642, 68998}, {3286, 42713}, {3292, 46108}, {3693, 7181}, {3717, 51653}, {3930, 6629}, {3932, 16702}, {4062, 18206}, {4088, 23889}, {4238, 14417}, {4760, 22116}, {5089, 6390}, {5468, 24290}, {14419, 42720}, {14439, 52759}, {16741, 20683}, {20752, 44146}, {21839, 30941}
X(70099) = barycentric quotient X(i)/X(j) for these {i,j}: {187, 105}, {351, 55261}, {468, 54235}, {518, 671}, {524, 2481}, {665, 69473}, {672, 897}, {896, 673}, {922, 1438}, {926, 69476}, {1648, 66290}, {2223, 111}, {2254, 62626}, {2284, 5380}, {2356, 36128}, {3263, 18023}, {3292, 1814}, {3712, 36796}, {3912, 46277}, {4238, 65350}, {5089, 17983}, {7181, 34018}, {9454, 923}, {9455, 32740}, {14210, 18031}, {14419, 62635}, {14439, 52747}, {14567, 64216}, {20752, 895}, {21839, 13576}, {23200, 32658}, {24290, 5466}, {25083, 30786}, {35293, 52764}, {42721, 36803}, {44102, 8751}, {46108, 46111}, {51653, 56783}, {52635, 7316}, {54353, 36085}, {55260, 53080}, {58331, 28132}

X(70100) = X(1)X(56165)∩X(55)X(17284)

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

X(70100) lies on these lines: {1, 56165}, {55, 17284}, {100, 17266}, {354, 3991}, {667, 20757}, {748, 2241}, {1001, 17308}, {1018, 20358}, {1083, 20769}, {1500, 3720}, {1621, 17292}, {1698, 3295}, {1734, 50518}, {1739, 3931}, {2223, 3912}, {2325, 21320}, {3008, 4433}, {3501, 64560}, {3675, 25083}, {3693, 20680}, {3706, 29433}, {3712, 62739}, {3760, 4387}, {3831, 21321}, {3834, 4436}, {3941, 17311}, {4068, 17384}, {4557, 41310}, {4721, 32930}, {5091, 58327}, {5284, 29610}, {8053, 17231}, {15624, 17267}, {16684, 17229}, {17230, 23407}, {17282, 64727}, {17296, 20992}, {17357, 64169}, {17798, 45765}, {20821, 23646}, {21010, 29573}, {22060, 69258}, {27020, 32942}, {29687, 54327}

X(70100) = X(i)-isoconjugate of X(j) for these (i,j): {105, 749}, {673, 30651}, {57947, 64216}
X(70100) = X(i)-Dao conjugate of X(j) for these (i,j): {17755, 57947}, {39046, 749}
X(70100) = crossdifference of every pair of points on line {29956, 30651}
X(70100) = barycentric product X(i)*X(j) for these {i,j}: {241, 4387}, {518, 4361}, {672, 3760}, {748, 3912}, {883, 4501}, {1026, 4382}, {2241, 3263}, {2284, 4408}, {2340, 7243}, {3717, 7225}, {4365, 18206}, {4447, 4496}
X(70100) = barycentric quotient X(i)/X(j) for these {i,j}: {672, 749}, {748, 673}, {2223, 30651}, {2241, 105}, {3760, 18031}, {3912, 57947}, {4361, 2481}, {4387, 36796}, {4501, 885}, {7225, 56783}
X(70100) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3912, 8299, 2223}, {4433, 44304, 3008}

X(70101) = X(55)X(21509)∩X(100)X(17310)

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

X(70101) lies on these lines: {55, 21509}, {100, 17310}, {171, 68898}, {518, 1026}, {665, 65874}, {668, 5205}, {750, 2242}, {752, 33845}, {851, 49990}, {899, 1015}, {999, 3679}, {1018, 1155}, {1376, 17294}, {1621, 29575}, {2223, 3912}, {2239, 3230}, {2325, 69723}, {2340, 39046}, {3218, 3799}, {3761, 7223}, {3930, 35293}, {3941, 17267}, {4378, 4379}, {4396, 7245}, {4433, 49765}, {4557, 17374}, {4715, 23343}, {5091, 56530}, {5284, 29620}, {5525, 67417}, {9025, 69029}, {9317, 17763}, {15624, 17311}, {16679, 17357}, {17231, 20990}, {17284, 21010}, {17296, 34247}, {17298, 64170}, {20683, 56714}, {20715, 68759}, {22060, 69295}, {23407, 29572}, {24268, 29649}, {24405, 31138}, {24593, 56811}, {27295, 37764}, {28538, 54333}, {29674, 37609}, {29687, 40956}, {41141, 44304}, {49979, 68841}, {57015, 67428}, {69261, 69300}

X(70101) = X(i)-isoconjugate of X(j) for these (i,j): {105, 751}, {673, 30650}, {57948, 64216}, {62635, 65832}
X(70101) = X(i)-Dao conjugate of X(j) for these (i,j): {17755, 57948}, {39046, 751}
X(70101) = crossdifference of every pair of points on line {29956, 30650}
X(70101) = barycentric product X(i)*X(j) for these {i,j}: {518, 4363}, {672, 3761}, {750, 3912}, {1025, 4474}, {1026, 4379}, {1458, 4494}, {2242, 3263}, {2254, 4482}, {2284, 4411}, {3252, 4495}, {3286, 4377}, {3693, 7223}, {4378, 42720}, {4390, 9436}, {4396, 22116}, {4506, 34230}, {4510, 14439}, {7245, 8299}
X(70101) = barycentric quotient X(i)/X(j) for these {i,j}: {672, 751}, {750, 673}, {2223, 30650}, {2242, 105}, {3761, 18031}, {3912, 57948}, {4363, 2481}, {4378, 62635}, {4390, 14942}, {4482, 51560}, {7223, 34018}, {7245, 67197}, {54325, 65832}
X(70101) = {X(3912),X(4447)}-harmonic conjugate of X(2223)

X(70102) = X(39)X(8620)∩X(518)X(2223)

Barycentrics   a*(a^2 - 2*b^2 - 2*c^2)*(a*b - b^2 + a*c - c^2) : :
X(70102) = X[2223] - 4 X[25083], 2 X[20544] + X[25257]

X(70102) lies on these lines: {39, 8620}, {518, 2223}, {574, 36263}, {2805, 35552}, {3263, 55260}, {3675, 3693}, {3906, 4141}, {5692, 37575}, {7801, 33161}, {7813, 32848}, {20544, 25257}, {37597, 61686}

X(70102) = midpoint of X(25257) and X(53373)
X(70102) = reflection of X(53373) in X(20544)
X(70102) = X(i)-isoconjugate of X(j) for these (i,j): {105, 55927}, {598, 1438}, {673, 1383}, {36057, 68566}, {36124, 43697}
X(70102) = X(i)-Dao conjugate of X(j) for these (i,j): {6184, 598}, {8542, 105}, {11165, 2481}, {17413, 55261}, {17436, 66290}, {20621, 68566}, {39046, 55927}, {62587, 40826}
X(70102) = crossdifference of every pair of points on line {1383, 55261}
X(70102) = barycentric product X(i)*X(j) for these {i,j}: {518, 599}, {574, 3263}, {918, 3908}, {2223, 9464}, {3912, 36263}, {5089, 69437}, {5094, 25083}, {9146, 24290}, {17414, 55260}
X(70102) = barycentric quotient X(i)/X(j) for these {i,j}: {518, 598}, {574, 105}, {599, 2481}, {672, 55927}, {2223, 1383}, {3263, 40826}, {3908, 666}, {5089, 68566}, {5094, 54235}, {8288, 66290}, {8541, 8751}, {17414, 55261}, {20752, 43697}, {24290, 8599}, {25083, 64982}, {36263, 673}

X(70103) = X(7)X(3596)∩X(75)X(49524)

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

X(70103) lies on these lines: {7, 3596}, {75, 49524}, {76, 24349}, {226, 51861}, {304, 3790}, {305, 32937}, {312, 31038}, {334, 52662}, {335, 3948}, {514, 20501}, {518, 64223}, {668, 4645}, {732, 894}, {1015, 26986}, {2533, 3805}, {2810, 20561}, {3263, 3717}, {3264, 59526}, {3266, 3952}, {3662, 6376}, {3703, 18138}, {3705, 21590}, {3751, 69052}, {3782, 18057}, {3932, 18157}, {3934, 27019}, {4110, 16284}, {4310, 18135}, {4554, 41352}, {4579, 12215}, {4710, 50307}, {4986, 49697}, {6381, 24231}, {6541, 14210}, {8024, 17165}, {16703, 69296}, {17140, 39998}, {17242, 18156}, {17368, 31997}, {17789, 66882}, {18067, 33103}, {20913, 31317}, {21404, 40075}, {21415, 33162}, {21416, 29673}, {21803, 59509}, {24524, 50289}, {27076, 27116}, {27538, 57518}, {27966, 28010}, {33101, 59510}, {33677, 40875}, {35551, 69690}, {36854, 57919}

X(70103) = isotomic conjugate of the isogonal conjugate of X(4447)
X(70103) = X(40217)-Ceva conjugate of X(64223)
X(70103) = X(i)-isoconjugate of X(j) for these (i,j): {105, 904}, {256, 64216}, {294, 66996}, {673, 7104}, {884, 29055}, {893, 1438}, {1178, 56853}, {1431, 2195}, {2481, 66931}, {6654, 9468}, {7116, 8751}, {14942, 67144}, {52030, 61385}
X(70103) = X(i)-Dao conjugate of X(j) for these (i,j): {3912, 18786}, {6184, 893}, {16587, 18785}, {16592, 1027}, {17755, 256}, {36905, 1432}, {39044, 6654}, {39046, 904}, {39063, 1431}, {40597, 1438}, {52656, 694}, {62587, 257}, {62650, 105}
X(70103) = crosssum of X(904) and X(61385)
X(70103) = barycentric product X(i)*X(j) for these {i,j}: {76, 4447}, {518, 1920}, {894, 3263}, {918, 69896}, {1215, 18157}, {1237, 18206}, {1909, 3912}, {1926, 3252}, {1966, 40217}, {1978, 53553}, {2533, 55260}, {3693, 7205}, {3717, 7196}, {3932, 8033}, {3963, 30941}, {3978, 22116}, {4374, 42720}, {7081, 40704}, {9436, 17787}, {14603, 40730}, {27919, 30642}, {30669, 64223}
X(70103) = barycentric quotient X(i)/X(j) for these {i,j}: {171, 1438}, {172, 64216}, {241, 1431}, {518, 893}, {672, 904}, {883, 37137}, {894, 105}, {1025, 29055}, {1215, 18785}, {1458, 66996}, {1818, 7116}, {1909, 673}, {1920, 2481}, {1966, 6654}, {2223, 7104}, {2295, 56853}, {2329, 2195}, {2533, 55261}, {3252, 1967}, {3263, 257}, {3287, 884}, {3805, 29956}, {3907, 1024}, {3912, 256}, {3930, 66971}, {3932, 52651}, {3955, 32658}, {3963, 13576}, {4367, 43929}, {4369, 1027}, {4374, 62635}, {4447, 6}, {4579, 919}, {6649, 36146}, {7009, 8751}, {7081, 294}, {7175, 1416}, {7176, 1462}, {7196, 56783}, {7200, 43921}, {7205, 34018}, {9436, 1432}, {9454, 66931}, {16720, 46149}, {17755, 18786}, {17787, 14942}, {18047, 36086}, {18157, 32010}, {18206, 1178}, {18787, 51866}, {20683, 40729}, {22116, 694}, {25083, 7015}, {30669, 52030}, {30941, 40432}, {40217, 1581}, {40704, 7249}, {40730, 9468}, {42720, 3903}, {52635, 67144}, {53553, 649}, {55260, 4594}, {64223, 17493}, {68998, 4603}, {69894, 32666}, {69896, 666}

X(70104) = X(69)X(72)∩X(75)X(4310)

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

X(70104) lies on these lines: {69, 72}, {75, 4310}, {76, 57791}, {99, 2754}, {141, 3721}, {274, 56137}, {321, 40030}, {348, 30681}, {518, 3263}, {525, 3267}, {668, 7112}, {670, 53204}, {1229, 21615}, {1231, 40364}, {1921, 37788}, {1930, 49511}, {3262, 46238}, {3264, 69746}, {3751, 33942}, {3827, 53332}, {4033, 69690}, {4437, 40704}, {5847, 14210}, {7182, 52406}, {16496, 33937}, {16703, 19835}, {17786, 69662}, {18156, 51192}, {20643, 30807}, {30693, 59200}, {30758, 59406}, {35543, 48380}, {42709, 69822}, {69734, 69752}

X(70104) = isotomic conjugate of X(8751)
X(70104) = isotomic conjugate of the isogonal conjugate of X(25083)
X(70104) = isotomic conjugate of the polar conjugate of X(3263)
X(70104) = X(25083)-cross conjugate of X(3263)
X(70104) = X(i)-isoconjugate of X(j) for these (i,j): {19, 64216}, {25, 1438}, {31, 8751}, {32, 36124}, {105, 1973}, {294, 1395}, {560, 54235}, {607, 1416}, {608, 2195}, {673, 1974}, {884, 32674}, {1096, 32658}, {1462, 2212}, {1474, 56853}, {1919, 65333}, {2203, 18785}, {2206, 68565}, {2207, 36057}, {2356, 41934}, {6591, 32666}, {8750, 43929}, {18031, 44162}, {31637, 36417}, {32676, 55261}, {51866, 57654}
X(70104) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 8751}, {6, 64216}, {2238, 57654}, {3912, 2201}, {6184, 25}, {6337, 105}, {6338, 1814}, {6374, 54235}, {6376, 36124}, {6503, 32658}, {6505, 1438}, {9296, 65333}, {15526, 55261}, {17755, 19}, {20621, 2207}, {23285, 66290}, {25083, 3290}, {26932, 43929}, {35072, 884}, {35094, 6591}, {36905, 34}, {39046, 1973}, {39063, 608}, {40603, 68565}, {40609, 607}, {40618, 1027}, {40626, 1024}, {51574, 56853}, {62564, 18785}, {62573, 10099}, {62584, 294}, {62587, 4}, {62604, 2481}, {62614, 13576}, {62647, 2195}
X(70104) = crossdifference of every pair of points on line {1974, 57097}
X(70104) = barycentric product X(i)*X(j) for these {i,j}: {69, 3263}, {76, 25083}, {241, 57919}, {304, 3912}, {305, 518}, {306, 18157}, {337, 64223}, {345, 40704}, {525, 55260}, {561, 1818}, {672, 40364}, {883, 35518}, {1502, 20752}, {2223, 40050}, {3693, 57918}, {3717, 7182}, {3718, 9436}, {3926, 46108}, {4088, 55202}, {4238, 52617}, {6386, 53550}, {9455, 40360}, {14208, 68998}, {15413, 42720}, {18206, 40071}, {20336, 30941}, {20778, 44172}, {24290, 52608}, {52406, 62786}
X(70104) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 8751}, {3, 64216}, {63, 1438}, {69, 105}, {72, 56853}, {75, 36124}, {76, 54235}, {77, 1416}, {78, 2195}, {241, 608}, {304, 673}, {305, 2481}, {306, 18785}, {321, 68565}, {326, 36057}, {337, 52030}, {339, 66290}, {345, 294}, {348, 1462}, {394, 32658}, {518, 25}, {521, 884}, {525, 55261}, {668, 65333}, {672, 1973}, {883, 108}, {905, 43929}, {918, 6591}, {1025, 32674}, {1026, 8750}, {1231, 66941}, {1265, 28071}, {1331, 32666}, {1332, 919}, {1458, 1395}, {1565, 43921}, {1814, 41934}, {1818, 31}, {1861, 1096}, {1876, 7337}, {2223, 1974}, {2340, 2212}, {3263, 4}, {3265, 10099}, {3286, 2203}, {3675, 42067}, {3693, 607}, {3717, 33}, {3718, 14942}, {3912, 19}, {3926, 1814}, {3930, 2333}, {3932, 1824}, {3933, 46149}, {4025, 1027}, {4238, 32713}, {4437, 5089}, {4561, 36086}, {4571, 52927}, {4684, 5338}, {4712, 2356}, {4966, 2355}, {5089, 2207}, {6332, 1024}, {6516, 32735}, {7182, 56783}, {8299, 57654}, {9436, 34}, {9455, 44162}, {15149, 5317}, {15413, 62635}, {15416, 28132}, {17755, 2201}, {18157, 27}, {18206, 1474}, {20336, 13576}, {20752, 32}, {20776, 9455}, {20778, 2210}, {23102, 42071}, {23225, 1980}, {23829, 57200}, {24290, 2489}, {24562, 2440}, {25083, 6}, {30941, 28}, {31637, 51838}, {34855, 1398}, {35518, 885}, {40364, 18031}, {40704, 278}, {42720, 1783}, {43042, 43923}, {46108, 393}, {50333, 18344}, {51390, 14571}, {52406, 6559}, {52616, 23696}, {53550, 667}, {54353, 32676}, {55260, 648}, {57918, 34018}, {57919, 36796}, {62429, 2969}, {62430, 68783}, {62786, 1435}, {64223, 242}, {65164, 36146}, {65744, 2223}, {68998, 162}, {69093, 1829}

X(70105) = X(75)X(24231)∩X(76)X(49450)

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

X(70105) lies on these lines: {75, 24231}, {76, 49450}, {319, 1269}, {518, 64223}, {668, 49698}, {674, 20561}, {1458, 68998}, {1930, 50315}, {3242, 69052}, {3263, 4966}, {3264, 49715}, {3836, 4986}, {4684, 18157}, {5224, 39731}, {9454, 27919}, {18052, 25006}, {33087, 33937}

X(70105) = X(i)-isoconjugate of X(j) for these (i,j): {1438, 65027}, {7241, 64216}
X(70105) = X(i)-Dao conjugate of X(j) for these (i,j): {6184, 65027}, {17755, 7241}
X(70105) = barycentric product X(i)*X(j) for these {i,j}: {3263, 3759}, {3896, 18157}, {4170, 55260}
X(70105) = barycentric quotient X(i)/X(j) for these {i,j}: {518, 65027}, {3759, 105}, {3896, 18785}, {3912, 7241}, {4170, 55261}, {4380, 1027}, {4401, 43929}, {7031, 64216}, {17127, 1438}

X(70106) = X(75)X(49529)∩X(320)X(668)

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

X(70106) lies on these lines: {75, 49529}, {76, 49499}, {209, 25282}, {320, 668}, {350, 24841}, {518, 64223}, {2340, 68998}, {3717, 18157}, {3758, 3997}, {4406, 4761}, {4439, 14210}, {4986, 49701}, {9026, 20561}, {16741, 50000}, {18138, 63147}, {33677, 69752}, {51560, 56898}, {64070, 69052}

X(70106) = X(i)-isoconjugate of X(j) for these (i,j): {1438, 65026}, {4492, 64216}
X(70106) = X(i)-Dao conjugate of X(j) for these (i,j): {6184, 65026}, {17755, 4492}, {62587, 57725}
X(70106) = barycentric product X(i)*X(j) for these {i,j}: {3263, 3758}, {3912, 64133}, {4406, 42720}, {4761, 55260}, {18157, 46897}, {43262, 64223}
X(70106) = barycentric quotient X(i)/X(j) for these {i,j}: {518, 65026}, {609, 64216}, {3263, 57725}, {3758, 105}, {3912, 4492}, {3997, 56853}, {4406, 62635}, {4761, 55261}, {7208, 43921}, {17126, 1438}, {43262, 52030}, {46897, 18785}, {47729, 1024}, {47762, 1027}, {62627, 36816}, {64133, 673}

X(70107) = X(69)X(2836)∩X(75)X(47358)

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

X(70107) lies on these lines: {69, 2836}, {75, 47358}, {141, 3125}, {321, 51050}, {518, 3263}, {524, 14210}, {599, 33936}, {690, 5181}, {918, 4437}, {4986, 9041}, {18156, 67964}, {20956, 30806}, {26234, 51003}, {30758, 47359}, {31130, 50999}, {33942, 64070}, {46238, 69726}, {62429, 64223}

X(70107) = midpoint of X(69) and X(53332)
X(70107) = reflection of X(3125) in X(141)
X(70107) = X(i)-isoconjugate of X(j) for these (i,j): {105, 923}, {111, 1438}, {673, 32740}, {897, 64216}, {919, 66945}, {1416, 5547}, {2195, 7316}, {8751, 36060}, {8753, 36057}, {14908, 36124}, {18031, 19626}, {32658, 36128}, {32666, 69473}, {36142, 55261}
X(70107) = X(i)-Dao conjugate of X(j) for these (i,j): {1560, 8751}, {2482, 105}, {6184, 111}, {6593, 64216}, {17755, 897}, {20621, 8753}, {23992, 55261}, {35094, 69473}, {38980, 66945}, {39046, 923}, {39063, 7316}, {40609, 5547}, {52881, 1814}, {62577, 66290}, {62587, 671}, {62594, 10099}
X(70107) = crossdifference of every pair of points on line {32740, 64216}
X(70107) = barycentric product X(i)*X(j) for these {i,j}: {518, 3266}, {524, 3263}, {690, 55260}, {918, 42721}, {3712, 40704}, {3912, 14210}, {3932, 16741}, {4062, 18157}, {4088, 24039}, {4238, 45807}, {6390, 46108}, {25083, 44146}, {30941, 42713}
X(70107) = barycentric quotient X(i)/X(j) for these {i,j}: {187, 64216}, {241, 7316}, {468, 8751}, {518, 111}, {524, 105}, {672, 923}, {690, 55261}, {896, 1438}, {918, 69473}, {1818, 36060}, {1861, 36128}, {2223, 32740}, {2254, 66945}, {3263, 671}, {3266, 2481}, {3292, 32658}, {3693, 5547}, {3712, 294}, {3912, 897}, {4062, 18785}, {4088, 23894}, {4750, 1027}, {5089, 8753}, {6390, 1814}, {7181, 1462}, {7813, 46149}, {9455, 19626}, {14210, 673}, {14417, 10099}, {14419, 43929}, {14432, 1024}, {20752, 14908}, {21839, 56853}, {24290, 9178}, {25083, 895}, {42713, 13576}, {42720, 5380}, {42721, 666}, {44146, 54235}, {46108, 17983}, {50333, 69476}, {51653, 1416}, {52628, 66290}, {54353, 36142}, {55260, 892}, {68998, 36085}

X(70108) = X(75)X(3844)∩X(76)X(3696)

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

X(70108) lies on these lines: {75, 3844}, {76, 3696}, {518, 64223}, {594, 20888}, {1386, 69052}, {1930, 17229}, {3673, 30473}, {3706, 8024}, {3760, 4361}, {4033, 20435}, {9037, 20561}, {17293, 32092}, {18040, 20880}, {18067, 21949}, {30596, 42696}, {40619, 59712}

X(70108) = X(i)-isoconjugate of X(j) for these (i,j): {749, 64216}, {1438, 30651}
X(70108) = X(i)-Dao conjugate of X(j) for these (i,j): {6184, 30651}, {17755, 749}
X(70108) = barycentric product X(i)*X(j) for these {i,j}: {3263, 4361}, {3717, 7243}, {3760, 3912}, {4365, 18157}, {4387, 40704}, {4408, 42720}
X(70108) = barycentric quotient X(i)/X(j) for these {i,j}: {518, 30651}, {748, 1438}, {2241, 64216}, {3760, 673}, {3912, 749}, {4361, 105}, {4365, 18785}, {4382, 1027}, {4387, 294}, {4408, 62635}, {4501, 884}, {7225, 1416}, {7243, 56783}

X(70109) = X(76)X(49483)∩X(305)X(3967)

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

X(70109) lies on these lines: {76, 49483}, {305, 3967}, {518, 64223}, {1086, 6381}, {3263, 62429}, {3266, 4009}, {3761, 4363}, {3838, 51861}, {4033, 30806}, {4505, 20924}, {4663, 69052}, {52716, 61344}, {57518, 59506}

X(70109) = X(i)-isoconjugate of X(j) for these (i,j): {751, 64216}, {1438, 30650}, {43929, 65832}
X(70109) = X(i)-Dao conjugate of X(j) for these (i,j): {6184, 30650}, {17755, 751}
X(70109) = barycentric product X(i)*X(j) for these {i,j}: {3263, 4363}, {3761, 3912}, {4377, 30941}, {4411, 42720}, {4494, 9436}, {4495, 40217}, {7245, 64223}
X(70109) = barycentric quotient X(i)/X(j) for these {i,j}: {518, 30650}, {750, 1438}, {1026, 65832}, {2242, 64216}, {3761, 673}, {3912, 751}, {4363, 105}, {4377, 13576}, {4378, 43929}, {4379, 1027}, {4390, 2195}, {4403, 43921}, {4411, 62635}, {4474, 1024}, {4482, 36086}, {4494, 14942}, {4495, 6654}, {7223, 1462}, {7245, 52030}

X(70110) = X(1)X(21)∩X(100)X(3286)

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

X(70110) lies on these lines: {1, 21}, {100, 3286}, {333, 35983}, {474, 5278}, {659, 3004}, {660, 741}, {765, 63918}, {799, 69833}, {901, 53707}, {1001, 26860}, {1150, 16405}, {1220, 17589}, {1778, 38869}, {2382, 34594}, {3218, 18191}, {3913, 20051}, {4184, 15621}, {4188, 37652}, {4191, 63060}, {4267, 5303}, {4436, 17162}, {4442, 69723}, {4921, 13588}, {5009, 30576}, {5035, 5276}, {5053, 63087}, {5057, 17197}, {5205, 16729}, {5284, 8025}, {7292, 16726}, {8731, 42045}, {10707, 14956}, {12513, 17539}, {16713, 33108}, {17178, 36635}, {17187, 32911}, {17198, 69743}, {17581, 64995}, {18164, 64149}, {18792, 33846}, {26229, 26280}, {26819, 32942}, {29824, 69008}, {31272, 69847}, {33985, 37449}, {34234, 52889}, {35978, 64072}, {36810, 68148}, {37129, 52897}, {50003, 69700}, {51443, 55942}

X(70110) = X(898)-Ceva conjugate of X(3733)
X(70110) = X(45751)-cross conjugate of X(69008)
X(70110) = X(i)-isoconjugate of X(j) for these (i,j): {523, 59071}, {4559, 60575}
X(70110) = X(i)-Dao conjugate of X(j) for these (i,j): {899, 3994}, {55067, 60575}
X(70110) = crosssum of X(i) and X(j) for these (i,j): {756, 52959}, {3125, 14404}
X(70110) = crossdifference of every pair of points on line {661, 1500}
X(70110) = barycentric product X(i)*X(j) for these {i,j}: {1, 69008}, {81, 29824}, {86, 45751}, {662, 68896}, {757, 68938}, {1019, 68989}, {1509, 44671}, {7192, 68812}, {52935, 69562}
X(70110) = barycentric quotient X(i)/X(j) for these {i,j}: {163, 59071}, {3737, 60575}, {29824, 321}, {40614, 3994}, {44671, 594}, {45751, 10}, {68812, 3952}, {68896, 1577}, {68938, 1089}, {68989, 4033}, {69008, 75}, {69562, 4036}
X(70110) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {31, 18192, 81}, {3286, 16704, 100}

X(70111) = X(1)X(75)∩X(76)X(17169)

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

X(70111) lies on these lines: {1, 75}, {76, 17169}, {350, 17205}, {668, 30941}, {3766, 6372}, {4583, 18827}, {5283, 27145}, {7035, 63918}, {16552, 29437}, {16696, 69528}, {16738, 69523}, {16742, 68973}, {16887, 18140}, {16971, 20892}, {16975, 17178}, {17179, 18145}, {17198, 69967}, {17208, 30957}, {17758, 29447}, {18152, 39734}, {18164, 20923}, {18184, 49755}, {18822, 65286}, {26813, 69256}, {26978, 34023}, {31035, 40773}, {40090, 53363}, {45751, 69008}, {62227, 62636}

X(70111) = X(889)-Ceva conjugate of X(7192)
X(70111) = X(29824)-cross conjugate of X(69008)
X(70111) = X(512)-isoconjugate of X(59071)
X(70111) = X(i)-Dao conjugate of X(j) for these (i,j): {39054, 59071}, {68938, 52959}
X(70111) = crossdifference of every pair of points on line {798, 7109}
X(70111) = barycentric product X(i)*X(j) for these {i,j}: {75, 69008}, {274, 29824}, {310, 45751}, {799, 68896}, {873, 68938}, {4623, 69562}, {7199, 68989}, {52619, 68812}
X(70111) = barycentric quotient X(i)/X(j) for these {i,j}: {662, 59071}, {18155, 60575}, {29824, 37}, {44671, 1500}, {45751, 42}, {68812, 4557}, {68896, 661}, {68938, 756}, {68989, 1018}, {69008, 1}, {69562, 4705}

X(70112) = X(2)X(39)∩X(190)X(646)

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

X(70112) lies on these lines: {2, 39}, {190, 646}, {350, 68967}, {3570, 55243}, {3770, 17340}, {4665, 24505}, {4692, 49456}, {17143, 57038}, {17499, 69245}, {27808, 65195}, {41314, 46780}, {53195, 53216}, {53366, 62619}

X(70112) = isotomic conjugate of the isogonal conjugate of X(68812)
X(70112) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {5381, 17135}, {34075, 17154}, {62763, 54102}
X(70112) = X(i)-isoconjugate of X(j) for these (i,j): {1015, 59071}, {1397, 60575}
X(70112) = X(i)-Dao conjugate of X(j) for these (i,j): {899, 3768}, {62585, 60575}, {68938, 891}
X(70112) = cevapoint of X(68896) and X(68938)
X(70112) = crosspoint of X(799) and X(889)
X(70112) = crosssum of X(798) and X(890)
X(70112) = trilinear pole of line {29824, 44671}
X(70112) = crossdifference of every pair of points on line {669, 3248}
X(70112) = barycentric product X(i)*X(j) for these {i,j}: {75, 68989}, {76, 68812}, {668, 29824}, {670, 44671}, {799, 68938}, {1978, 45751}, {4033, 69008}, {4601, 69562}, {7035, 68896}
X(70112) = barycentric quotient X(i)/X(j) for these {i,j}: {312, 60575}, {765, 59071}, {29824, 513}, {40614, 3768}, {44671, 512}, {45751, 649}, {68812, 6}, {68896, 244}, {68938, 661}, {68989, 1}, {69008, 1019}, {69562, 3125}
X(70112) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {39, 29706, 18140}, {76, 29397, 29447}, {76, 29713, 29397}, {194, 29425, 29454}, {194, 29736, 29425}, {20081, 29544, 29486}

X(70113) = X(2)X(21894)∩X(239)X(514)

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

X(70113) lies on these lines: {2, 21894}, {88, 65264}, {99, 51357}, {190, 4576}, {239, 514}, {335, 39698}, {812, 8042}, {2786, 3995}, {3733, 47805}, {4145, 17154}, {4366, 69904}, {4481, 47759}, {4897, 31296}, {6652, 50456}, {7199, 47869}, {16726, 16727}, {16728, 16729}, {16751, 26775}, {17147, 53333}, {18155, 26822}, {21297, 23825}, {27013, 29402}, {31035, 53339}, {37639, 68837}, {39747, 64237}, {69312, 69972}, {69323, 69517}

X(70113) = X(3227)-Ceva conjugate of X(16726)
X(70113) = X(37)-isoconjugate of X(59071)
X(70113) = X(i)-Dao conjugate of X(j) for these (i,j): {40589, 59071}, {68896, 69562}
X(70113) = barycentric product X(i)*X(j) for these {i,j}: {86, 68896}, {514, 69008}, {1509, 69562}, {7192, 29824}, {7199, 45751}, {16727, 68812}, {17205, 68989}
X(70113) = barycentric quotient X(i)/X(j) for these {i,j}: {58, 59071}, {17197, 60575}, {29824, 3952}, {44671, 40521}, {45751, 1018}, {68896, 10}, {68938, 4103}, {69008, 190}, {69562, 594}
X(70113) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1019, 7192, 47763}, {16751, 26775, 27115}, {17496, 47763, 17494}, {18155, 26822, 26985}

X(70114) = X(2)X(37)∩X(292)X(39698)

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

X(70014) lies on these lines: {2, 37}, {292, 39698}, {661, 69012}, {874, 17494}, {1018, 3952}, {1978, 54118}, {4427, 24052}, {6184, 36791}, {6382, 40637}, {6544, 68132}, {17780, 68825}, {53363, 65169}, {68812, 68989}

X(70114) = X(69562)-cross conjugate of X(68938)
X(70114) = X(i)-isoconjugate of X(j) for these (i,j): {1408, 60575}, {16726, 59071}
X(70114) = X(i)-Dao conjugate of X(j) for these (i,j): {29824, 47776}, {59577, 60575}
X(70114) = cevapoint of X(68938) and X(69562)
X(70114) = trilinear pole of line {44671, 68938}
X(70114) = barycentric product X(i)*X(j) for these {i,j}: {10, 68989}, {190, 68938}, {321, 68812}, {668, 44671}, {1016, 69562}, {3952, 29824}, {4033, 45751}, {4103, 69008}
X(70114) = barycentric quotient X(i)/X(j) for these {i,j}: {2321, 60575}, {29824, 7192}, {44671, 513}, {45751, 1019}, {68812, 81}, {68896, 17205}, {68938, 514}, {68989, 86}, {69562, 1086}
X(70114) = {X(61163),X(61165)}-harmonic conjugate of X(3952)

X(70115) = X(1)X(50343)∩X(36)X(238)

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

X(70115) lies on these lines: {1, 50343}, {36, 238}, {100, 43076}, {106, 53707}, {291, 66937}, {2787, 56191}, {2832, 8042}, {3293, 9508}, {4089, 17205}, {4560, 48282}, {8300, 69906}, {21786, 68814}, {47970, 69843}, {48292, 69317}

X(70115) = X(10)-isoconjugate of X(59071)
X(70115) = crossdifference of every pair of points on line {37, 14752}
X(70115) = barycentric product X(i)*X(j) for these {i,j}: {81, 68896}, {513, 69008}, {757, 69562}, {1019, 29824}, {7192, 45751}, {16726, 68989}, {17205, 68812}
X(70115) = barycentric quotient X(i)/X(j) for these {i,j}: {1333, 59071}, {18191, 60575}, {29824, 4033}, {44671, 4103}, {45751, 3952}, {68896, 321}, {69008, 668}, {69562, 1089}

X(70116) = X(1)X(3952)∩X(238)X(239)

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

X(70116) lies on these lines: {1, 3952}, {190, 16482}, {238, 239}, {274, 40619}, {659, 3766}, {748, 24294}, {2795, 4359}, {3720, 68873}, {3759, 69560}, {3948, 68949}, {4368, 27846}, {4384, 4781}, {4422, 69897}, {5029, 68972}, {5251, 16823}, {8299, 69899}, {16497, 32931}, {16552, 46148}, {16815, 32917}, {16826, 32944}, {16833, 32929}, {17175, 61403}, {29824, 40614}, {30109, 69017}, {62755, 68958}

X(70116) = X(876)-isoconjugate of X(59071)
X(70116) = barycentric product X(i)*X(j) for these {i,j}: {239, 29824}, {350, 45751}, {740, 69008}, {812, 68989}, {3570, 68896}, {3766, 68812}, {30940, 44671}, {33295, 68938}
X(70116) = barycentric quotient X(i)/X(j) for these {i,j}: {3716, 60575}, {29824, 335}, {45751, 291}, {68812, 660}, {68896, 4444}, {68938, 43534}, {68989, 4562}, {69008, 18827}, {69562, 35352}, {69889, 59071}

X(70117) = X(36)X(3685)∩X(239)X(2234)

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

X(70117) lies on these lines: {36, 3685}, {75, 16679}, {171, 385}, {239, 2234}, {314, 64010}, {513, 69907}, {524, 69899}, {744, 68990}, {804, 1966}, {896, 5205}, {1045, 17187}, {1086, 68949}, {3218, 69974}, {3747, 68993}, {3948, 69723}, {3956, 60731}, {4039, 53541}, {4436, 30939}, {4447, 69897}, {5429, 24342}, {6173, 26238}, {10436, 62834}, {16467, 68966}, {16726, 68986}, {16878, 32929}, {17260, 32918}, {18164, 25295}, {18206, 53338}, {20984, 64909}, {23205, 33845}, {26237, 50116}, {44671, 68989}, {47805, 69029}, {52897, 69503}, {56801, 63049}

X(70117) = midpoint of X(68989) and X(69008)
X(70117) = barycentric product X(i)*X(j) for these {i,j}: {894, 29824}, {1215, 69008}, {1909, 45751}, {4369, 68989}, {4374, 68812}, {8033, 44671}, {17103, 68938}, {18047, 68896}
X(70117) = barycentric quotient X(i)/X(j) for these {i,j}: {3907, 60575}, {29824, 257}, {44671, 52651}, {45751, 256}, {68812, 3903}, {68989, 27805}, {69008, 32010}, {69894, 59071}

X(70118) = X(6)X(1018)∩X(238)X(1914)

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

X(70118) lies on these lines: {6, 1018}, {86, 17761}, {100, 38346}, {238, 1914}, {528, 16503}, {812, 4366}, {2280, 50300}, {3248, 68861}, {3722, 61164}, {4390, 32941}, {4432, 69901}, {4557, 24491}, {4649, 14839}, {8649, 16484}, {13576, 50302}, {16788, 48805}, {35342, 54333}, {40614, 68812}, {44671, 45751}, {52897, 68960}, {68885, 68968}

X(70118) = X(4444)-isoconjugate of X(59071)
X(70118) = crossdifference of every pair of points on line {876, 68953}
X(70118) = barycentric product X(i)*X(j) for these {i,j}: {238, 29824}, {239, 45751}, {659, 68989}, {812, 68812}, {2238, 69008}, {3573, 68896}, {33295, 44671}, {68938, 69887}
X(70118) = barycentric quotient X(i)/X(j) for these {i,j}: {4435, 60575}, {29824, 334}, {44671, 43534}, {45751, 335}, {68812, 4562}, {68896, 66286}, {68989, 4583}, {69008, 40017}, {69890, 59071}

X(70119) = X(171)X(172)∩X(238)X(1977)

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

X(70119) lies on these lines: {171, 172}, {187, 56530}, {238, 1977}, {385, 4369}, {649, 69903}, {896, 69901}, {940, 16783}, {3286, 61234}, {3684, 4969}, {4434, 61164}, {62740, 69502}

X(70119) = X(29055)-isoconjugate of X(60575)
X(70119) = barycentric product X(i)*X(j) for these {i,j}: {171, 29824}, {894, 45751}, {2295, 69008}, {4367, 68989}, {4369, 68812}, {4579, 68896}, {17103, 44671}, {68938, 69891}
X(70119) = barycentric quotient X(i)/X(j) for these {i,j}: {3287, 60575}, {29824, 7018}, {45751, 257}, {68812, 27805}, {68989, 56241}, {69895, 59071}

X(70120) = X(2)X(4033)∩X(239)X(350)

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

X(70120) lies on these lines: {2, 4033}, {239, 350}, {668, 17761}, {812, 46387}, {1909, 16829}, {4441, 54280}, {4494, 17026}, {4553, 17135}, {4783, 52908}, {17029, 17790}, {24494, 61183}, {29824, 44671}, {37756, 62234}

X(70120) = X(3572)-isoconjugate of X(59071)
X(70120) = barycentric product X(i)*X(j) for these {i,j}: {350, 29824}, {874, 68896}, {1921, 45751}, {3766, 68989}, {3948, 69008}, {30940, 68938}, {65101, 68812}
X(70120) = barycentric quotient X(i)/X(j) for these {i,j}: {3573, 59071}, {29824, 291}, {45751, 292}, {68812, 813}, {68896, 876}, {68989, 660}, {69008, 37128}

X(70121) = X(75)X(17497)∩X(350)X(538)

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

X(70121) lies on these lines: {75, 17497}, {76, 29438}, {312, 50154}, {350, 538}, {524, 40875}, {732, 894}, {1655, 16696}, {3218, 3975}, {3578, 19809}, {3618, 34284}, {3978, 4369}, {16574, 30092}, {17758, 29397}, {18145, 29491}, {30941, 65169}, {30963, 50184}, {35102, 35544}, {50160, 60706}

X(70121) = barycentric product X(i)*X(j) for these {i,j}: {1909, 29824}, {1920, 45751}, {3963, 69008}, {4374, 68989}, {8033, 68938}, {68896, 69896}
X(70121) = barycentric quotient X(i)/X(j) for these {i,j}: {4579, 59071}, {29824, 256}, {44671, 66971}, {45751, 893}, {68938, 52651}, {68989, 3903}, {69008, 40432}

X(70122) = X(239)X(69503)∩X(750)X(4363)

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

X(70122) lies on these lines: {239, 69503}, {750, 4363}, {3685, 4436}, {4361, 63504}, {4378, 4411}, {4716, 18792}, {5205, 23343}, {16679, 20892}, {16777, 24659}, {29824, 68989}, {38315, 50023}

X(70122) = barycentric product X(i)*X(j) for these {i,j}: {3761, 45751}, {4363, 29824}, {4379, 68989}, {4411, 68812}, {4482, 68896}
X(70122) = barycentric quotient X(i)/X(j) for these {i,j}: {4474, 60575}, {45751, 751}

X(70123) = X(238)X(69503)∩X(896)X(69975)

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

X(70123) lies on these lines: {238, 69503}, {896, 69975}, {2234, 4974}, {2239, 24487}, {3246, 41847}, {3286, 3685}, {3758, 17126}, {4257, 4676}, {17335, 61686}, {39995, 69723}, {45751, 68989}

X(70123) = barycentric product X(i)*X(j) for these {i,j}: {3758, 29824}, {4406, 68812}, {45751, 64133}, {46897, 69008}, {47762, 68989}
X(70123) = barycentric quotient X(i)/X(j) for these {i,j}: {29824, 57725}, {45751, 4492}, {47729, 60575}

X(70124) = X(1)X(21)∩X(812)X(1019)

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

X(70124) lies on these lines: {1, 21}, {812, 1019}, {1475, 17200}, {3953, 16735}, {4251, 33792}, {6173, 17179}, {14829, 17682}, {14964, 30941}, {16549, 33954}, {16704, 31061}, {17030, 27152}, {17034, 37639}, {17103, 39950}, {17137, 33793}, {18184, 51369}, {19623, 24727}, {26801, 26810}, {29742, 29754}, {30109, 69073}, {33295, 45751}, {68950, 68984}

X(70124) = X(57024)-cross conjugate of X(69073)
X(70124) = X(1500)-isoconjugate of X(2368)
X(70124) = cevapoint of X(57024) and X(69074)
X(70124) = crossdifference of every pair of points on line {661, 872}
X(70124) = barycentric product X(i)*X(j) for these {i,j}: {1, 69073}, {81, 30109}, {86, 57024}, {274, 69074}, {662, 69075}, {757, 68939}, {873, 2388}
X(70124) = barycentric quotient X(i)/X(j) for these {i,j}: {757, 2368}, {2388, 756}, {30109, 321}, {57024, 10}, {68939, 1089}, {69073, 75}, {69074, 37}, {69075, 1577}
X(70124) = {X(81),X(54391)}-harmonic conjugate of X(69832)

X(70125) = X(2)X(39)∩X(100)X(190)

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

X(70125) lies on these lines: {2, 39}, {100, 190}, {650, 42721}, {874, 17494}, {1978, 46725}, {4576, 61234}, {31052, 41242}, {42723, 61406}, {48000, 69012}, {54118, 69896}, {68812, 68998}

X(70125) = X(53195)-anticomplementary conjugate of X(21293)
X(70125) = X(69075)-cross conjugate of X(30109)
X(70125) = X(798)-isoconjugate of X(2368)
X(70125) = X(31998)-Dao conjugate of X(2368)
X(70125) = cevapoint of X(30109) and X(69075)
X(70125) = crosspoint of X(190) and X(53195)
X(70125) = trilinear pole of line {2388, 30109}
X(70125) = crossdifference of every pair of points on line {669, 1015}
X(70125) = barycentric product X(i)*X(j) for these {i,j}: {99, 68939}, {190, 30109}, {668, 57024}, {670, 2388}, {1016, 69075}, {1978, 69074}, {3952, 69073}
X(70125) = barycentric quotient X(i)/X(j) for these {i,j}: {99, 2368}, {2388, 512}, {30109, 514}, {57024, 513}, {68939, 523}, {69073, 7192}, {69074, 649}, {69075, 1086}

X(70126) = X(44)X(68890)∩X(238)X(239)

Barycentrics   (a^2 - b*c)*(a^2*b^2 - a*b^3 + a*b^2*c - b^3*c + a^2*c^2 + a*b*c^2 - a*c^3 - b*c^3) : :
X(70126) = 3 X[24508] - X[54101]

X(70126) lies on these lines: {44, 68890}, {190, 16552}, {238, 239}, {537, 16829}, {812, 46387}, {1086, 16887}, {1500, 4422}, {2388, 30109}, {3826, 29494}, {3925, 29470}, {3952, 26846}, {4437, 9052}, {4568, 5701}, {14839, 57038}, {24508, 54101}, {26801, 40857}, {29431, 49524}, {29786, 69253}

X(70126) = midpoint of X(190) and X(17143)
X(70126) = reflection of X(1500) in X(4422)
X(70126) = barycentric product X(i)*X(j) for these {i,j}: {239, 30109}, {350, 57024}, {740, 69073}, {1921, 69074}, {3570, 69075}, {33295, 68939}
X(70126) = barycentric quotient X(i)/X(j) for these {i,j}: {30109, 335}, {33295, 2368}, {57024, 291}, {68939, 43534}, {69073, 18827}, {69074, 292}, {69075, 4444}

X(70127) = X(171)X(385)∩X(661)X(69959)

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

X(70127) lies on these lines: {171, 385}, {661, 69959}, {732, 16592}, {3218, 17755}, {3978, 4369}, {16574, 69263}, {16696, 21838}, {18157, 61234}, {26235, 29494}, {29470, 39998}, {29514, 61160}

X(70127) = X(2368)-isoconjugate of X(40729)
X(70127) = barycentric product X(i)*X(j) for these {i,j}: {894, 30109}, {1215, 69073}, {1909, 57024}, {1920, 69074}, {17103, 68939}, {18047, 69075}
X(70127) = barycentric quotient X(i)/X(j) for these {i,j}: {2388, 66971}, {17103, 2368}, {30109, 257}, {57024, 256}, {69073, 32010}, {69074, 893}

X(70128) = X(523)X(661)∩X(1111)X(3120)

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

X(70128) lies on these lines: {523, 661}, {1111, 3120}, {4455, 6546}, {4468, 58300}, {6536, 24459}, {9148, 69376}, {23788, 30970}, {47790, 48272}, {48082, 50497}, {48278, 48393}, {49278, 51317}

X(70128) = X(692)-isoconjugate of X(2368)
X(70128) = X(1086)-Dao conjugate of X(2368)
X(70128) = crossdifference of every pair of points on line {58, 32739}
X(70128) = barycentric product X(i)*X(j) for these {i,j}: {10, 69075}, {514, 68939}, {523, 30109}, {850, 69074}, {1577, 57024}, {2388, 3261}, {4024, 69073}
X(70128) = barycentric quotient X(i)/X(j) for these {i,j}: {514, 2368}, {2388, 101}, {30109, 99}, {57024, 662}, {68939, 190}, {69073, 4610}, {69074, 110}, {69075, 86}

X(70129) = X(2)X(59275)∩X(3)X(161)

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

X(70129) lies on the cubics K009 and K526 and these lines: {2, 59275}, {3, 161}, {4, 18401}, {32, 39019}, {128, 6640}, {1147, 50463}, {6662, 39504}, {7577, 70074}, {10255, 58746}, {15318, 52295}, {31074, 52441}, {32352, 35442}, {32902, 45971}

X(70129) = isogonal conjugate of X(58079)
X(70129) = X(20626)-Ceva conjugate of X(6368)
X(70129) = X(184)-cross conjugate of X(68465)
X(70129) = X(i)-isoconjugate of X(j) for these (i,j): {1, 58079}, {19, 57474}, {2190, 7488}, {16040, 65221}
X(70129) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 58079}, {5, 7488}, {6, 57474}, {6368, 20625}, {15450, 16040}
X(70129) = cevapoint of X(15451) and X(39019)
X(70129) = barycentric product X(i)*X(j) for these {i,j}: {343, 6145}, {6368, 16039}, {20626, 60597}
X(70129) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 57474}, {6, 58079}, {216, 7488}, {6145, 275}, {8798, 67119}, {15451, 16040}, {16039, 18831}, {20626, 16813}, {39019, 20625}, {42445, 41590}

X(70130) = X(3)X(34135)∩X(132)X(5000)

Barycentrics   (Sqrt[(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(-a^2 + b^2 + c^2)*(a^2 + b^2 + c^2)] + 2*(-a^2 + b^2 + c^2)*S)/(-((-a^2 + b^2 + c^2)*Sqrt[(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(-a^2 + b^2 + c^2)*(a^2 + b^2 + c^2)]) + 2*(-a^4 + b^4 + c^4)*S) : :

X(70130) lies on the cubics K039 and K570 and these lines: {3, 34135}, {132, 5000}, {5003, 30737}, {8779, 41197}, {9475, 41196}, {34146, 42671}, {40079, 70005}, {40080, 70006}

X(70130) = isogonal conjugate of X(34239)
X(70130) = circumcircle-inverse of X(34135)
X(70130) = X(237)-cross conjugate of X(41196)
X(70130) = X(1)-isoconjugate of X(34239)
X(70130) = crosspoint of X(1297) and X(32619)
X(70130) = crosssum of X(i) and X(j) for these (i,j): {1503, 5001}, {5002, 60068}
X(70130) = barycentric product X(34135)*X(41198)
X(70130) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 34239}, {34135, 41194}, {41196, 5003}

X(70131) = X(3)X(34136)∩X(132)X(5001)

Barycentrics   (Sqrt[(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(-a^2 + b^2 + c^2)*(a^2 + b^2 + c^2)] - 2*(-a^2 + b^2 + c^2)*S)/((-a^2 + b^2 + c^2)*Sqrt[(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(-a^2 + b^2 + c^2)*(a^2 + b^2 + c^2)] + 2*(-a^4 + b^4 + c^4)*S) : :

X(70131) lies on the cubics K039 and K570 and these lines: {3, 34136}, {132, 5001}, {5002, 30737}, {8779, 41196}, {9475, 41197}, {34146, 42671}, {40079, 70006}, {40080, 70005}

X(70131) = isogonal conjugate of X(34240)
X(70131) = circumcircle-inverse of X(34136)
X(70131) = X(237)-cross conjugate of X(41197)
X(70131) = X(1)-isoconjugate of X(34240)
X(70131) = crosspoint of X(1297) and X(32618)
X(70131) = crosssum of X(i) and X(j) for these (i,j): {1503, 5000}, {5003, 60067}
X(70131) = barycentric product X(34136)*X(41199)
X(70131) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 34240}, {34136, 41195}, {41197, 5002}

X(70132) = X(20)X(394)∩X(1217)X(39268)

Barycentrics   (a^2 - b^2 - c^2)*(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)*(a^8 + 4*a^6*b^2 - 10*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*a^6*c^2 + 4*a^4*b^2*c^2 + 4*a^2*b^4*c^2 - 4*b^6*c^2 + 6*a^4*c^4 - 4*a^2*b^2*c^4 + 6*b^4*c^4 - 4*a^2*c^6 - 4*b^2*c^6 + c^8)*(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8 + 4*a^6*c^2 + 4*a^4*b^2*c^2 - 4*a^2*b^4*c^2 - 4*b^6*c^2 - 10*a^4*c^4 + 4*a^2*b^2*c^4 + 6*b^4*c^4 + 4*a^2*c^6 - 4*b^2*c^6 + c^8) : :

X(70132) lies on the cubics K071 and K096 and these lines: {20, 394}, {1217, 39268}, {3344, 46829}, {5562, 42459}, {15341, 16391}, {31363, 40813}, {31943, 54746}, {59077, 67740}

X(70132) = X(i)-cross conjugate of X(j) for these (i,j): {53, 343}, {8798, 5}
X(70132) = X(i)-isoconjugate of X(j) for these (i,j): {54, 1712}, {1033, 2167}, {1498, 2190}, {2148, 14361}, {2169, 6523}, {6527, 62268}, {58895, 65221}
X(70132) = X(i)-Dao conjugate of X(j) for these (i,j): {5, 1498}, {216, 14361}, {3350, 38808}, {14363, 6523}, {15450, 58895}, {40588, 1033}, {45249, 6616}, {52032, 6527}
X(70132) = barycentric product X(i)*X(j) for these {i,j}: {5, 1032}, {311, 28783}, {343, 3346}, {8798, 47633}, {14213, 47849}, {42459, 64986}
X(70132) = barycentric quotient X(i)/X(j) for these {i,j}: {5, 14361}, {51, 1033}, {53, 6523}, {216, 1498}, {343, 6527}, {1032, 95}, {1953, 1712}, {3344, 38808}, {3346, 275}, {5562, 6617}, {8798, 3343}, {15451, 58895}, {28783, 54}, {42459, 6616}, {47849, 2167}

X(70133) = X(4)X(5965)∩X(69)X(60034)

Barycentrics   (a^2 + b^2 - 4*c^2)*(a^2 - 4*b^2 + c^2)*(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4) : :
X(70133) = 20 X[56738] - 19 X[61886]

X(70133) lies on the the circumconic {{A,B,C,X(4),X(5)}}, the cubics K117 and K616 and these lines: {4, 5965}, {69, 60034}, {376, 1141}, {1487, 56738}, {3146, 15619}, {3459, 3525}, {3613, 63021}, {3839, 38305}, {11082, 11488}, {11087, 11489}, {19712, 63105}, {19713, 63106}, {36809, 39530}

X(70133) = X(i)-isoconjugate of X(j) for these (i,j): {2148, 3629}, {2167, 35007}, {2169, 62978}, {32478, 36134}
X(70133) = X(i)-Dao conjugate of X(j) for these (i,j): {137, 32478}, {216, 3629}, {14363, 62978}, {40588, 35007}
X(70133) = barycentric product X(i)*X(j) for these {i,j}: {5, 43676}, {18314, 53884}
X(70133) = barycentric quotient X(i)/X(j) for these {i,j}: {5, 3629}, {51, 35007}, {53, 62978}, {12077, 32478}, {36300, 67115}, {36301, 67116}, {43676, 95}, {53884, 18315}

X(70134) = X(2)X(60823)∩X(4)X(60822)

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

X(70134) lies on the cubics K127 and K841 and these lines: {2, 60823}, {4, 60822}, {20, 5896}, {64, 3146}, {253, 32816}, {459, 3515}, {6622, 33630}, {10151, 31942}, {62545, 66732}

X(70134) = isogonal conjugate of X(45248)
X(70134) = isogonal conjugate of the anticomplement of X(43592)
X(70134) = isogonal conjugate of the complement of X(15077)
X(70134) = isotomic conjugate of the isogonal conjugate of X(33585)
X(70134) = X(i)-cross conjugate of X(j) for these (i,j): {6, 459}, {68009, 4}
X(70134) = X(i)-isoconjugate of X(j) for these (i,j): {1, 45248}, {255, 34286}, {610, 37672}
X(70134) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 45248}, {6523, 34286}, {14092, 37672}, {40839, 32001}
X(70134) = cevapoint of X(46473) and X(46476)
X(70134) = trilinear pole of line {53496, 59652}
X(70134) = barycentric product X(i)*X(j) for these {i,j}: {64, 66732}, {76, 33585}, {253, 51316}, {459, 15077}, {14572, 60822}, {16080, 63864}
X(70134) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 45248}, {64, 37672}, {253, 32831}, {393, 34286}, {459, 32001}, {15077, 37669}, {33585, 6}, {41489, 3515}, {51316, 20}, {60822, 40170}, {63864, 11064}, {66732, 14615}

X(70135) = X(25)X(39265)∩X(32)X(51250)

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

X(70135) lies on the cubics K128 and K786 and these lines: {25, 39265}, {32, 51250}, {76, 8861}, {297, 385}, {401, 8782}, {441, 6393}, {511, 3506}, {3505, 3511}, {8779, 36212}, {9474, 36790}, {11328, 40804}, {35910, 37344}

X(70135) = isogonal conjugate of X(70014)
X(70135) = isotomic conjugate of the polar conjugate of X(34130)
X(70135) = isogonal conjugate of the polar conjugate of X(9473)
X(70135) = X(9473)-Ceva conjugate of X(34130)
X(70135) = X(i)-cross conjugate of X(j) for these (i,j): {248, 3}, {694, 3504}, {64975, 1073}
X(70135) = X(i)-isoconjugate of X(j) for these (i,j): {1, 70014}, {4, 16559}, {19, 147}, {75, 57262}, {92, 52162}, {240, 36899}, {56679, 69652}
X(70135) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 70014}, {6, 147}, {206, 57262}, {22391, 52162}, {36033, 16559}, {39085, 36899}
X(70135) = crosssum of X(52162) and X(57262)
X(70135) = barycentric product X(i)*X(j) for these {i,j}: {3, 9473}, {69, 34130}, {248, 63894}, {36214, 70029}
X(70135) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 147}, {6, 70014}, {32, 57262}, {48, 16559}, {184, 52162}, {248, 36899}, {9473, 264}, {15391, 69652}, {34130, 4}, {47388, 61496}, {63894, 44132}, {70029, 17984}

X(70136) = X(4)X(110)∩X(131)X(53788)

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

X(70136) lies on the cubics K186 and K568 and these lines: {4, 110}, {131, 53788}, {523, 925}, {4563, 18878}, {13496, 39986}, {13558, 66078}, {15328, 61182}, {30512, 55136}

X(70136) = reflection of X(i) in X(j) for these {i,j}: {1300, 15454}, {56686, 131}
X(70136) = antigonal image of X(56686)
X(70136) = symgonal image of X(15454)
X(70136) = X(55136)-cross conjugate of X(1300)
X(70136) = X(1725)-isoconjugate of X(43709)
X(70136) = X(i)-Dao conjugate of X(j) for these (i,j): {131, 55121}, {12095, 60342}, {15454, 523}, {35235, 16221}
X(70136) = trilinear pole of line {16310, 53788}
X(70136) = barycentric product X(i)*X(j) for these {i,j}: {648, 53788}, {687, 44665}, {2986, 30512}, {4558, 58084}, {16310, 18878}
X(70136) = barycentric quotient X(i)/X(j) for these {i,j}: {10420, 43756}, {14910, 43709}, {16310, 55121}, {30512, 3580}, {32662, 39373}, {32708, 1299}, {44665, 6334}, {53788, 525}, {56686, 65614}, {58084, 14618}, {63845, 60342}

X(70137) = X(6)X(904)∩X(32)X(67001)

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

X(70137) lies on the cubics K224 and K532 and these lines: {6, 904}, {32, 67001}, {384, 3494}, {694, 51321}, {902, 58981}, {17970, 66999}, {40729, 57264}, {51858, 66998}

X(70137) = X(694)-Ceva conjugate of X(67001)
X(70137) = X(7166)-isoconjugate of X(41318)
X(70137) = X(70075)-Dao conjugate of X(3978)
X(70137) = barycentric product X(3507)*X(51974)
X(70137) = barycentric quotient X(51921)/X(41318)

X(70138) = X(6)X(22)∩X(23)X(827)

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

X(70138) lies on the cubics K537 and K730 and these lines: {6, 22}, {23, 827}, {30, 9076}, {111, 52696}, {148, 20063}, {382, 12505}, {1799, 62967}, {5169, 7761}, {7664, 16095}, {37901, 38946}, {37913, 69875}

X(70138) = reflection of X(53945) in X(23)

X(70139) = X(2)X(66974)∩X(183)X(1350)

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

X(70139) lies on the cubics K677 and K1037, the curve Q124, and these lines: {2, 66974}, {183, 1350}, {290, 69771}, {458, 3329}, {1007, 8842}, {7766, 46806}, {20023, 37668}, {56882, 60737}

X(70139) = isotomic conjugate of X(6194)
X(70139) = anticomplement of X(67187)
X(70139) = polar conjugate of X(47738)
X(70139) = cyclocevian conjugate of X(54124)
X(70139) = isotomic conjugate of the anticomplement of X(262)
X(70139) = isotomic conjugate of the complement of X(44434)
X(70139) = isotomic conjugate of the isogonal conjugate of X(69992)
X(70139) = X(i)-cross conjugate of X(j) for these (i,j): {262, 2}, {19222, 2998}, {59256, 253}
X(70139) = X(i)-isoconjugate of X(j) for these (i,j): {31, 6194}, {48, 47738}
X(70139) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 6194}, {1249, 47738}
X(70139) = cevapoint of X(2) and X(44434)
X(70139) = trilinear pole of line {23878, 45336}
X(70139) = barycentric product X(76)*X(69992)
X(70139) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 6194}, {4, 47738}, {262, 67187}, {69992, 6}

X(70140) = X(69)X(34156)∩X(147)X(325)

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

X(70140) lies on the cubics K738 and K779 and these lines: {69, 34156}, {147, 325}, {441, 6393}, {1502, 51257}, {3978, 44132}, {9476, 57549}, {18906, 51960}, {47388, 57761}

X(70140) = isogonal conjugate of X(57262)
X(70140) = isotomic conjugate of X(70014)
X(70140) = antitomic image of X(69780)
X(70140) = isotomic conjugate of the polar conjugate of X(9473)
X(70140) = X(i)-cross conjugate of X(j) for these (i,j): {287, 69}, {1916, 43714}
X(70140) = X(i)-isoconjugate of X(j) for these (i,j): {1, 57262}, {19, 52162}, {25, 16559}, {31, 70014}, {147, 1973}, {36899, 57653}, {56679, 69996}
X(70140) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 70014}, {3, 57262}, {6, 52162}, {6337, 147}, {6505, 16559}
X(70140) = trilinear pole of line {6333, 68791}
X(70140) = barycentric product X(i)*X(j) for these {i,j}: {69, 9473}, {287, 63894}, {305, 34130}, {40708, 70029}
X(70140) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 70014}, {3, 52162}, {6, 57262}, {63, 16559}, {69, 147}, {287, 36899}, {9473, 4}, {15391, 69996}, {34130, 25}, {63894, 297}, {69780, 69652}, {70029, 419}

X(70141) = X(172)X(18267)∩X(385)X(1911)

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

X(70141) lies on the cubics K775 and K991 and these lines: {172, 18267}, {385, 1911}, {904, 66998}, {1914, 1927}, {1933, 18897}, {2106, 3009}, {21788, 51907}, {32748, 70034}

X(70141) = isogonal conjugate of X(19581)
X(70141) = isogonal conjugate of the isotomic conjugate of X(24576)
X(70141) = X(1)-cross conjugate of X(1911)
X(70141) = X(i)-isoconjugate of X(j) for these (i,j): {1, 19581}, {2, 19579}, {6, 18277}, {75, 19580}, {76, 18274}, {238, 19567}, {239, 19565}, {350, 3510}, {385, 40849}, {561, 30634}, {1580, 69956}, {1914, 18275}, {1921, 18278}, {1926, 57265}, {1966, 69935}, {3978, 51979}, {4366, 64233}, {8300, 51868}, {8875, 18037}, {23186, 40717}, {40755, 62553}
X(70141) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 19581}, {9, 18277}, {206, 19580}, {9467, 69935}, {9470, 19567}, {32664, 19579}, {36906, 18275}, {39092, 69956}, {40368, 30634}
X(70141) = cevapoint of X(1) and X(7168)
X(70141) = barycentric product X(i)*X(j) for these {i,j}: {1, 63893}, {6, 24576}, {31, 70052}, {32, 30633}, {291, 51919}, {292, 7168}, {335, 70034}, {694, 51920}, {1581, 67073}, {1911, 69954}, {1967, 39933}, {8868, 30648}, {9468, 52175}, {40782, 63881}
X(70141) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 18277}, {6, 19581}, {31, 19579}, {32, 19580}, {291, 18275}, {292, 19567}, {560, 18274}, {694, 69956}, {1501, 30634}, {1911, 19565}, {1922, 3510}, {1927, 51979}, {1967, 40849}, {7168, 1921}, {8789, 57265}, {9468, 69935}, {14598, 18278}, {24576, 76}, {30633, 1502}, {39933, 1926}, {51919, 350}, {51920, 3978}, {52175, 14603}, {52205, 51868}, {63893, 75}, {67073, 1966}, {69954, 18891}, {70018, 64233}, {70034, 239}, {70052, 561}

X(70142) = X(3)X(51997)∩X(4)X(70032)

Barycentrics   a^2*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6 - a^6*c^2 + a^4*b^2*c^2 + a^2*b^4*c^2 - b^6*c^2 + 4*a^4*c^4 + 7*a^2*b^2*c^4 + 4*b^4*c^4 - 3*a^2*c^6 - 3*b^2*c^6)*(a^6*b^2 - 4*a^4*b^4 + 3*a^2*b^6 - a^6*c^2 - a^4*b^2*c^2 - 7*a^2*b^4*c^2 + 3*b^6*c^2 + 2*a^4*c^4 - a^2*b^2*c^4 - 4*b^4*c^4 - a^2*c^6 + b^2*c^6) : :

X(70142) lies on the cubics K708 and K757 and these lines: {3, 51997}, {4, 70032}, {182, 33874}, {287, 10796}, {1351, 18906}, {2080, 5651}, {6234, 32524}, {10358, 14383}, {12110, 34386}, {21460, 32463}, {47643, 67741}

X(70142) = isogonal conjugate of X(7709)
X(70142) = antitomic image of X(54998)
X(70142) = isogonal conjugate of the anticomplement of X(7697)
X(70142) = X(1)-isoconjugate of X(7709)
X(70142) = barycentric quotient X(6)/X(7709)

X(70143) = X(1)X(21)∩X(6)X(2350)

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

X(70143) lies on these lines: {1, 21}, {6, 2350}, {42, 3286}, {86, 748}, {101, 57397}, {171, 4651}, {238, 8025}, {333, 750}, {593, 5009}, {601, 64419}, {614, 18164}, {741, 1171}, {757, 873}, {859, 54310}, {902, 18185}, {967, 37492}, {985, 39747}, {1106, 64382}, {1203, 52564}, {1333, 2280}, {1408, 1451}, {1412, 1471}, {2177, 4184}, {2308, 40153}, {3217, 65027}, {3720, 18166}, {3736, 61358}, {4683, 17202}, {4722, 20964}, {5021, 36808}, {5115, 63099}, {5156, 37685}, {5235, 17124}, {5247, 19874}, {5278, 37522}, {5333, 17125}, {7303, 61385}, {8300, 30581}, {9350, 35983}, {11115, 32945}, {16696, 17017}, {16717, 23543}, {16738, 32772}, {17126, 20011}, {17127, 26860}, {17167, 24725}, {17173, 33097}, {17174, 33096}, {17197, 41011}, {17440, 22400}, {18191, 40970}, {18601, 29821}, {18792, 32911}, {19518, 19734}, {20963, 22060}, {25496, 27163}, {27636, 27644}, {29766, 30942}, {29767, 31330}, {29789, 30107}, {30939, 32930}, {30984, 31237}, {32912, 64581}, {32924, 62636}, {32942, 69008}, {35978, 50581}, {37109, 37666}, {37652, 56768}, {40984, 61670}, {51443, 60673}

X(70143) = isogonal conjugate of the isotomic conjugate of X(17175)
X(70143) = X(i)-Ceva conjugate of X(j) for these (i,j): {101, 3733}, {4610, 57129}
X(70143) = X(20963)-cross conjugate of X(18166)
X(70143) = X(i)-isoconjugate of X(j) for these (i,j): {10, 40433}, {37, 32009}, {321, 57397}, {523, 8708}, {594, 40408}, {756, 40439}, {762, 59147}, {3952, 50520}
X(70143) = X(i)-Dao conjugate of X(j) for these (i,j): {3121, 4024}, {3739, 1089}, {16589, 313}, {17205, 3261}, {40589, 32009}, {62646, 321}
X(70143) = crosspoint of X(58) and X(757)
X(70143) = crosssum of X(i) and X(j) for these (i,j): {10, 756}, {37, 40607}
X(70143) = crossdifference of every pair of points on line {661, 4151}
X(70143) = barycentric product X(i)*X(j) for these {i,j}: {1, 18166}, {6, 17175}, {27, 22060}, {31, 16748}, {58, 3739}, {81, 3720}, {86, 20963}, {99, 68881}, {110, 47672}, {284, 4059}, {593, 21020}, {662, 6372}, {757, 16589}, {763, 21699}, {849, 53478}, {873, 21753}, {1014, 3691}, {1019, 4436}, {1178, 4754}, {1333, 20888}, {1412, 3706}, {1444, 40975}, {1509, 2667}, {2185, 39793}, {4556, 48393}, {4565, 48264}, {4610, 50497}, {6628, 21820}, {17187, 18089}, {53363, 57129}
X(70143) = barycentric quotient X(i)/X(j) for these {i,j}: {58, 32009}, {163, 8708}, {593, 40439}, {849, 40408}, {1333, 40433}, {2206, 57397}, {2667, 594}, {3691, 3701}, {3706, 30713}, {3720, 321}, {3739, 313}, {4059, 349}, {4436, 4033}, {4754, 1237}, {6372, 1577}, {16589, 1089}, {16748, 561}, {17175, 76}, {18089, 56251}, {18166, 75}, {20888, 27801}, {20963, 10}, {21020, 28654}, {21753, 756}, {21820, 6535}, {22060, 306}, {22369, 3949}, {39793, 6358}, {40975, 41013}, {47672, 850}, {48393, 52623}, {50497, 4024}, {57129, 50520}, {68881, 523}
X(70143) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {31, 81, 62740}, {58, 81, 31}, {58, 1468, 10457}, {58, 38832, 39673}, {81, 10458, 62821}, {81, 39673, 38832}, {81, 70110, 18169}, {18169, 69840, 81}, {18192, 62841, 81}, {38832, 39673, 31}

X(70144) = X(6)X(33846)∩X(100)X(101)

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

X(70144) lies on these lines: {6, 33846}, {31, 1979}, {41, 750}, {48, 17275}, {100, 101}, {110, 28841}, {284, 37675}, {649, 53280}, {661, 61220}, {662, 799}, {787, 8709}, {813, 8701}, {899, 9454}, {1030, 41423}, {1213, 24938}, {2112, 25748}, {2177, 5168}, {2238, 68748}, {2280, 9345}, {2305, 3217}, {2340, 20857}, {3204, 69230}, {3207, 64752}, {3231, 41333}, {3684, 32919}, {3909, 21383}, {4191, 36808}, {4251, 37633}, {4427, 69901}, {4436, 61163}, {4557, 35326}, {6016, 28230}, {8693, 8694}, {9090, 39630}, {14716, 32664}, {16704, 70119}, {17780, 61164}, {20470, 69074}, {20769, 24602}, {20970, 61670}, {25813, 25819}, {28196, 43077}, {28852, 59033}, {29459, 69073}, {35338, 61160}, {38346, 54333}, {48275, 53349}, {61168, 61197}

X(70144) = X(4600)-Ceva conjugate of X(31)
X(70144) = X(68881)-cross conjugate of X(20963)
X(70144) = X(i)-isoconjugate of X(j) for these (i,j): {2, 50520}, {513, 32009}, {514, 40433}, {523, 40408}, {661, 40439}, {693, 57397}, {1086, 8708}, {4705, 59147}
X(70144) = X(i)-Dao conjugate of X(j) for these (i,j): {3121, 3120}, {3720, 58361}, {3739, 1577}, {16589, 3261}, {32664, 50520}, {36830, 40439}, {39026, 32009}, {62646, 693}
X(70144) = cevapoint of X(20963) and X(68881)
X(70144) = crosspoint of X(i) and X(j) for these (i,j): {100, 65256}, {101, 662}
X(70144) = crosssum of X(i) and X(j) for these (i,j): {514, 661}, {1577, 20909}
X(70144) = trilinear pole of line {2667, 20963}
X(70144) = crossdifference of every pair of points on line {244, 17761}
X(70144) = barycentric product X(i)*X(j) for these {i,j}: {1, 4436}, {31, 53363}, {59, 48264}, {81, 61163}, {99, 2667}, {100, 3720}, {101, 3739}, {109, 3706}, {110, 21020}, {163, 53478}, {190, 20963}, {643, 39793}, {651, 3691}, {662, 16589}, {692, 20888}, {765, 6372}, {799, 21753}, {811, 22369}, {1016, 68881}, {1018, 18166}, {1252, 47672}, {1293, 4891}, {1332, 40975}, {1414, 4111}, {1897, 22060}, {3939, 4059}, {4556, 52579}, {4557, 17175}, {4570, 48393}, {4600, 50497}, {4610, 21820}, {16748, 69826}, {18089, 46148}, {21699, 52935}, {24041, 50538}, {62646, 65256}
X(70144) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 50520}, {101, 32009}, {110, 40439}, {163, 40408}, {692, 40433}, {1110, 8708}, {2667, 523}, {3691, 4391}, {3706, 35519}, {3720, 693}, {3739, 3261}, {4059, 52621}, {4111, 4086}, {4436, 75}, {4556, 59147}, {6372, 1111}, {16589, 1577}, {17175, 52619}, {18166, 7199}, {20888, 40495}, {20963, 514}, {21020, 850}, {21699, 4036}, {21753, 661}, {21820, 4024}, {22060, 4025}, {22369, 656}, {32739, 57397}, {39793, 4077}, {40975, 17924}, {47672, 23989}, {48264, 34387}, {48393, 21207}, {50497, 3120}, {50538, 1109}, {52579, 52623}, {53363, 561}, {53478, 20948}, {61163, 321}, {62646, 58361}, {68881, 1086}
X(70144) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 101, 69826}, {100, 68812, 61234}, {100, 69826, 68825}, {899, 9454, 69836}, {3231, 41333, 62740}, {4557, 35326, 46148}, {35342, 61234, 100}

X(70145) = X(1)X(1655)∩X(2)X(17205)

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

X(70145) lies on these lines: {1, 1655}, {2, 17205}, {9, 3761}, {10, 56024}, {76, 16552}, {99, 3570}, {100, 6013}, {148, 1654}, {190, 646}, {191, 17739}, {194, 3216}, {274, 29460}, {350, 45751}, {385, 52680}, {391, 69453}, {514, 4115}, {538, 2238}, {644, 4482}, {645, 57249}, {672, 6381}, {799, 4602}, {894, 56191}, {956, 69866}, {1015, 4465}, {1023, 18047}, {1026, 3952}, {1107, 4721}, {1111, 17755}, {1211, 50159}, {1213, 25468}, {1330, 30625}, {1334, 29699}, {1475, 29750}, {1573, 24330}, {1714, 6392}, {1724, 7754}, {1759, 20609}, {1909, 3294}, {2832, 3799}, {2895, 17294}, {3125, 68870}, {3293, 25264}, {3501, 29691}, {3670, 25994}, {3691, 20888}, {3730, 29381}, {3731, 26110}, {3760, 21384}, {3765, 62817}, {3780, 69255}, {3948, 18206}, {3975, 20367}, {3985, 14210}, {3992, 70090}, {4009, 70101}, {4037, 8682}, {4075, 25263}, {4103, 42720}, {4253, 18135}, {4257, 17001}, {4383, 22253}, {4391, 61233}, {4424, 49514}, {4427, 24074}, {4473, 27295}, {4554, 63203}, {4562, 6540}, {4692, 49516}, {4713, 16975}, {4737, 51052}, {4754, 16589}, {4783, 53410}, {5134, 20553}, {5179, 63817}, {5540, 17738}, {6376, 16549}, {6390, 69729}, {16514, 69088}, {16611, 69015}, {16748, 62646}, {16887, 27040}, {17007, 48835}, {17136, 30729}, {17149, 29391}, {17210, 52538}, {17277, 29479}, {17304, 27320}, {17310, 63071}, {17336, 29509}, {17350, 30114}, {17489, 24068}, {17497, 68895}, {17759, 31855}, {17778, 29573}, {18140, 29440}, {18145, 37686}, {18148, 29425}, {18152, 29448}, {18153, 29436}, {18159, 46894}, {18164, 25660}, {20081, 69277}, {20331, 27076}, {20347, 30109}, {20893, 70095}, {21044, 70094}, {23354, 68959}, {24287, 55260}, {24291, 69281}, {24398, 26138}, {24505, 24821}, {24690, 69512}, {25590, 26045}, {25683, 69009}, {25735, 52353}, {29401, 52043}, {29615, 43990}, {30941, 68938}, {31290, 56811}, {32041, 53658}, {33946, 33948}, {35068, 68862}, {37657, 69559}, {37658, 69380}, {37678, 69528}, {40883, 59586}, {41676, 61226}, {46519, 49991}, {47286, 68946}, {47959, 61167}, {53363, 61163}, {54985, 57960}, {61235, 65185}, {65191, 65205}

X(70145) = reflection of X(i) in X(j) for these {i,j}: {1, 4368}, {14210, 3985}, {30941, 68938}, {53332, 4115}, {62755, 2238}, {69015, 16611}
X(70145) = anticomplement of X(17205)
X(70145) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {59, 3873}, {213, 54102}, {692, 17154}, {765, 17135}, {1016, 17137}, {1018, 150}, {1110, 1}, {1252, 75}, {1262, 17158}, {2149, 3875}, {3952, 21293}, {4069, 33650}, {4103, 21294}, {4557, 149}, {4564, 20244}, {4567, 17143}, {4570, 17140}, {4601, 54112}, {5377, 62872}, {6065, 3869}, {6632, 17217}, {7035, 17138}, {9268, 17145}, {15742, 20242}, {23990, 17147}, {31615, 4374}, {40521, 3448}, {57731, 512}, {57950, 44445}, {59149, 7192}, {61402, 21287}, {65573, 3434}, {69826, 4440}
X(70145) = X(190)-Ceva conjugate of X(61163)
X(70145) = X(i)-cross conjugate of X(j) for these (i,j): {6372, 17175}, {47672, 3739}, {48264, 20888}, {61163, 4436}, {68881, 3720}
X(70145) = X(i)-isoconjugate of X(j) for these (i,j): {6, 50520}, {512, 40408}, {513, 57397}, {649, 40433}, {667, 32009}, {798, 40439}, {1015, 8708}, {50487, 59147}
X(70145) = X(i)-Dao conjugate of X(j) for these (i,j): {9, 50520}, {3121, 3122}, {3739, 661}, {4698, 47917}, {5375, 40433}, {6631, 32009}, {16589, 514}, {25092, 48409}, {31998, 40439}, {39026, 57397}, {39054, 40408}, {53478, 20909}, {62646, 513}
X(70145) = cevapoint of X(i) and X(j) for these (i,j): {3691, 48264}, {3720, 68881}, {3739, 47672}, {6372, 16589}
X(70145) = crosspoint of X(190) and X(799)
X(70145) = crosssum of X(i) and X(j) for these (i,j): {513, 50524}, {649, 798}, {661, 17458}
X(70145) = trilinear pole of line {2667, 3706}
X(70145) = crossdifference of every pair of points on line {3248, 4117}
X(70145) = barycentric product X(i)*X(j) for these {i,j}: {1, 53363}, {75, 4436}, {99, 21020}, {100, 20888}, {190, 3739}, {274, 61163}, {662, 53478}, {664, 3706}, {668, 3720}, {670, 2667}, {799, 16589}, {1016, 47672}, {1018, 16748}, {1978, 20963}, {3691, 4554}, {3699, 4059}, {3952, 17175}, {4033, 18166}, {4111, 4625}, {4568, 18089}, {4600, 48393}, {4602, 21753}, {4610, 52579}, {4623, 21699}, {4754, 27805}, {4891, 53647}, {4998, 48264}, {6372, 7035}, {7257, 39793}, {21820, 52612}, {22369, 57968}, {24037, 50538}, {29773, 54118}, {31625, 68881}
X(70145) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 50520}, {99, 40439}, {100, 40433}, {101, 57397}, {190, 32009}, {662, 40408}, {765, 8708}, {2667, 512}, {3691, 650}, {3706, 522}, {3720, 513}, {3739, 514}, {4059, 3676}, {4111, 4041}, {4436, 1}, {4610, 59147}, {4754, 4369}, {4891, 3667}, {6372, 244}, {16589, 661}, {16748, 7199}, {17175, 7192}, {18089, 10566}, {18166, 1019}, {20888, 693}, {20963, 649}, {21020, 523}, {21699, 4705}, {21753, 798}, {21820, 4079}, {22060, 1459}, {22369, 810}, {29773, 17494}, {39793, 4017}, {40975, 6591}, {47672, 1086}, {48264, 11}, {48393, 3120}, {50497, 3122}, {50538, 2643}, {52579, 4024}, {53363, 75}, {53478, 1577}, {59219, 4824}, {61163, 37}, {68881, 1015}
X(70145) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {76, 16552, 29433}, {99, 3570, 35342}, {190, 668, 1018}, {190, 3732, 33952}, {190, 65161, 3882}, {274, 46196, 29460}, {668, 1018, 23891}, {668, 70112, 65169}, {672, 6381, 69869}, {1655, 17499, 1}, {1909, 3294, 29383}, {3691, 20888, 29773}, {3760, 21384, 29742}, {3948, 18206, 29456}, {3952, 65195, 4568}, {4253, 18135, 29438}, {4754, 16589, 17175}, {5179, 70091, 63817}, {6376, 16549, 29375}, {18047, 69865, 1023}, {18140, 68950, 29440}, {65161, 65169, 668}

X(70146) = X(2)X(39)∩X(320)X(350)

Barycentrics   b*(a + b)*c*(a + c)*(a*b + a*c - 2*b*c) : :
X(70146) = 3 X[2] - 4 X[69013]

X(70146) lies on these lines: {2, 39}, {11, 69076}, {75, 27812}, {86, 55919}, {99, 5990}, {192, 6385}, {312, 16703}, {320, 350}, {321, 16739}, {384, 69488}, {536, 35543}, {561, 17147}, {668, 19998}, {726, 23824}, {740, 53363}, {799, 16704}, {811, 14954}, {874, 18075}, {899, 6381}, {1575, 36957}, {1909, 29822}, {1920, 3995}, {1921, 17495}, {1965, 17150}, {1966, 4427}, {1975, 11322}, {1978, 62227}, {3210, 40072}, {3240, 33296}, {3286, 69833}, {3672, 44154}, {3760, 16887}, {3840, 17208}, {3944, 16891}, {3952, 52049}, {3994, 41314}, {4009, 62627}, {4080, 4639}, {4358, 16727}, {4365, 59505}, {4389, 4441}, {4465, 52897}, {4495, 32845}, {4651, 25280}, {4850, 21615}, {4871, 17205}, {5235, 60735}, {6384, 39734}, {7244, 32936}, {7754, 11339}, {8025, 8033}, {9295, 41535}, {10453, 58814}, {16405, 69380}, {16708, 18743}, {16726, 41144}, {16738, 34022}, {17135, 17144}, {17163, 51863}, {17169, 30947}, {17174, 51370}, {17175, 30950}, {17176, 18169}, {17203, 69173}, {17210, 20888}, {17499, 69518}, {17756, 56023}, {17759, 31625}, {18021, 61407}, {18052, 40013}, {18056, 32929}, {18059, 27804}, {18066, 24731}, {18171, 69256}, {20012, 25296}, {20345, 32842}, {20530, 40508}, {21443, 46901}, {21877, 27104}, {23632, 26973}, {25264, 69527}, {25958, 69844}, {26844, 56660}, {30660, 33100}, {30965, 33151}, {31002, 70111}, {31025, 60719}, {31330, 32104}, {39044, 68958}, {40030, 60071}, {46238, 62305}, {52896, 69660}, {57785, 61413}, {68750, 69088}, {68877, 68954}

X(70146) = reflection of X(2229) in X(69013)
X(70146) = anticomplement of X(2229)
X(70146) = isotomic conjugate of the isogonal conjugate of X(52897)
X(70146) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {715, 2}, {18826, 69}
X(70146) = X(i)-cross conjugate of X(j) for these (i,j): {536, 62755}, {4728, 41314}
X(70146) = X(i)-isoconjugate of X(j) for these (i,j): {6, 62763}, {32, 41683}, {42, 739}, {100, 69480}, {213, 37129}, {512, 34075}, {560, 60288}, {661, 32718}, {669, 4607}, {692, 69478}, {798, 898}, {889, 1924}, {1018, 23349}, {1918, 3227}, {2205, 31002}, {4557, 23892}, {32739, 35353}, {43928, 69826}
X(70146) = X(i)-Dao conjugate of X(j) for these (i,j): {9, 62763}, {536, 52959}, {1086, 69478}, {1646, 14404}, {6374, 60288}, {6376, 41683}, {6381, 714}, {6626, 37129}, {8054, 69480}, {9428, 889}, {13466, 37}, {14434, 3121}, {31998, 898}, {34021, 3227}, {36830, 32718}, {39011, 512}, {39054, 34075}, {40592, 739}, {40614, 42}, {40618, 69483}, {40619, 35353}, {40620, 43928}, {40625, 69481}, {52875, 1500}, {52882, 10}, {68938, 44671}
X(70146) = cevapoint of X(i) and X(j) for these (i,j): {536, 6381}, {714, 68938}
X(70146) = crosspoint of X(86) and X(18826)
X(70146) = crosssum of X(42) and X(68987)
X(70146) = trilinear pole of line {891, 52882}
X(70146) = crossdifference of every pair of points on line {213, 669}
X(70146) = barycentric product X(i)*X(j) for these {i,j}: {75, 62755}, {76, 52897}, {81, 35543}, {86, 6381}, {274, 536}, {305, 52890}, {310, 899}, {314, 43037}, {333, 69660}, {561, 62740}, {670, 891}, {799, 4728}, {873, 3994}, {890, 4609}, {3230, 6385}, {3768, 4602}, {4009, 57785}, {4465, 40017}, {4601, 52626}, {4623, 14431}, {4625, 14430}, {4634, 30583}, {4639, 14433}, {7192, 41314}, {7199, 23891}, {16739, 62761}, {18155, 69659}, {18157, 36816}, {18826, 52882}, {23343, 52619}, {28660, 52896}, {30939, 52755}, {40072, 62739}
X(70146) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 62763}, {75, 41683}, {76, 60288}, {81, 739}, {86, 37129}, {99, 898}, {110, 32718}, {274, 3227}, {310, 31002}, {314, 36798}, {514, 69478}, {536, 37}, {649, 69480}, {662, 34075}, {670, 889}, {693, 35353}, {799, 4607}, {890, 669}, {891, 512}, {899, 42}, {1019, 23892}, {1646, 3121}, {3230, 213}, {3733, 23349}, {3768, 798}, {3994, 756}, {4009, 210}, {4025, 69483}, {4465, 2238}, {4526, 3709}, {4560, 69481}, {4601, 5381}, {4609, 57994}, {4706, 37593}, {4728, 661}, {6381, 10}, {7192, 43928}, {7199, 62619}, {13466, 52959}, {14404, 50487}, {14426, 50491}, {14430, 4041}, {14431, 4705}, {14433, 21832}, {14434, 14404}, {14437, 14407}, {16704, 69479}, {16741, 52757}, {17139, 63852}, {19945, 3122}, {23343, 4557}, {23891, 1018}, {28603, 4770}, {30583, 4730}, {30592, 4983}, {30939, 36872}, {30941, 64612}, {35543, 321}, {36816, 18785}, {41314, 3952}, {43037, 65}, {52626, 3125}, {52755, 4674}, {52882, 714}, {52890, 25}, {52896, 1400}, {52897, 6}, {52901, 28658}, {52902, 56853}, {52959, 1500}, {54308, 62769}, {61672, 51377}, {62627, 46897}, {62739, 1402}, {62740, 31}, {62755, 1}, {62760, 56190}, {68825, 69826}, {69658, 4559}, {69659, 4551}, {69660, 226}
X(70146) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 310, 16748}, {2, 1655, 69524}, {39, 30955, 2}, {76, 30964, 2}, {194, 31000, 2}, {274, 31008, 62709}, {274, 62709, 2}, {310, 30964, 16705}, {310, 31008, 2}, {310, 62709, 274}, {350, 62234, 29824}, {799, 30940, 16704}, {2229, 69013, 2}, {3948, 69054, 3266}, {4358, 16727, 18157}, {18152, 34020, 2}, {39995, 69702, 69079}

X(70147) = X(190)X(646)∩X(514)X(33948)

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

X(70147) lies on these lines: {190, 646}, {514, 33948}, {664, 61170}, {799, 4598}, {1268, 50160}, {1655, 60724}, {1909, 59207}, {2176, 21219}, {3679, 17328}, {3761, 17277}, {3807, 65195}, {3952, 33946}, {3985, 49779}, {4115, 61187}, {4422, 27295}, {4465, 9263}, {4482, 69865}, {4562, 47915}, {4756, 23354}, {5224, 69098}, {6376, 17754}, {6381, 37686}, {6540, 53648}, {6631, 65189}, {17755, 18159}, {18047, 57192}, {18140, 29811}, {18145, 45751}, {20943, 21384}, {20947, 35102}, {21138, 33888}, {21904, 33296}, {25280, 56024}, {65166, 69899}

X(70147) = X(48399)-cross conjugate of X(4699)
X(70147) = X(i)-isoconjugate of X(j) for these (i,j): {649, 39972}, {667, 39738}, {1015, 29199}, {1919, 56212}
X(70147) = X(i)-Dao conjugate of X(j) for these (i,j): {4687, 47666}, {5375, 39972}, {6631, 39738}, {9296, 56212}
X(70147) = cevapoint of X(i) and X(j) for these (i,j): {649, 31313}, {4699, 48399}
X(70147) = crosssum of X(4826) and X(50491)
X(70147) = trilinear pole of line {4699, 26102}
X(70147) = crossdifference of every pair of points on line {3248, 23470}
X(70147) = barycentric product X(i)*X(j) for these {i,j}: {99, 62226}, {190, 4699}, {668, 26102}, {1016, 48399}, {7035, 29198}
X(70147) = barycentric quotient X(i)/X(j) for these {i,j}: {100, 39972}, {190, 39738}, {668, 56212}, {765, 29199}, {4699, 514}, {26102, 513}, {29198, 244}, {48399, 1086}, {62226, 523}
X(70147) = {X(190),X(668)}-harmonic conjugate of X(4595)

X(70148) = X(100)X(58117)∩X(190)X(646)

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

X(70148) lies on these lines: {100, 58117}, {190, 646}, {319, 20258}, {664, 53648}, {1026, 42343}, {1146, 17233}, {3570, 57192}, {3679, 17228}, {3699, 23354}, {3799, 61166}, {3807, 21272}, {4050, 20943}, {4103, 61187}, {4561, 6631}, {4562, 53647}, {6559, 36628}, {7257, 69086}, {16969, 40598}, {17234, 52871}, {17294, 30827}, {17752, 21904}, {17754, 24524}, {20331, 31298}, {20532, 34063}, {25280, 59207}, {27191, 27295}, {29615, 55095}, {30730, 33946}, {43290, 69899}

X(70148) = X(4598)-Ceva conjugate of X(190)
X(70148) = X(59522)-cross conjugate of X(1278)
X(70148) = X(i)-isoconjugate of X(j) for these (i,j): {513, 36614}, {649, 36598}, {667, 38247}, {1015, 29227}, {1919, 40027}, {36630, 43924}
X(70148) = X(i)-Dao conjugate of X(j) for these (i,j): {192, 3835}, {5375, 36598}, {6631, 38247}, {9296, 40027}, {39026, 36614}
X(70148) = cevapoint of X(i) and X(j) for these (i,j): {1278, 59522}, {21868, 29226}
X(70148) = crosssum of X(3249) and X(38986)
X(70148) = trilinear pole of line {1278, 4135}
X(70148) = barycentric product X(i)*X(j) for these {i,j}: {99, 4135}, {100, 20943}, {190, 1278}, {664, 4903}, {668, 16569}, {799, 21868}, {1016, 59522}, {1978, 16969}, {3699, 17090}, {4050, 4554}, {4598, 40598}, {4600, 59521}, {7035, 29226}
X(70148) = barycentric quotient X(i)/X(j) for these {i,j}: {100, 36598}, {101, 36614}, {190, 38247}, {644, 36630}, {668, 40027}, {765, 29227}, {1278, 514}, {4050, 650}, {4135, 523}, {4903, 522}, {16569, 513}, {16969, 649}, {17090, 3676}, {20943, 693}, {21868, 661}, {22149, 1459}, {23560, 3249}, {29226, 244}, {40598, 3835}, {59521, 3120}, {59522, 1086}
X(70148) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {668, 4595, 190}, {668, 23891, 4595}, {30730, 61186, 33946}

X(70149) = X(1)X(75)∩X(2)X(4754)

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

X(70149) lies on these lines: {1, 75}, {2, 4754}, {6, 16911}, {10, 17180}, {45, 25508}, {81, 16816}, {190, 31996}, {194, 15668}, {239, 42028}, {310, 30950}, {333, 16815}, {873, 69955}, {1125, 16712}, {1434, 1447}, {1698, 17179}, {3175, 16826}, {3214, 60706}, {3616, 16711}, {3617, 30941}, {3626, 33297}, {3634, 16887}, {4234, 24331}, {4352, 16714}, {4384, 41629}, {4393, 42025}, {4518, 18827}, {4595, 24656}, {4658, 50018}, {4670, 16827}, {4724, 16737}, {4751, 21384}, {5224, 17529}, {5333, 29595}, {5437, 18206}, {5550, 16705}, {7176, 55096}, {9534, 17378}, {9780, 17169}, {16672, 56023}, {16700, 25507}, {16710, 32005}, {16818, 27191}, {16822, 37792}, {16948, 17103}, {16994, 33863}, {17021, 30599}, {17205, 19862}, {17210, 19872}, {17245, 69415}, {17322, 24214}, {17499, 36812}, {17749, 37678}, {18198, 27164}, {18600, 46934}, {19701, 24621}, {20018, 63110}, {24161, 41879}, {27148, 30997}, {29591, 30965}, {32014, 34475}, {37682, 69417}, {39740, 56066}, {46922, 69277}

X(70149) = X(i)-isoconjugate of X(j) for these (i,j): {42, 39972}, {213, 39738}, {512, 29199}, {1918, 56212}
X(70149) = X(i)-Dao conjugate of X(j) for these (i,j): {6626, 39738}, {34021, 56212}, {39054, 29199}, {40592, 39972}
X(70149) = cevapoint of X(4699) and X(26102)
X(70149) = barycentric product X(i)*X(j) for these {i,j}: {86, 4699}, {99, 48399}, {274, 26102}, {799, 29198}, {1509, 62226}
X(70149) = barycentric quotient X(i)/X(j) for these {i,j}: {81, 39972}, {86, 39738}, {274, 56212}, {662, 29199}, {4699, 10}, {26102, 37}, {29198, 661}, {48399, 523}, {62226, 594}
X(70149) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {86, 274, 33296}, {274, 17175, 86}, {274, 70111, 10471}, {25526, 33955, 86}

X(70150) = X(1)X(75)∩X(6)X(16913)

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

X(70150) lies on these lines: {1, 75}, {6, 16913}, {8, 16711}, {10, 16712}, {45, 32107}, {76, 17749}, {81, 39740}, {190, 16827}, {194, 17277}, {239, 41629}, {310, 899}, {319, 24215}, {320, 59303}, {330, 4361}, {333, 16722}, {350, 28352}, {1278, 16969}, {1434, 3212}, {1654, 24364}, {1909, 3214}, {2238, 40908}, {3240, 16748}, {3244, 17180}, {3617, 18600}, {3621, 30941}, {3625, 17205}, {3626, 16887}, {3632, 17179}, {3752, 16815}, {4234, 50023}, {4352, 5224}, {4393, 42028}, {4420, 20436}, {4441, 28370}, {4479, 21214}, {4685, 65077}, {7799, 24880}, {9534, 17271}, {9780, 16705}, {14829, 24621}, {16569, 20943}, {16672, 25508}, {16714, 42696}, {16750, 67097}, {16752, 29579}, {16948, 33295}, {17012, 30599}, {17117, 17448}, {17169, 20050}, {17273, 24214}, {17319, 25130}, {17378, 20018}, {18827, 53647}, {20036, 42697}, {20081, 37673}, {20924, 64185}, {24366, 31090}, {25507, 29595}, {27191, 29960}, {27627, 28660}, {29578, 44417}, {30038, 37756}, {31008, 62711}, {33135, 41879}, {34284, 37678}, {36647, 52897}, {37596, 55095}, {37650, 69419}, {37679, 69420}, {39736, 56066}, {50018, 56018}, {50575, 64133}, {51415, 69422}, {56283, 57214}, {60708, 65018}, {68966, 69277}

X(70150) = X(i)-isoconjugate of X(j) for these (i,j): {37, 36614}, {42, 36598}, {213, 38247}, {512, 29227}, {1400, 36630}, {1918, 40027}
X(70150) = X(i)-Dao conjugate of X(j) for these (i,j): {192, 3971}, {6626, 38247}, {34021, 40027}, {39054, 29227}, {40582, 36630}, {40589, 36614}, {40592, 36598}
X(70150) = cevapoint of X(1278) and X(16569)
X(70150) = barycentric product X(i)*X(j) for these {i,j}: {81, 20943}, {86, 1278}, {99, 59522}, {274, 16569}, {310, 16969}, {333, 17090}, {799, 29226}, {873, 21868}, {1434, 4903}, {1509, 4135}, {4050, 57785}, {4610, 59521}, {22149, 44129}
X(70150) = barycentric quotient X(i)/X(j) for these {i,j}: {21, 36630}, {58, 36614}, {81, 36598}, {86, 38247}, {274, 40027}, {662, 29227}, {1278, 10}, {4050, 210}, {4135, 594}, {4903, 2321}, {16569, 37}, {16969, 42}, {17090, 226}, {20943, 321}, {21868, 756}, {22149, 71}, {29226, 661}, {40598, 3971}, {59521, 4024}, {59522, 523}
X(70150) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 16711, 33947}, {274, 33296, 86}, {274, 62755, 33296}, {2669, 60735, 86}

X(70151) = X(2)X(6)∩X(310)X(6327)

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

X(70151) lies on these lines: {2, 6}, {310, 6327}, {3416, 16703}, {4362, 16891}, {4645, 16748}, {7357, 21285}, {16705, 33083}, {16739, 33075}, {16887, 33080}, {17137, 17140}, {17203, 17763}, {17208, 33085}, {18157, 33078}, {32948, 62755}

X(70152) = X(2)X(740)∩X(8)X(210)

Barycentrics   (a - b - c)*(a*b + a*c + 3*b*c) : :
X(70152) = X[8] - 4 X[3714], X[8] + 2 X[4673], 2 X[3714] + X[4673], 2 X[4066] + X[50625], 4 X[4646] - 7 X[9780], 8 X[4719] - 11 X[5550]

X(70152) lies on these lines: {2, 740}, {8, 210}, {75, 3742}, {145, 1215}, {192, 3741}, {314, 3794}, {319, 24703}, {321, 3873}, {333, 4387}, {354, 42029}, {391, 3985}, {518, 42034}, {758, 10449}, {894, 39594}, {982, 1278}, {1001, 55095}, {1043, 56177}, {1699, 17294}, {1920, 4441}, {1999, 62845}, {2321, 3705}, {2345, 29837}, {2886, 17233}, {2887, 17230}, {3158, 3886}, {3210, 4365}, {3212, 17762}, {3616, 31993}, {3632, 4090}, {3661, 24210}, {3679, 59517}, {3685, 4512}, {3696, 18743}, {3703, 36481}, {3729, 35613}, {3740, 20942}, {3757, 62856}, {3760, 59505}, {3769, 49484}, {3773, 33141}, {3790, 4847}, {3813, 20487}, {3840, 17490}, {3919, 4717}, {3921, 46937}, {3923, 37683}, {3944, 49560}, {3967, 49450}, {3969, 11680}, {3996, 36488}, {4011, 17349}, {4046, 5233}, {4061, 62297}, {4066, 50625}, {4102, 11238}, {4133, 24239}, {4135, 49448}, {4195, 5429}, {4253, 24044}, {4358, 59296}, {4359, 30947}, {4393, 25496}, {4402, 30748}, {4418, 37684}, {4425, 17238}, {4427, 5372}, {4431, 11019}, {4442, 33172}, {4461, 70090}, {4485, 44140}, {4518, 56086}, {4527, 32855}, {4645, 34255}, {4646, 9780}, {4661, 4671}, {4693, 32916}, {4699, 26102}, {4703, 17343}, {4709, 16569}, {4719, 5550}, {4740, 24165}, {4741, 33099}, {4835, 5232}, {4970, 29827}, {4980, 64149}, {5141, 27558}, {5205, 63131}, {5272, 17117}, {5274, 17452}, {5695, 14829}, {5739, 17777}, {6535, 33120}, {6542, 26098}, {6682, 49452}, {6685, 49469}, {7226, 62227}, {10176, 48850}, {16816, 17123}, {17063, 30948}, {17143, 59518}, {17144, 41318}, {17156, 27064}, {17162, 63074}, {17232, 17889}, {17236, 33154}, {17280, 33137}, {17281, 33121}, {17299, 33071}, {17350, 32853}, {17358, 25453}, {17373, 32946}, {17375, 33097}, {17591, 28522}, {17697, 27368}, {18135, 51863}, {19785, 26150}, {19804, 26103}, {20007, 27409}, {20012, 32931}, {20017, 33107}, {20055, 32861}, {20146, 67024}, {20880, 40493}, {20947, 26105}, {21242, 33092}, {21283, 33091}, {22034, 49447}, {24280, 37655}, {24477, 50107}, {24552, 62855}, {24620, 30957}, {25123, 25591}, {25492, 64185}, {27268, 59312}, {27512, 28795}, {28605, 29824}, {29814, 31025}, {30568, 60731}, {30758, 32087}, {30818, 59298}, {31136, 32925}, {31330, 41839}, {32772, 58820}, {32926, 36534}, {32930, 37652}, {33069, 48642}, {33087, 48643}, {33101, 50315}, {33103, 48641}, {33152, 50311}, {33169, 48644}, {33171, 37759}, {37674, 68999}, {38473, 62819}, {42044, 46909}, {44417, 49470}, {49459, 59295}, {50310, 64162}

X(70152) = reflection of X(4734) in X(2)
X(70152) = X(56087)-Ceva conjugate of X(8)
X(70152) = X(i)-isoconjugate of X(j) for these (i,j): {56, 39972}, {604, 39738}, {1397, 56212}, {29199, 43924}
X(70152) = X(i)-Dao conjugate of X(j) for these (i,j): {1, 39972}, {3161, 39738}, {62585, 56212}
X(70152) = barycentric product X(i)*X(j) for these {i,j}: {8, 4699}, {312, 26102}, {333, 62226}, {646, 29198}, {3699, 48399}
X(70152) = barycentric quotient X(i)/X(j) for these {i,j}: {8, 39738}, {9, 39972}, {312, 56212}, {644, 29199}, {4699, 7}, {26102, 57}, {29198, 3669}, {48399, 3676}, {62226, 226}
X(70152) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 312, 27538}, {8, 4903, 210}, {210, 312, 4903}, {210, 4903, 27538}, {312, 3706, 8}, {321, 10453, 24349}, {3696, 18743, 26038}, {3706, 4519, 312}, {3714, 4673, 8}, {3840, 49474, 17490}, {4365, 30942, 3210}, {4514, 69089, 8}, {4671, 17135, 32937}, {26102, 62226, 4699}, {44417, 49470, 59297}, {49459, 59511, 59295}

X(70153) = X(38)X(1930)∩X(244)X(16739)

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

X(70153) lies on these lines: {38, 1930}, {244, 16739}, {756, 18157}, {1962, 16705}, {3741, 16727}, {3846, 17198}, {4359, 17205}, {16708, 31330}, {16748, 21020}, {17177, 25760}, {18600, 32860}, {24325, 39734}, {26819, 68992}, {30941, 62867}, {59622, 69073}

X(70153) = X(i)-isoconjugate of X(j) for these (i,j): {8708, 18105}, {18098, 57397}
X(70153) = X(i)-Dao conjugate of X(j) for these (i,j): {16589, 18082}, {17205, 10566}, {62646, 18098}
X(70153) = crosspoint of X(40004) and X(57992)
X(70153) = barycentric product X(i)*X(j) for these {i,j}: {38, 16748}, {141, 17175}, {1930, 18166}, {3720, 16703}, {3739, 16887}, {4576, 47672}, {6372, 55239}, {16696, 20888}, {21020, 61407}
X(70153) = barycentric quotient X(i)/X(j) for these {i,j}: {3720, 18098}, {3739, 18082}, {4059, 18097}, {4754, 18099}, {6372, 55240}, {16696, 40433}, {16748, 3112}, {16887, 32009}, {17175, 83}, {17187, 57397}, {18166, 82}, {20888, 56186}, {21020, 61405}, {47672, 58784}, {61407, 40439}, {68881, 18105}
X(70153) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {16703, 16887, 38}, {16739, 17208, 244}

X(70154) = X(65)X(33936)∩X(69)X(72)

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

X(70154) lies on these lines: {65, 33936}, {69, 72}, {75, 3555}, {85, 10449}, {86, 16817}, {210, 33942}, {306, 3933}, {319, 33943}, {320, 17762}, {354, 33945}, {392, 18156}, {517, 17137}, {518, 1930}, {599, 69285}, {740, 24214}, {910, 29473}, {942, 20911}, {960, 14210}, {1043, 5088}, {1104, 33953}, {1330, 4872}, {1565, 41014}, {3263, 34790}, {3631, 59515}, {3664, 49598}, {3666, 16887}, {3673, 10453}, {3687, 53597}, {3693, 40006}, {3695, 70091}, {3696, 32092}, {3697, 30758}, {3702, 20347}, {3706, 4059}, {3714, 3761}, {3739, 17175}, {3902, 20244}, {3912, 16601}, {3916, 17206}, {3999, 24166}, {4006, 40883}, {4018, 24282}, {4357, 6051}, {4359, 17169}, {4385, 36854}, {4417, 17181}, {4673, 17753}, {4875, 30109}, {4920, 33064}, {5045, 26234}, {5295, 34284}, {5439, 30962}, {5692, 59504}, {5814, 45962}, {6706, 29433}, {8682, 21240}, {9957, 17152}, {10452, 24471}, {10914, 21281}, {14994, 17760}, {16583, 30945}, {17026, 24774}, {17135, 20880}, {17205, 64185}, {17274, 50122}, {17296, 18726}, {17344, 21879}, {17497, 26562}, {17751, 30806}, {17866, 20448}, {18697, 54344}, {20924, 33297}, {20947, 59582}, {21839, 59554}, {25242, 29616}, {25590, 31327}, {26932, 52881}, {27248, 49496}, {29960, 43065}, {33932, 59586}, {33944, 41851}, {34255, 69377}, {49468, 63585}, {50011, 69097}, {59303, 68995}, {60729, 69858}, {69083, 69280}, {69264, 69279}

X(70154) = reflection of X(41015) in X(21240)
X(70154) = isotomic conjugate of the isogonal conjugate of X(22060)
X(70154) = isotomic conjugate of the polar conjugate of X(3739)
X(70154) = X(i)-Ceva conjugate of X(j) for these (i,j): {52608, 905}, {52609, 4025}
X(70154) = X(22060)-cross conjugate of X(3739)
X(70154) = X(i)-isoconjugate of X(j) for these (i,j): {19, 57397}, {25, 40433}, {1973, 32009}, {2333, 40408}, {8750, 50520}
X(70154) = X(i)-Dao conjugate of X(j) for these (i,j): {6, 57397}, {3121, 2489}, {3739, 1824}, {6337, 32009}, {6505, 40433}, {16589, 4}, {17205, 17925}, {26932, 50520}, {62646, 19}
X(70154) = barycentric product X(i)*X(j) for these {i,j}: {63, 20888}, {69, 3739}, {72, 16748}, {76, 22060}, {304, 3720}, {305, 20963}, {306, 17175}, {345, 4059}, {348, 3706}, {905, 53363}, {1444, 53478}, {3691, 7182}, {3933, 18089}, {4436, 15413}, {4561, 47672}, {4563, 48393}, {4754, 7019}, {6385, 22369}, {17206, 21020}, {18166, 20336}, {48264, 65164}, {50497, 52608}, {61163, 69830}
X(70154) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 57397}, {63, 40433}, {69, 32009}, {905, 50520}, {1332, 8708}, {1444, 40408}, {2667, 2333}, {3691, 33}, {3706, 281}, {3720, 19}, {3739, 4}, {4059, 278}, {4436, 1783}, {4754, 7009}, {6372, 6591}, {16589, 1824}, {16748, 286}, {17175, 27}, {17206, 40439}, {18089, 32085}, {18166, 28}, {20888, 92}, {20963, 25}, {21020, 1826}, {22060, 6}, {22369, 213}, {29773, 14004}, {39793, 1880}, {40975, 1096}, {47672, 7649}, {48264, 3064}, {48393, 2501}, {50497, 2489}, {52579, 7140}, {53363, 6335}, {53478, 41013}
X(70154) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 304, 72}, {3706, 4059, 20888}, {20911, 30941, 942}

X(70155) = X(519)X(7200)∩X(524)X(14210)

Barycentrics   (a*b + a*c + 2*b*c)*(2*a^2 - b^2 - c^2) : :
X(70155) = 3 X[3125] - 2 X[17497], X[17497] - 3 X[30941]

X(70155) lies on these lines: {519, 7200}, {524, 14210}, {3125, 8682}, {3555, 4686}, {3629, 46899}, {3739, 17175}, {4062, 7813}, {4754, 52579}, {4760, 6629}, {5692, 40341}, {6155, 16887}, {6372, 47672}, {7202, 17374}, {17169, 69633}, {63071, 68871}

X(70155) = reflection of X(i) in X(j) for these {i,j}: {3125, 30941}, {21839, 14210}
X(70155) = X(i)-isoconjugate of X(j) for these (i,j): {111, 40433}, {897, 57397}, {923, 32009}, {8708, 66945}
X(70155) = X(i)-Dao conjugate of X(j) for these (i,j): {2482, 32009}, {3121, 9178}, {6593, 57397}, {16589, 671}, {62646, 897}
X(70155) = crosspoint of X(524) and X(16741)
X(70155) = barycentric product X(i)*X(j) for these {i,j}: {524, 3739}, {896, 20888}, {3266, 20963}, {3706, 7181}, {3712, 4059}, {3720, 14210}, {4062, 17175}, {5468, 48393}, {6372, 42721}, {6629, 21020}, {7813, 18089}, {14419, 53363}, {16589, 16741}, {16702, 53478}, {16748, 21839}, {18166, 42713}, {22060, 44146}
X(70155) = barycentric quotient X(i)/X(j) for these {i,j}: {187, 57397}, {524, 32009}, {896, 40433}, {3720, 897}, {3739, 671}, {4436, 5380}, {6372, 69473}, {6629, 40439}, {14419, 50520}, {16702, 40408}, {20888, 46277}, {20963, 111}, {22060, 895}, {40975, 36128}, {47672, 62626}, {48393, 5466}, {50497, 9178}, {68881, 66945}

X(70156) = X(10)X(537)∩X(75)X(1500)

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

X(70156) lies on these lines: {2, 32026}, {10, 537}, {39, 32092}, {75, 1500}, {76, 4699}, {116, 23897}, {142, 69621}, {274, 1015}, {350, 36812}, {538, 16819}, {594, 17758}, {1573, 34284}, {1698, 9466}, {2241, 20181}, {3730, 17118}, {3739, 16589}, {3925, 7794}, {3934, 20671}, {4465, 29460}, {4665, 40006}, {4739, 52959}, {4754, 29773}, {4772, 26817}, {6533, 27918}, {7801, 19854}, {7863, 24953}, {7888, 31245}, {8728, 69258}, {9341, 16915}, {16711, 26826}, {16817, 50164}, {17245, 21070}, {17750, 25590}, {19853, 48840}, {19878, 41144}, {20913, 28654}, {21138, 68961}, {21208, 61342}, {21240, 24199}, {26806, 33297}, {26965, 50160}, {27156, 50179}, {28604, 69002}, {31025, 36791}, {31419, 69261}, {35068, 59746}, {37756, 50163}, {40908, 69523}, {49598, 50025}, {61076, 70030}

X(70156) = complement of X(32026)
X(70156) = X(31625)-Ceva conjugate of X(53363)
X(70156) = X(40433)-isoconjugate of X(57397)
X(70156) = X(i)-Dao conjugate of X(j) for these (i,j): {6372, 1015}, {16589, 32009}, {62646, 40433}
X(70156) = crosspoint of X(i) and X(j) for these (i,j): {3739, 16748}, {31625, 53363}
X(70156) = crosssum of X(6) and X(38853)
X(70156) = barycentric product X(i)*X(j) for these {i,j}: {668, 68124}, {3706, 4059}, {3720, 20888}, {3739, 3739}, {6372, 53363}, {16589, 16748}, {17175, 21020}, {18166, 53478}
X(70156) = barycentric quotient X(i)/X(j) for these {i,j}: {3720, 40433}, {3739, 32009}, {4436, 8708}, {6372, 50520}, {17175, 40439}, {18166, 40408}, {20963, 57397}, {68124, 513}
X(70156) = {X(3739),X(20888)}-harmonic conjugate of X(16589)

X(70157) = X(1)X(21070)∩X(8)X(9)

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

X(70157) lies on these lines: {1, 21070}, {2, 21071}, {8, 9}, {37, 31339}, {39, 30942}, {41, 1043}, {43, 27040}, {69, 56024}, {75, 21808}, {194, 31027}, {312, 28659}, {321, 69284}, {672, 10449}, {1212, 3706}, {1229, 21422}, {1475, 10453}, {1655, 3661}, {1698, 68938}, {1909, 17233}, {2170, 4673}, {2276, 21024}, {2295, 17281}, {2329, 49492}, {2340, 3974}, {2345, 59305}, {3061, 3702}, {3496, 32929}, {3501, 17751}, {3687, 28809}, {3693, 3714}, {3704, 4165}, {3729, 17137}, {3761, 40006}, {3765, 3969}, {3767, 29846}, {3780, 17299}, {3831, 17756}, {3875, 26965}, {3876, 3985}, {3902, 4051}, {3912, 34284}, {3930, 4385}, {3954, 32925}, {4023, 38930}, {4037, 69285}, {4044, 30961}, {4109, 33077}, {4418, 69217}, {4431, 30030}, {4441, 29960}, {4517, 6057}, {4754, 4851}, {4968, 51058}, {5021, 32919}, {5258, 62426}, {5280, 48863}, {5282, 7283}, {5283, 31330}, {5286, 33171}, {5295, 16601}, {6542, 26223}, {9534, 59207}, {10479, 25092}, {16502, 32943}, {16583, 32860}, {16589, 26037}, {16600, 64184}, {16968, 27368}, {17026, 27109}, {17033, 17280}, {17050, 29986}, {17135, 21384}, {17143, 30036}, {17230, 20081}, {17284, 26978}, {17294, 56025}, {17355, 67976}, {19874, 59772}, {20888, 30949}, {20911, 27474}, {20963, 48864}, {21029, 69279}, {21096, 39581}, {21281, 50107}, {25264, 69625}, {25760, 69096}, {27318, 30967}, {29573, 50155}, {29616, 36854}, {30109, 32104}, {30110, 62755}, {31448, 32918}, {32847, 49782}, {32914, 69215}, {32930, 54406}, {32932, 69242}, {32941, 69210}, {33935, 49753}, {35633, 63066}, {37657, 59302}, {40779, 45032}, {45751, 50625}, {54331, 54416}

X(70157) = X(i)-isoconjugate of X(j) for these (i,j): {604, 2296}, {785, 3669}, {1218, 1397}, {57181, 57959}
X(70157) = X(i)-Dao conjugate of X(j) for these (i,j): {3161, 2296}, {10472, 57}, {62585, 1218}
X(70157) = barycentric product X(i)*X(j) for these {i,j}: {8, 31330}, {210, 10471}, {312, 5283}, {333, 69621}, {341, 10473}, {645, 69620}, {784, 3699}, {1185, 28659}, {2321, 27164}, {3701, 10458}, {3939, 35559}, {4391, 68821}
X(70157) = barycentric quotient X(i)/X(j) for these {i,j}: {8, 2296}, {312, 1218}, {784, 3676}, {1185, 604}, {2978, 43924}, {3699, 57959}, {3939, 785}, {5283, 57}, {7257, 59093}, {10458, 1014}, {10471, 57785}, {10473, 269}, {27164, 1434}, {31330, 7}, {35559, 52621}, {68821, 651}, {69620, 7178}, {69621, 226}
X(70157) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 346, 1334}, {8, 27523, 3691}, {2082, 3886, 69640}, {3704, 40997, 4165}, {5283, 69621, 31330}, {17135, 26770, 21384}

X(70158) = X(1)X(48864)∩X(44)X(519)

Barycentrics   (2*a - b - c)*(a*b^2 + a*b*c + b^2*c + a*c^2 + b*c^2) : :
X(70158) = 3 X[4908] - X[52964], 3 X[17264] - X[40859]

X(70158) lies on these lines: {1, 48864}, {39, 3840}, {44, 519}, {536, 30109}, {538, 3912}, {712, 3797}, {730, 6541}, {740, 49758}, {784, 69620}, {1107, 21070}, {1573, 2321}, {1575, 49993}, {2087, 4742}, {2276, 69512}, {3230, 68971}, {3693, 68897}, {3727, 4099}, {3771, 5309}, {3997, 17340}, {4037, 57015}, {5283, 31330}, {7757, 31028}, {16601, 69549}, {17023, 48860}, {17147, 46902}, {17242, 64133}, {17264, 40859}, {17281, 30116}, {17284, 48840}, {17316, 48869}, {20012, 27523}, {20331, 49999}, {20963, 26770}, {21024, 25092}, {21240, 25264}, {21331, 68895}, {22036, 69284}, {28581, 50012}, {29579, 48838}, {29596, 48844}, {29960, 69255}, {31027, 69528}, {32934, 36283}, {33296, 58452}, {41232, 42033}, {50028, 68969}

X(70158) = midpoint of X(3797) and X(49753)
X(70158) = reflection of X(52963) in X(2325)
X(70158) = X(i)-isoconjugate of X(j) for these (i,j): {785, 1022}, {2296, 9456}
X(70158) = X(i)-Dao conjugate of X(j) for these (i,j): {4370, 2296}, {10472, 88}, {62571, 1218}
X(70158) = barycentric product X(i)*X(j) for these {i,j}: {519, 31330}, {784, 17780}, {3762, 68821}, {3943, 27164}, {3992, 10458}, {4358, 5283}, {4723, 10473}, {10471, 21805}, {16704, 69621}, {23344, 35559}, {69620, 69839}
X(70158) = barycentric quotient X(i)/X(j) for these {i,j}: {519, 2296}, {784, 6548}, {1185, 9456}, {2978, 23345}, {4358, 1218}, {5283, 88}, {10473, 56049}, {17780, 57959}, {23344, 785}, {31330, 903}, {55243, 59093}, {68821, 3257}, {69620, 4049}, {69621, 4080}

X(70159) = X(2)X(20963)∩X(10)X(39)

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

X(70159) lies on these lines: {2, 20963}, {6, 19858}, {10, 39}, {386, 17275}, {594, 25092}, {966, 2300}, {984, 22036}, {1100, 1125}, {1104, 19868}, {1475, 59306}, {1698, 45751}, {2140, 17237}, {2238, 19863}, {3634, 25629}, {3666, 69633}, {3691, 30970}, {3702, 21816}, {3739, 16887}, {3741, 16589}, {3846, 6537}, {3954, 4981}, {4253, 17303}, {4263, 5257}, {4359, 52572}, {5224, 17030}, {5235, 69210}, {5283, 31330}, {5743, 31466}, {10479, 69512}, {16502, 19732}, {16519, 54335}, {16777, 50625}, {16819, 21240}, {16828, 24512}, {16929, 20180}, {16975, 31339}, {17210, 29773}, {17259, 30110}, {17277, 27274}, {17362, 59301}, {17750, 19853}, {21242, 69259}, {21384, 59312}, {23632, 26037}, {24592, 25499}, {24603, 36812}, {25458, 62234}, {27156, 30941}, {31323, 33939}, {31416, 50295}, {31442, 50314}

X(70159) = X(i)-isoconjugate of X(j) for these (i,j): {785, 47947}, {2296, 28615}
X(70159) = X(i)-Dao conjugate of X(j) for these (i,j): {1213, 2296}, {10472, 1255}, {62588, 1218}
X(70159) = crosspoint of X(27164) and X(31330)
X(70159) = barycentric product X(i)*X(j) for these {i,j}: {784, 4427}, {1125, 31330}, {1213, 27164}, {1962, 10471}, {3702, 10473}, {4359, 5283}, {4647, 10458}, {4978, 68821}, {8025, 69621}, {35327, 35559}
X(70159) = barycentric quotient X(i)/X(j) for these {i,j}: {784, 4608}, {1125, 2296}, {1185, 28615}, {2978, 50344}, {4359, 1218}, {4427, 57959}, {5283, 1255}, {10458, 40438}, {27164, 32014}, {31330, 1268}, {35327, 785}, {68821, 37212}, {69620, 31010}, {69621, 6539}
X(70159) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1125, 3686, 20970}, {3691, 30970, 52538}, {5283, 31330, 69621}, {6537, 31488, 3846}, {16819, 30966, 21240}, {17277, 27274, 58452}

X(70160) = X(43)X(192)∩X(75)X(756)

Barycentrics   (a*b + a*c - b*c)*(a*b^2 + a*b*c + b^2*c + a*c^2 + b*c^2) : :
X(70160) = 6 X[2] - X[17157], 3 X[2] + 2 X[21080], X[17157] + 4 X[21080], 4 X[37] - 9 X[64178], X[192] - 6 X[3971], X[192] + 4 X[59565], 3 X[3971] + 2 X[59565], 2 X[75] + 3 X[32925], 4 X[3159] + X[49474], 8 X[3739] - 3 X[17155], 7 X[27268] - 2 X[42027], 7 X[27268] - 12 X[59517], X[42027] - 6 X[59517], 3 X[32860] - 8 X[58655], 3 X[42054] + 2 X[64545], X[49520] - 6 X[59718]

X(70160) lies on these lines: {2, 17157}, {37, 4009}, {38, 20923}, {43, 192}, {75, 756}, {312, 3728}, {714, 4687}, {726, 1698}, {740, 3876}, {982, 29982}, {984, 3701}, {1740, 31036}, {3097, 27102}, {3159, 49474}, {3661, 21713}, {3739, 17155}, {3778, 30830}, {3993, 5312}, {3995, 25277}, {4022, 30957}, {4850, 25106}, {17368, 59735}, {17391, 68873}, {17591, 27311}, {18137, 30942}, {18743, 21330}, {25295, 31035}, {25624, 59212}, {25957, 53476}, {27268, 42027}, {30090, 49447}, {32860, 58655}, {32936, 64727}, {42054, 64545}, {49520, 59718}, {49530, 56311}, {58365, 68892}

X(70160) = X(5283)-Ceva conjugate of X(31330)
X(70160) = X(i)-isoconjugate of X(j) for these (i,j): {785, 43931}, {2296, 7121}
X(70160) = X(i)-Dao conjugate of X(j) for these (i,j): {75, 1218}, {10472, 87}, {40598, 2296}
X(70160) = barycentric product X(i)*X(j) for these {i,j}: {192, 31330}, {784, 4595}, {3971, 27164}, {4110, 10473}, {5283, 6376}, {10471, 20691}, {20906, 68821}, {33296, 69621}, {35559, 69085}, {62530, 69620}
X(70160) = barycentric quotient X(i)/X(j) for these {i,j}: {192, 2296}, {1185, 7121}, {4595, 57959}, {5283, 87}, {6376, 1218}, {10473, 7153}, {31330, 330}, {36860, 59093}, {68821, 932}, {69085, 785}, {69621, 42027}
X(70160) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 21080, 17157}, {3971, 59565, 192}, {18137, 69624, 30942}, {42027, 59517, 27268}

X(70161) = X(37)X(31264)∩X(75)X(3971)

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

X(70161) lies on these lines: {37, 31264}, {75, 3971}, {536, 899}, {537, 49999}, {714, 4358}, {726, 24168}, {784, 69620}, {872, 59596}, {984, 4125}, {2228, 3948}, {3634, 49493}, {3739, 3989}, {3764, 28809}, {3831, 49447}, {3840, 4022}, {3952, 64869}, {4043, 59565}, {4664, 6685}, {18040, 21095}, {68981, 69697}

X(70161) = X(i)-isoconjugate of X(j) for these (i,j): {785, 43928}, {23349, 57959}
X(70161) = X(i)-Dao conjugate of X(j) for these (i,j): {10472, 37129}, {13466, 2296}, {52882, 1218}
X(70161) = barycentric product X(i)*X(j) for these {i,j}: {536, 31330}, {784, 23891}, {3994, 27164}, {5283, 6381}, {10471, 52959}, {35559, 68825}, {62755, 69621}
X(70161) = barycentric quotient X(i)/X(j) for these {i,j}: {536, 2296}, {784, 62619}, {2978, 23892}, {5283, 37129}, {6381, 1218}, {23891, 57959}, {31330, 3227}, {68821, 898}, {68825, 785}, {69620, 35353}, {69621, 41683}
X(70161) = {X(18137),X(21080)}-harmonic conjugate of X(4022)

X(70162) = X(2)X(22316)∩X(10)X(18137)

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

X(70162) lies on these lines: {2, 22316}, {10, 18137}, {11, 56953}, {37, 4519}, {75, 982}, {740, 19863}, {872, 44417}, {984, 4066}, {1125, 4709}, {1193, 3696}, {2667, 3706}, {4673, 31327}, {4688, 58571}, {4699, 29824}, {4732, 25106}, {4793, 66674}, {27166, 31329}, {31238, 37593}, {48628, 68951}, {59565, 69525}

X(70162) = X(785)-isoconjugate of X(50520)
X(70162) = X(i)-Dao conjugate of X(j) for these (i,j): {10472, 40433}, {16589, 2296}
X(70162) = crosspoint of X(i) and X(j) for these (i,j): {310, 56051}, {10471, 31330}
X(70162) = barycentric product X(i)*X(j) for these {i,j}: {3739, 31330}, {5283, 20888}, {10458, 53478}, {10471, 16589}, {17175, 69621}, {21020, 27164}
X(70162) = barycentric quotient X(i)/X(j) for these {i,j}: {3739, 2296}, {5283, 40433}, {10458, 40408}, {20888, 1218}, {27164, 40439}, {31330, 32009}, {68821, 8708}
X(70162) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 3741, 4022}, {3706, 3739, 2667}

X(70163) = X(1)X(21)∩X(8)X(4469)

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

X(70163) lies on these lines: {1, 21}, {8, 4469}, {69, 1655}, {86, 3721}, {257, 1921}, {274, 3735}, {333, 69271}, {3727, 33296}, {3948, 17550}, {3954, 33297}, {17202, 33890}, {17669, 52651}, {18189, 30966}, {27274, 68871}

X(70163) = {X(18189),X(69285)}-harmonic conjugate of X(30966)

X(70164) = X(2)X(6)∩X(274)X(2887)

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

X(70164) lies on these lines: {2, 6}, {274, 2887}, {304, 51863}, {310, 25760}, {873, 30984}, {2669, 33730}, {3846, 31008}, {4469, 30179}, {7018, 18891}, {16748, 25958}, {16891, 69252}, {17203, 32778}, {25960, 62709}, {32773, 33296}, {33084, 33297}

X(70165) = X(3)X(69)∩X(141)X(194)

Barycentrics   (a^2 - b^2 - c^2)*(b^2 - b*c + c^2)*(b^2 + b*c + c^2) : :
X(70165) = 3 X[33246] - 2 X[59232]

X(70165) lies on these lines: {2, 60232}, {3, 69}, {6, 7836}, {76, 3399}, {99, 48898}, {125, 305}, {141, 194}, {147, 1350}, {182, 7799}, {193, 33225}, {315, 48873}, {316, 48904}, {325, 5480}, {511, 7796}, {524, 33246}, {599, 59236}, {698, 5025}, {1352, 32833}, {1503, 32820}, {1691, 7891}, {1975, 5207}, {1992, 33220}, {2076, 7893}, {3094, 3314}, {3098, 7768}, {3589, 7945}, {3618, 33217}, {3619, 5286}, {3620, 33021}, {3763, 7797}, {3818, 69426}, {5017, 7779}, {5028, 7908}, {5039, 7905}, {6309, 7794}, {7750, 59548}, {7777, 24256}, {7782, 33751}, {7793, 59695}, {7802, 48920}, {7809, 48901}, {7811, 14810}, {7813, 32451}, {7814, 19130}, {7837, 10334}, {7860, 29317}, {7877, 41413}, {7907, 8177}, {7932, 34573}, {10007, 16986}, {10516, 69420}, {11057, 48885}, {11180, 32896}, {14036, 42421}, {14148, 65417}, {14561, 69431}, {14853, 32825}, {14994, 51397}, {20081, 53475}, {28419, 28433}, {31406, 63119}, {32113, 37896}, {32458, 50640}, {32830, 37336}, {32836, 40330}, {34254, 37894}, {35431, 39099}, {37668, 40236}, {40050, 40360}, {40250, 69380}, {40825, 50249}, {41716, 65748}, {43461, 51373}, {44882, 59634}, {46264, 69451}, {53484, 63021}

X(70165) = isotomic conjugate of the polar conjugate of X(3314)
X(70165) = X(i)-isoconjugate of X(j) for these (i,j): {19, 18898}, {1096, 43722}, {1973, 3407}, {1974, 3113}, {44162, 46281}
X(70165) = X(i)-Dao conjugate of X(j) for these (i,j): {6, 18898}, {3117, 10311}, {6337, 3407}, {6503, 43722}, {10335, 4}, {19602, 25}, {52658, 1974}, {62604, 3114}
X(70165) = barycentric product X(i)*X(j) for these {i,j}: {63, 56784}, {69, 3314}, {304, 51836}, {305, 3094}, {3116, 40364}, {3117, 40050}, {3926, 5117}, {3933, 62699}, {9865, 40708}, {18899, 40360}, {50549, 52608}
X(70165) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 18898}, {69, 3407}, {304, 3113}, {305, 3114}, {394, 43722}, {3094, 25}, {3116, 1973}, {3117, 1974}, {3314, 4}, {3784, 40746}, {3933, 14617}, {4558, 58111}, {4563, 33514}, {5117, 393}, {6393, 8840}, {9865, 419}, {12215, 64981}, {17415, 57204}, {18899, 44162}, {40364, 46281}, {43977, 61383}, {46507, 1096}, {50549, 2489}, {51836, 19}, {52658, 10311}, {56784, 92}, {56920, 2207}, {62699, 32085}
X(70165) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 3926, 12215}, {69, 69444, 25406}, {3933, 6393, 69}, {4121, 4175, 305}, {10519, 69409, 69}

X(70166) = X(6)X(7799)∩X(69)X(33008)

Barycentrics   (2*a^2 - b^2 - c^2)*(b^2 - b*c + c^2)*(b^2 + b*c + c^2) : :
X(70166) = X[6] - 3 X[7799], 2 X[115] - 3 X[5031], X[115] - 3 X[51371], X[193] - 3 X[12151], 3 X[325] - X[53505], 3 X[6393] - X[15993], 3 X[1691] - X[50249], 7 X[3619] - 3 X[19570], 5 X[3763] - 3 X[14568], 3 X[5207] + X[20094], 3 X[6034] - 5 X[7925], X[11054] - 3 X[21358], 3 X[12215] - X[64092], 3 X[13196] - 2 X[41672], 3 X[35297] - X[50253], X[53499] - 3 X[59634]

X(70166) lies on these lines: {6, 7799}, {69, 33008}, {115, 698}, {141, 538}, {187, 524}, {193, 12151}, {325, 5969}, {511, 51872}, {542, 14148}, {599, 7831}, {732, 6393}, {1648, 3266}, {1691, 50249}, {3094, 3314}, {3619, 19570}, {3630, 45759}, {3763, 14568}, {3815, 24256}, {3926, 34870}, {4121, 59768}, {5104, 7779}, {5207, 20094}, {6034, 7925}, {6791, 59765}, {7796, 44453}, {7840, 35705}, {7882, 55606}, {7906, 13330}, {7916, 52987}, {11054, 21358}, {11645, 15301}, {12215, 64092}, {13196, 16385}, {18906, 53504}, {20194, 59545}, {22165, 40344}, {32448, 40107}, {35297, 50253}, {53499, 59634}

X(70166) = midpoint of X(i) and X(j) for these {i,j}: {3094, 9865}, {5104, 7779}, {7813, 50567}
X(70166) = reflection of X(i) in X(j) for these {i,j}: {141, 51397}, {5026, 6390}, {5031, 51371}, {24256, 51373}
X(70166) = X(i)-isoconjugate of X(j) for these (i,j): {897, 18898}, {923, 3407}, {3113, 32740}, {19626, 46281}, {23894, 58111}, {33514, 69475}, {36128, 43722}
X(70166) = X(i)-Dao conjugate of X(j) for these (i,j): {2482, 3407}, {6593, 18898}, {10335, 671}, {19602, 111}, {52658, 32740}
X(70166) = crossdifference of every pair of points on line {9178, 18898}
X(70166) = barycentric product X(i)*X(j) for these {i,j}: {524, 3314}, {896, 56784}, {3094, 3266}, {5117, 6390}, {7813, 62699}, {14210, 51836}
X(70166) = barycentric quotient X(i)/X(j) for these {i,j}: {187, 18898}, {524, 3407}, {3094, 111}, {3116, 923}, {3117, 32740}, {3266, 3114}, {3292, 43722}, {3314, 671}, {5026, 64981}, {5117, 17983}, {5467, 58111}, {5468, 33514}, {7813, 14617}, {9865, 60863}, {14210, 3113}, {18899, 19626}, {46507, 36128}, {50549, 9178}, {50567, 8840}, {51836, 897}, {56784, 46277}, {56920, 8753}
X(70166) = {X(18906),X(63021)}-harmonic conjugate of X(53504)

X(70167) = X(6)X(7796)∩X(69)X(1691)

Barycentrics   (b^2 + c^2)*(b^2 - b*c + c^2)*(b^2 + b*c + c^2) : :
X(70167) = X[6] - 5 X[7881], 5 X[3763] - X[7754], X[4048] - 3 X[7801], X[5017] + 3 X[7788]

X(70167) lies on these lines: {6, 7796}, {39, 141}, {69, 1691}, {76, 5031}, {182, 7908}, {325, 24256}, {511, 7895}, {524, 7880}, {538, 51848}, {599, 5116}, {626, 698}, {1350, 43460}, {1352, 35002}, {2076, 7768}, {3094, 3314}, {3098, 7896}, {3530, 3564}, {3589, 7764}, {3620, 12055}, {3763, 7754}, {3788, 8177}, {4048, 5162}, {4175, 21248}, {5017, 7788}, {5039, 7916}, {5103, 7821}, {5305, 34573}, {5969, 32458}, {7767, 59695}, {7777, 40332}, {7779, 12212}, {7795, 42534}, {7820, 42421}, {7831, 59236}, {7835, 59232}, {7848, 14810}, {7882, 41413}, {7897, 18906}, {7906, 13331}, {8024, 16893}, {8290, 60702}, {9698, 51126}, {12829, 37671}, {14981, 44882}, {18800, 22165}, {21358, 66703}, {24206, 32515}, {32821, 50659}, {33751, 35022}, {34507, 52995}, {37668, 43450}, {45201, 59563}, {46900, 52906}, {48876, 51872}, {52568, 59995}, {53475, 69415}

X(70167) = midpoint of X(i) and X(j) for these {i,j}: {141, 3933}, {7882, 41413}
X(70167) = reflection of X(5305) in X(34573)
X(70167) = X(i)-isoconjugate of X(j) for these (i,j): {82, 18898}, {3113, 46288}, {3407, 46289}, {55240, 58111}, {64981, 67149}
X(70167) = X(i)-Dao conjugate of X(j) for these (i,j): {39, 3407}, {141, 18898}, {6665, 14617}, {10335, 83}, {19602, 251}, {52658, 46288}, {61063, 64981}
X(70167) = barycentric product X(i)*X(j) for these {i,j}: {38, 56784}, {141, 3314}, {1930, 51836}, {3094, 8024}, {3117, 52568}, {3933, 5117}, {7794, 62699}, {9865, 56977}, {59995, 62696}
X(70167) = barycentric quotient X(i)/X(j) for these {i,j}: {39, 18898}, {141, 3407}, {732, 64981}, {1634, 58111}, {1930, 3113}, {3094, 251}, {3116, 46289}, {3117, 46288}, {3314, 83}, {3917, 43722}, {4576, 33514}, {5117, 32085}, {7794, 14617}, {8024, 3114}, {9865, 56976}, {50549, 18105}, {51371, 8840}, {51836, 82}, {56784, 3112}, {62696, 59996}, {62699, 52395}
X(70167) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 7836, 1691}, {3314, 9865, 51582}, {7794, 51371, 141}, {8024, 16893, 40379}

X(70168) = X(30)X(511)∩X(647)X(1194)

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

X(70168) lies on these lines: {30, 511}, {647, 1194}, {850, 2528}, {878, 46609}, {2394, 60614}, {2508, 52590}, {2525, 23301}, {2531, 57222}, {3268, 17414}, {4108, 14420}, {5996, 14424}, {6563, 50545}, {8267, 31296}, {9865, 17415}, {10189, 30476}, {10278, 31174}, {11123, 36900}, {12075, 59568}, {14223, 54731}, {23285, 30870}, {30474, 45689}, {33294, 50552}, {47128, 50554}, {58262, 65612}, {62663, 63786}

X(70168) = isogonal conjugate of X(58111)
X(70168) = isotomic conjugate of X(33514)
X(70168) = isotomic conjugate of the isogonal conjugate of X(50549)
X(70168) = crossdifference of every pair of points on line {6, 6660}
X(70168) = barycentric product X(37483)*X(40720)
X(70168) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2525, 47126, 23301}, {33294, 50552, 68787}

X(70169) = X(1)X(21)∩X(9)X(17210)

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

X(70169) lies on these lines: {1, 21}, {9, 17210}, {86, 17736}, {274, 1759}, {3219, 27274}, {3496, 62755}, {3509, 17175}, {3916, 16728}, {4426, 18167}, {5282, 16887}, {5291, 18189}, {7096, 16551}, {16574, 17381}, {17203, 30103}, {18157, 29473}, {33296, 69241}

X(70170) = X(1)X(513)∩X(106)X(269)

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

X(70170) lies on these lines: {1, 513}, {19, 1743}, {88, 36277}, {106, 269}, {165, 901}, {516, 2398}, {614, 43922}, {1168, 18421}, {1318, 53058}, {1320, 2801}, {1417, 5575}, {3257, 5223}, {3361, 16944}, {3752, 45140}, {4049, 67726}, {4312, 60578}, {4555, 53217}, {7987, 62703}, {7991, 29374}, {8056, 36042}, {9499, 66515}, {9819, 39148}, {10980, 40215}, {11531, 61768}, {16469, 51838}, {17220, 49683}, {28225, 47043}, {36887, 50836}, {39264, 69267}, {42753, 67518}, {43930, 61477}, {50865, 52753}, {60868, 64299}

X(70170) = X(i)-isoconjugate of X(j) for these (i,j): {2, 45144}, {44, 36101}, {103, 519}, {677, 900}, {902, 18025}, {911, 4358}, {1815, 8756}, {1960, 57928}, {2251, 57996}, {2338, 3911}, {2400, 23344}, {2424, 17780}, {3689, 43736}, {3762, 36039}, {4528, 24016}, {5440, 36122}, {9503, 14439}, {14427, 65245}, {22356, 52781}, {32642, 65867}, {32657, 46109}, {36056, 38462}, {51406, 59195}, {53532, 65218}, {55257, 69839}, {61437, 68238}
X(70170) = X(i)-Dao conjugate of X(j) for these (i,j): {1566, 3762}, {9460, 57996}, {20622, 38462}, {23972, 4358}, {32664, 45144}, {40594, 18025}, {40595, 36101}, {46095, 5440}, {50441, 4723}
X(70170) = crosssum of X(3689) and X(14439)
X(70170) = crossdifference of every pair of points on line {44, 14427}
X(70170) = barycentric product X(i)*X(j) for these {i,j}: {1, 63851}, {88, 516}, {106, 30807}, {676, 3257}, {679, 51406}, {903, 910}, {1022, 2398}, {1320, 43035}, {1456, 4997}, {4674, 14953}, {9456, 35517}, {23345, 42719}, {26006, 36125}, {40869, 56049}, {57995, 69806}
X(70170) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 45144}, {88, 18025}, {106, 36101}, {516, 4358}, {676, 3762}, {903, 57996}, {910, 519}, {1022, 2400}, {1456, 3911}, {1886, 38462}, {2398, 24004}, {2426, 1023}, {3257, 57928}, {8752, 36122}, {9456, 103}, {14953, 30939}, {17747, 3992}, {30807, 3264}, {32659, 36056}, {32665, 677}, {32719, 36039}, {36058, 1815}, {36125, 52781}, {40869, 4723}, {41339, 2325}, {42077, 51406}, {43035, 69734}, {46392, 4528}, {51406, 4738}, {51436, 21805}, {53579, 4487}, {56049, 52156}, {63851, 75}, {65664, 1639}, {69806, 902}

X(70171) = X(1)X(905)∩X(63)X(100)

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

X(70171) lies on these lines: {1, 905}, {8, 67567}, {63, 100}, {78, 54232}, {144, 67632}, {900, 61437}, {1018, 56787}, {1023, 5440}, {1743, 36039}, {2717, 3062}, {2751, 40116}, {3403, 57996}, {3689, 23703}, {3911, 69463}, {3977, 17780}, {4597, 18025}, {4900, 43736}, {5218, 67468}, {8056, 23052}, {11714, 24010}, {15634, 67571}, {52213, 66469}, {57287, 59431}, {57928, 65955}, {65218, 65249}

X(70171) = X(53531)-cross conjugate of X(519)
X(70171) = X(i)-isoconjugate of X(j) for these (i,j): {6, 63851}, {88, 910}, {106, 516}, {676, 901}, {1318, 53529}, {1320, 1456}, {1797, 1886}, {2226, 51406}, {2316, 43035}, {2398, 23345}, {2426, 6548}, {4241, 66924}, {8752, 26006}, {9456, 30807}, {20568, 69806}, {34230, 56639}, {41339, 56049}
X(70171) = X(i)-Dao conjugate of X(j) for these (i,j): {9, 63851}, {214, 516}, {4370, 30807}, {38979, 676}, {62571, 35517}
X(70171) = cevapoint of X(3689) and X(14439)
X(70171) = trilinear pole of line {44, 14427}
vbarycentric product X(i)*X(j) for these {i,j}: {44, 18025}, {75, 45144}, {103, 4358}, {519, 36101}, {677, 3762}, {902, 57996}, {911, 3264}, {1023, 2400}, {1635, 57928}, {1815, 38462}, {2325, 43736}, {2338, 69734}, {2424, 24004}, {3689, 52156}, {3977, 36122}, {4528, 65245}, {5440, 52781}, {14427, 65294}, {15634, 69823}, {36039, 65867}, {36056, 46109}, {55243, 55257}
X(70171) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 63851}, {44, 516}, {103, 88}, {519, 30807}, {677, 3257}, {678, 51406}, {902, 910}, {911, 106}, {1023, 2398}, {1319, 43035}, {1404, 1456}, {1635, 676}, {2338, 1320}, {2424, 1022}, {3689, 40869}, {4358, 35517}, {5440, 26006}, {9459, 69806}, {14439, 50441}, {17780, 42719}, {18025, 20568}, {21805, 17747}, {32642, 32665}, {32657, 36058}, {36039, 901}, {36056, 1797}, {36101, 903}, {36122, 6336}, {45144, 1}, {51406, 24014}, {52680, 14953}, {53531, 39063}, {53532, 39470}, {55243, 55256}, {55257, 55244}, {57996, 57995}, {65218, 65336}

X(70172) = X(1)X(650)∩X(9)X(165)

Barycentrics   a*(a^5 - a^4*b - 4*a^3*b^2 + 8*a^2*b^3 - 5*a*b^4 + b^5 - a^4*c + 9*a^3*b*c - 8*a^2*b^2*c - 3*a*b^3*c + 3*b^4*c - 4*a^3*c^2 - 8*a^2*b*c^2 + 16*a*b^2*c^2 - 4*b^3*c^2 + 8*a^2*c^3 - 3*a*b*c^3 - 4*b^2*c^3 - 5*a*c^4 + 3*b*c^4 + c^5) : ::
X(70172) = 2 X[41798] + X[68401]

X(70172) lies on these lines: {1, 650}, {2, 67571}, {9, 165}, {100, 28345}, {200, 69717}, {1146, 11219}, {1566, 7988}, {1699, 33573}, {1768, 3119}, {2291, 51768}, {2801, 41798}, {4413, 67417}, {4521, 24410}, {5010, 46408}, {5218, 67462}, {5540, 60782}, {6174, 65808}, {6544, 68831}, {8545, 15727}, {9318, 10196}, {13609, 34789}, {43960, 64155}, {46917, 68768}, {61730, 67660}

X(70172) = incircle-inverse of X(65700)
X(70172) = Stevanovic-circle-inverse of X(1)

X(70173) = X(1)X(6)∩X(100)X(68401)

Barycentrics   a*(a^5 - 5*a^4*b + 8*a^3*b^2 - 4*a^2*b^3 - a*b^4 + b^5 - 5*a^4*c + 9*a^3*b*c - 8*a^2*b^2*c + 5*a*b^3*c - b^4*c + 8*a^3*c^2 - 8*a^2*b*c^2 - 4*a^2*c^3 + 5*a*b*c^3 - a*c^4 - b*c^4 + c^5) : ::
X(70173) = 4 X[1083] - 3 X[66515], 2 X[41391] - 3 X[68254], 2 X[18343] - 3 X[38052]

X(70173) lies on these lines: {1, 6}, {100, 68401}, {144, 67571}, {200, 69717}, {644, 2801}, {2717, 6078}, {2951, 3309}, {4513, 5696}, {5531, 35341}, {5732, 38502}, {11372, 14661}, {14151, 24036}, {15104, 38876}, {18343, 38052}, {28345, 57192}

X(70173) = reflection of X(i) in X(j) for these {i,j}: {5223, 67385}, {11372, 14661}

X(70174) = X(4)X(512)∩X(110)X(685)

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

X(70174) lies on these lines: {4, 512}, {98, 40118}, {110, 685}, {351, 468}, {523, 2967}, {690, 44146}, {804, 68695}, {924, 53174}, {2395, 68785}, {2501, 2970}, {2974, 65772}, {3267, 46236}, {7482, 62489}, {14295, 44132}, {16230, 44145}, {33919, 37778}, {46953, 53173}, {52038, 60428}, {52477, 58754}, {60199, 60226}

X(70174) = incircle-inverse of X(24515)
X(70174) = polar conjugate of the isogonal conjugate of X(52038)
X(70174) = X(i)-isoconjugate of X(j) for these (i,j): {895, 23997}, {897, 68647}, {923, 68648}, {1755, 65321}, {2421, 36060}, {3289, 36085}, {4575, 5968}, {4592, 51980}, {36142, 36212}
X(70174) = X(i)-Dao conjugate of X(j) for these (i,j): {136, 5968}, {1560, 2421}, {1649, 684}, {2482, 68648}, {5139, 51980}, {6593, 68647}, {21905, 39469}, {23992, 36212}, {36899, 65321}, {38988, 3289}, {48317, 511}, {62562, 895}, {62577, 6333}, {62594, 51386}
X(70174) = trilinear pole of line {14273, 21906}
X(70174) = crossdifference of every pair of points on line {3289, 68647}
X(70174) = barycentric product X(i)*X(j) for these {i,j}: {264, 52038}, {290, 14273}, {351, 60199}, {468, 43665}, {524, 68624}, {685, 52628}, {690, 16081}, {879, 37778}, {1648, 22456}, {2395, 44146}, {2501, 52145}, {3266, 53149}, {5967, 14618}, {6531, 35522}, {21906, 65272}, {33919, 41174}, {46786, 53156}, {50942, 52491}, {52076, 57496}, {52475, 60869}
X(70174) = barycentric quotient X(i)/X(j) for these {i,j}: {98, 65321}, {187, 68647}, {351, 3289}, {468, 2421}, {524, 68648}, {685, 66929}, {690, 36212}, {1648, 684}, {2395, 895}, {2422, 14908}, {2489, 51980}, {2501, 5968}, {2970, 62629}, {5967, 4558}, {6531, 691}, {8754, 8430}, {14273, 511}, {14417, 51386}, {16081, 892}, {21906, 39469}, {22456, 52940}, {33919, 41172}, {35522, 6393}, {36120, 36085}, {37778, 877}, {41174, 64460}, {43665, 30786}, {44102, 14966}, {44146, 2396}, {51441, 10097}, {52038, 3}, {52076, 57481}, {52145, 4563}, {52475, 35910}, {52476, 57493}, {52491, 50941}, {52628, 6333}, {53149, 111}, {53156, 46787}, {57260, 32729}, {58780, 9155}, {60179, 45773}, {60199, 53080}, {60428, 4230}, {68624, 671}

X(70175) = X(4)X(8)∩X(25)X(5695)

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

X(70175) lies on these lines: {4, 8}, {25, 5695}, {33, 42708}, {100, 40118}, {422, 4601}, {424, 2501}, {429, 4647}, {431, 3704}, {468, 3712}, {740, 44113}, {860, 4442}, {2355, 61408}, {3702, 40985}, {4037, 5089}, {4231, 64010}, {4365, 57652}, {6353, 42710}, {10603, 20336}, {20902, 69456}, {21839, 60428}, {26377, 50044}, {39579, 42031}, {60590, 69593}

X(70175) = polar conjugate of the isotomic conjugate of X(42713)
X(70175) = polar conjugate of the isogonal conjugate of X(21839)
X(70175) = X(21839)-cross conjugate of X(42713)
X(70175) = X(i)-isoconjugate of X(j) for these (i,j): {58, 895}, {81, 36060}, {86, 14908}, {111, 1790}, {283, 7316}, {649, 65321}, {691, 1459}, {897, 1437}, {905, 36142}, {923, 1444}, {1331, 43926}, {2206, 30786}, {4025, 32729}, {4556, 10097}, {4558, 66945}, {4575, 69473}, {17206, 32740}, {18604, 36128}, {22383, 36085}, {32661, 62626}
X(70175) = X(i)-Dao conjugate of X(j) for these (i,j): {10, 895}, {136, 69473}, {1560, 81}, {1649, 18210}, {2482, 1444}, {5375, 65321}, {5521, 43926}, {6593, 1437}, {23992, 905}, {38988, 22383}, {40586, 36060}, {40600, 14908}, {40603, 30786}, {48317, 513}, {55065, 69477}, {62594, 131}
X(70175) = crosssum of X(14908) and X(36060)
X(70175) = crossdifference of every pair of points on line {1437, 22383}
X(70175) = barycentric product X(i)*X(j) for these {i,j}: {4, 42713}, {37, 44146}, {72, 37778}, {92, 4062}, {264, 21839}, {321, 468}, {524, 41013}, {668, 14273}, {690, 6335}, {811, 69572}, {1783, 35522}, {1824, 3266}, {1826, 14210}, {2501, 42721}, {3712, 40149}, {4036, 4235}, {4086, 69464}, {5379, 52628}, {7140, 16741}, {7141, 16702}, {14432, 65207}, {20336, 60428}, {27801, 44102}, {42716, 52475}, {42724, 52477}, {56186, 64724}, {58078, 69600}, {68109, 68629}, {68565, 70107}
X(70175) = barycentric quotient X(i)/X(j) for these {i,j}: {37, 895}, {42, 36060}, {100, 65321}, {187, 1437}, {213, 14908}, {321, 30786}, {351, 22383}, {468, 81}, {524, 1444}, {690, 905}, {896, 1790}, {1648, 18210}, {1783, 691}, {1824, 111}, {1826, 897}, {1880, 7316}, {1897, 36085}, {2333, 923}, {2501, 69473}, {2642, 1459}, {3292, 18604}, {3712, 1812}, {4024, 69477}, {4036, 14977}, {4062, 63}, {4235, 52935}, {4705, 10097}, {4750, 69828}, {5095, 16702}, {5379, 66929}, {6335, 892}, {6591, 43926}, {8750, 36142}, {12828, 18609}, {14210, 17206}, {14273, 513}, {14417, 4131}, {14419, 7254}, {21839, 3}, {21874, 6091}, {24006, 62626}, {34336, 16741}, {35522, 15413}, {37778, 286}, {41013, 671}, {41586, 16697}, {42713, 69}, {42721, 4563}, {44102, 1333}, {44146, 274}, {58331, 23090}, {58780, 14419}, {60428, 28}, {64724, 16696}, {69464, 1414}, {69572, 656}

X(70176) = X(4)X(9)∩X(25)X(8013)

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

X(70176) lies on these lines: {4, 9}, {25, 8013}, {101, 40118}, {306, 10603}, {423, 4600}, {468, 4062}, {607, 21674}, {672, 60438}, {860, 68800}, {1973, 20653}, {2501, 4024}, {6353, 21085}, {16611, 68779}, {17442, 27714}, {18669, 47321}, {21046, 69610}, {21698, 31409}, {21718, 57654}, {37982, 69727}, {52068, 52477}, {52475, 69572}, {60590, 69592}

X(70176) = polar conjugate of the isotomic conjugate of X(4062)
X(70176) = X(i)-isoconjugate of X(j) for these (i,j): {81, 895}, {86, 36060}, {111, 1444}, {274, 14908}, {513, 65321}, {671, 1437}, {691, 905}, {892, 22383}, {897, 1790}, {923, 17206}, {1332, 43926}, {1333, 30786}, {1459, 36085}, {1812, 7316}, {4025, 36142}, {4556, 69477}, {4558, 69473}, {4575, 62626}, {4592, 66945}, {5380, 7254}, {10097, 52935}, {15398, 16702}, {15413, 32729}, {17983, 18604}, {18210, 66929}, {23224, 65350}
X(70176) = X(i)-Dao conjugate of X(j) for these (i,j): {37, 30786}, {136, 62626}, {468, 17172}, {1560, 86}, {1649, 4466}, {2482, 17206}, {5139, 66945}, {6593, 1790}, {23992, 4025}, {38988, 1459}, {39026, 65321}, {40586, 895}, {40600, 36060}, {48317, 514}, {55065, 14977}, {62594, 30805}
X(70176) = crosssum of X(895) and X(36060)
X(70176) = trilinear pole of line {14273, 69572}
X(70176) = crossdifference of every pair of points on line {1459, 1790}
X(70176) = barycentric product X(i)*X(j) for these {i,j}: {4, 4062}, {10, 468}, {19, 42713}, {42, 44146}, {71, 37778}, {92, 21839}, {190, 14273}, {225, 3712}, {306, 60428}, {313, 44102}, {430, 31013}, {524, 1826}, {648, 69572}, {690, 1897}, {896, 41013}, {1824, 14210}, {2333, 3266}, {2642, 6335}, {3700, 69464}, {4024, 4235}, {4028, 5203}, {6629, 7140}, {7181, 53008}, {8750, 35522}, {14432, 61178}, {17983, 52068}, {18082, 64724}, {21016, 52898}, {21017, 51823}, {52623, 61207}, {56601, 69610}, {68129, 68629}, {68565, 70094}
X(70176) = barycentric quotient X(i)/X(j) for these {i,j}: {10, 30786}, {42, 895}, {101, 65321}, {187, 1790}, {213, 36060}, {351, 1459}, {468, 86}, {524, 17206}, {690, 4025}, {896, 1444}, {922, 1437}, {1560, 17172}, {1648, 4466}, {1783, 36085}, {1824, 897}, {1826, 671}, {1897, 892}, {1918, 14908}, {2333, 111}, {2489, 66945}, {2501, 62626}, {2642, 905}, {3712, 332}, {4024, 14977}, {4062, 69}, {4079, 10097}, {4235, 4610}, {4705, 69477}, {4750, 15419}, {5095, 6629}, {8750, 691}, {14273, 514}, {14417, 30805}, {14419, 69828}, {14424, 69393}, {21016, 31125}, {21043, 51258}, {21839, 63}, {31013, 57854}, {33919, 21134}, {37778, 44129}, {41013, 46277}, {42713, 304}, {42721, 55202}, {44102, 58}, {44146, 310}, {52068, 6390}, {55206, 69476}, {57652, 7316}, {58331, 57081}, {58780, 4750}, {60428, 27}, {61207, 4556}, {64724, 16887}, {69464, 4573}, {69572, 525}, {69610, 36894}
X(70176) = {X(10),X(2333)}-harmonic conjugate of X(21016)

X(70177) = X(4)X(51)∩X(107)X(37777)

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

X(70177) lies on these lines: {4, 51}, {107, 37777}, {264, 10603}, {324, 1995}, {393, 14580}, {421, 32713}, {450, 3260}, {468, 37778}, {770, 2501}, {858, 6530}, {14569, 54381}, {15466, 16051}, {34334, 47309}, {41202, 44096}, {41586, 44146}, {41678, 47195}, {44131, 61506}, {56296, 67904}, {60828, 67237}

X(70177) = polar conjugate of the isotomic conjugate of X(37778)
X(70177) = polar conjugate of the isogonal conjugate of X(60428)
X(70177) = X(60428)-cross conjugate of X(37778)
X(70177) = X(i)-isoconjugate of X(j) for these (i,j): {111, 6507}, {255, 895}, {326, 14908}, {394, 36060}, {671, 4100}, {822, 65321}, {897, 1092}, {923, 3964}, {1102, 32740}, {23606, 46277}, {30786, 52430}, {32320, 36085}, {36142, 52613}, {37754, 66929}
X(70177) = X(i)-Dao conjugate of X(j) for these (i,j): {1560, 394}, {1649, 2972}, {2482, 3964}, {6523, 895}, {6593, 1092}, {15259, 14908}, {21905, 34980}, {23992, 52613}, {38988, 32320}, {48317, 520}
X(70177) = crossdifference of every pair of points on line {1092, 32320}
X(70177) = barycentric product X(i)*X(j) for these {i,j}: {4, 37778}, {264, 60428}, {393, 44146}, {468, 2052}, {524, 1093}, {690, 15352}, {896, 6521}, {3266, 6524}, {4235, 66299}, {5203, 21447}, {6520, 14210}, {6528, 14273}, {6529, 35522}, {8794, 41586}, {18027, 44102}, {32230, 52628}, {58071, 66126}
X(70177) = barycentric quotient X(i)/X(j) for these {i,j}: {107, 65321}, {187, 1092}, {351, 32320}, {393, 895}, {468, 394}, {524, 3964}, {690, 52613}, {896, 6507}, {922, 4100}, {1093, 671}, {1096, 36060}, {1648, 2972}, {2052, 30786}, {2207, 14908}, {3266, 4176}, {5140, 53782}, {5203, 60839}, {5523, 51253}, {6520, 897}, {6521, 46277}, {6524, 111}, {6529, 691}, {14210, 1102}, {14273, 520}, {14567, 23606}, {15352, 892}, {21906, 34980}, {32230, 66929}, {35522, 4143}, {36126, 36085}, {36434, 8753}, {37778, 69}, {44102, 577}, {44146, 3926}, {52439, 32740}, {52475, 62665}, {53156, 35911}, {58757, 10097}, {60428, 3}, {62524, 64258}, {66299, 14977}, {69464, 6517}

X(70178) = X(1)X(4)∩X(25)X(24725)

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

X(70178) lies on these lines: {1, 4}, {25, 24725}, {108, 59827}, {109, 40118}, {307, 10603}, {415, 4620}, {431, 2650}, {468, 896}, {661, 2501}, {860, 4892}, {3120, 44113}, {4231, 33097}, {5089, 69727}, {6353, 24695}, {7178, 47500}, {14210, 44146}, {32674, 36150}, {39793, 44092}

X(70178) = X(i)-isoconjugate of X(j) for these (i,j): {21, 895}, {111, 1812}, {283, 897}, {314, 14908}, {332, 923}, {333, 36060}, {521, 691}, {650, 65321}, {652, 36085}, {671, 2193}, {892, 1946}, {1444, 5547}, {1792, 7316}, {2194, 30786}, {4558, 69476}, {4571, 43926}, {4612, 10097}, {4636, 69477}, {5380, 23189}, {6332, 36142}, {6514, 36128}, {8753, 68650}, {17983, 68649}, {32729, 35518}, {36054, 65350}, {53560, 66929}
X(70178) = X(i)-Dao conjugate of X(j) for these (i,j): {1214, 30786}, {1560, 333}, {2482, 332}, {6593, 283}, {23992, 6332}, {38988, 652}, {39053, 892}, {40611, 895}, {47345, 671}, {48317, 522}, {62594, 52616}
X(70178) = trilinear pole of line {2642, 14273}
X(70178) = crossdifference of every pair of points on line {283, 652}
X(70178) = barycentric product X(i)*X(j) for these {i,j}: {34, 42713}, {73, 37778}, {187, 57809}, {225, 524}, {226, 468}, {273, 21839}, {278, 4062}, {307, 60428}, {349, 44102}, {351, 46404}, {523, 69464}, {653, 690}, {664, 14273}, {896, 40149}, {922, 52575}, {1400, 44146}, {1826, 7181}, {1880, 14210}, {2642, 18026}, {3266, 57652}, {4235, 66287}, {4750, 61178}, {6629, 8736}, {14417, 36127}, {14419, 65207}, {14432, 52607}, {16702, 56285}, {18097, 64724}, {23889, 66297}, {32674, 35522}, {41013, 51653}, {42721, 55208}
X(70178) = barycentric quotient X(i)/X(j) for these {i,j}: {108, 36085}, {109, 65321}, {187, 283}, {225, 671}, {226, 30786}, {351, 652}, {468, 333}, {524, 332}, {653, 892}, {690, 6332}, {896, 1812}, {922, 2193}, {1400, 895}, {1402, 36060}, {1880, 897}, {2333, 5547}, {2642, 521}, {3292, 6514}, {4062, 345}, {7181, 17206}, {14273, 522}, {14417, 52616}, {14432, 15411}, {21839, 78}, {32674, 691}, {36127, 65350}, {37778, 44130}, {40149, 46277}, {42713, 3718}, {42721, 55207}, {44102, 284}, {44146, 28660}, {46404, 53080}, {51653, 1444}, {52038, 66881}, {52575, 57999}, {52938, 59762}, {55208, 69473}, {57185, 69477}, {57652, 111}, {57809, 18023}, {58780, 14432}, {60428, 29}, {61207, 4636}, {66287, 14977}, {66928, 10097}, {69464, 99}, {69572, 52355}

X(70179) = X(4)X(94)∩X(25)X(476)

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

X(70179) lies on these lines: {4, 94}, {25, 476}, {53, 2501}, {235, 39170}, {264, 18020}, {328, 10603}, {381, 10688}, {403, 68471}, {427, 14356}, {428, 14583}, {468, 9176}, {1596, 34209}, {1597, 56400}, {1885, 51254}, {1906, 68474}, {1989, 44467}, {2052, 54554}, {3426, 43707}, {3518, 58926}, {3575, 58725}, {5627, 62966}, {6403, 65317}, {7576, 38896}, {10301, 43087}, {14592, 57586}, {18533, 52056}, {35139, 58782}, {35235, 46106}, {44080, 56397}, {47179, 68431}, {51479, 52475}, {51847, 54381}, {56395, 60428}

X(70179) = polar conjugate of the isotomic conjugate of X(43084)
X(70179) = polar conjugate of the isogonal conjugate of X(56395)
X(70179) = X(i)-cross conjugate of X(j) for these (i,j): {12828, 468}, {56395, 43084}
X(70179) = X(i)-isoconjugate of X(j) for these (i,j): {63, 52668}, {323, 36060}, {656, 51478}, {895, 6149}, {897, 22115}, {923, 52437}, {2624, 65321}, {4575, 9213}, {8552, 36142}, {52603, 69477}
X(70179) = X(i)-Dao conjugate of X(j) for these (i,j): {136, 9213}, {1560, 323}, {1649, 16186}, {2482, 52437}, {3162, 52668}, {6593, 22115}, {14993, 895}, {15295, 14908}, {23992, 8552}, {40596, 51478}, {42426, 57470}, {48317, 526}
X(70179) = trilinear pole of line {14273, 51479}
X(70179) = barycentric product X(i)*X(j) for these {i,j}: {4, 43084}, {94, 468}, {187, 18817}, {264, 56395}, {265, 37778}, {328, 60428}, {524, 6344}, {648, 51479}, {690, 46456}, {1989, 44146}, {2052, 66125}, {3266, 18384}, {4235, 10412}, {12828, 40427}, {14273, 35139}, {14559, 14618}, {20573, 44102}, {41586, 65360}, {43089, 56601}, {52449, 57496}
X(70179) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 52668}, {94, 30786}, {112, 51478}, {187, 22115}, {468, 323}, {476, 65321}, {524, 52437}, {690, 8552}, {1648, 16186}, {1989, 895}, {2501, 9213}, {2682, 47414}, {4235, 10411}, {6103, 57470}, {6344, 671}, {8737, 66873}, {8738, 66872}, {10412, 14977}, {11060, 14908}, {12828, 34834}, {14273, 526}, {14559, 4558}, {15475, 10097}, {18384, 111}, {18817, 18023}, {35522, 45792}, {36129, 36085}, {37778, 340}, {43084, 69}, {43087, 51405}, {43089, 36894}, {44102, 50}, {44146, 7799}, {46456, 892}, {51479, 525}, {52039, 44719}, {52040, 44718}, {52449, 57481}, {56395, 3}, {58780, 44814}, {60428, 186}, {61207, 52603}, {66125, 394}
X(70179) = {X(58723),X(58733)}-harmonic conjugate of X(14254)

X(70180) = X(4)X(147)∩X(25)X(18020)

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

X(70180) lies on these lines: {4, 147}, {25, 18020}, {427, 2501}, {428, 14052}, {468, 11053}, {805, 40118}, {2211, 51511}, {5094, 65351}, {10603, 40708}, {10685, 22240}, {12294, 16068}, {18872, 60428}, {35908, 36897}, {40810, 60590}, {68023, 69780}

X(70180) = polar conjugate of X(60863)
X(70180) = polar conjugate of the isogonal conjugate of X(18872)
X(70180) = X(i)-isoconjugate of X(j) for these (i,j): {48, 60863}, {385, 36060}, {895, 1580}, {923, 12215}, {1933, 30786}, {1966, 14908}, {10097, 56982}, {24284, 36142}, {36128, 58354}, {56980, 69477}
X(70180) = X(i)-Dao conjugate of X(j) for these (i,j): {1249, 60863}, {1560, 385}, {2482, 12215}, {9467, 14908}, {23992, 24284}, {39092, 895}, {48317, 804}
X(70180) = trilinear pole of line {14273, 64724}
X(70180) = barycentric product X(i)*X(j) for these {i,j}: {264, 18872}, {468, 1916}, {524, 68575}, {690, 65351}, {694, 44146}, {3266, 17980}, {4235, 66267}, {14273, 18829}, {14970, 64724}, {18896, 44102}, {36214, 37778}, {40708, 60428}, {56981, 61207}
X(70180) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 60863}, {468, 385}, {524, 12215}, {690, 24284}, {694, 895}, {805, 65321}, {882, 10097}, {1916, 30786}, {1967, 36060}, {3292, 58354}, {4235, 17941}, {5095, 5026}, {9468, 14908}, {14273, 804}, {17980, 111}, {18872, 3}, {37778, 17984}, {44102, 1691}, {44146, 3978}, {58780, 11183}, {60428, 419}, {61207, 56980}, {64724, 732}, {65351, 892}, {66267, 14977}, {68575, 671}

X(70181) = X(2)X(61383)∩X(4)X(83)

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

X(70181) lies on these lines: {2, 61383}, {4, 83}, {24, 10548}, {25, 59180}, {186, 51862}, {232, 51906}, {251, 6353}, {297, 14052}, {403, 21458}, {419, 2501}, {420, 18020}, {451, 27067}, {468, 3793}, {631, 26224}, {827, 37943}, {1235, 52570}, {1799, 10603}, {3147, 28724}, {3431, 42299}, {3542, 10547}, {5203, 37855}, {5523, 34294}, {6622, 51508}, {8889, 39668}, {9076, 10423}, {10130, 52290}, {10788, 42288}, {11380, 37125}, {18533, 58852}, {22105, 52475}, {27005, 52252}, {37912, 41676}, {41370, 46288}, {42037, 62979}, {44089, 46511}, {44102, 44146}, {52580, 56921}

X(70181) = polar conjugate of X(31125)
X(70181) = polar conjugate of the isotomic conjugate of X(52898)
X(70181) = X(i)-isoconjugate of X(j) for these (i,j): {38, 895}, {48, 31125}, {63, 46154}, {141, 36060}, {304, 41272}, {656, 36827}, {671, 4020}, {897, 3917}, {923, 3933}, {1634, 69477}, {1930, 14908}, {1964, 30786}, {2525, 36142}, {8061, 65321}, {20775, 46277}, {57999, 68651}
X(70181) = X(i)-Dao conjugate of X(j) for these (i,j): {1249, 31125}, {1560, 141}, {2482, 3933}, {3162, 46154}, {6593, 3917}, {23992, 2525}, {40596, 36827}, {41884, 30786}, {48317, 826}
X(70181) = cevapoint of X(468) and X(44102)
X(70181) = trilinear pole of line {14273, 22105}
X(70181) = barycentric product X(i)*X(j) for these {i,j}: {4, 52898}, {83, 468}, {187, 46104}, {251, 44146}, {308, 44102}, {524, 32085}, {648, 22105}, {690, 42396}, {1176, 37778}, {1799, 60428}, {4235, 58784}, {4577, 14273}, {14567, 68630}, {21458, 56601}, {21459, 65712}, {32581, 51541}, {52395, 64724}, {52618, 61207}
X(70181) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 31125}, {25, 46154}, {83, 30786}, {112, 36827}, {187, 3917}, {251, 895}, {468, 141}, {524, 3933}, {690, 2525}, {827, 65321}, {922, 4020}, {1974, 41272}, {4235, 4576}, {4750, 69393}, {5095, 7813}, {7813, 4175}, {14273, 826}, {14567, 20775}, {18105, 10097}, {21458, 36894}, {21459, 59422}, {22105, 525}, {32085, 671}, {32581, 42008}, {33632, 6091}, {34294, 51258}, {37778, 1235}, {42396, 892}, {44102, 39}, {44146, 8024}, {46104, 18023}, {46288, 14908}, {46289, 36060}, {51823, 46165}, {52898, 69}, {55240, 69477}, {56601, 64974}, {58780, 14424}, {58784, 14977}, {60428, 427}, {61207, 1634}, {61383, 32740}, {64724, 7794}
X(70181) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {83, 32085, 32581}, {32085, 32581, 4}, {37912, 44090, 41676}

X(70182) = X(4)X(52)∩X(23)X(925)

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

X(70182) lies on these lines: {4, 52}, {23, 925}, {421, 18020}, {686, 2501}, {2165, 3291}, {7493, 39116}, {7530, 46200}, {10603, 20563}, {37981, 60590}, {45171, 54061}, {52582, 54778}

X(70182) = X(i)-cross conjugate of X(j) for these (i,j): {187, 37778}, {41586, 468}
X(70182) = X(i)-isoconjugate of X(j) for these (i,j): {47, 895}, {563, 671}, {691, 63832}, {897, 1147}, {923, 9723}, {1993, 36060}, {14908, 44179}, {30451, 36085}, {36142, 52584}, {46277, 52435}, {55216, 65321}
X(70182) = X(i)-Dao conjugate of X(j) for these (i,j): {1560, 1993}, {2482, 9723}, {6593, 1147}, {23992, 52584}, {34853, 895}, {37864, 14908}, {38988, 30451}, {48317, 924}
X(70182) = crossdifference of every pair of points on line {1147, 30451}
X(70182) = barycentric product X(i)*X(j) for these {i,j}: {68, 37778}, {187, 55553}, {468, 5392}, {524, 847}, {690, 30450}, {896, 57716}, {922, 57898}, {2165, 44146}, {3266, 14593}, {5962, 43084}, {14273, 46134}, {20563, 60428}, {35522, 65176}, {44102, 57904}
X(70182) = barycentric quotient X(i)/X(j) for these {i,j}: {187, 1147}, {351, 30451}, {468, 1993}, {524, 9723}, {690, 52584}, {847, 671}, {922, 563}, {925, 65321}, {2165, 895}, {2642, 63832}, {5392, 30786}, {5967, 51776}, {14273, 924}, {14567, 52435}, {14593, 111}, {27367, 41272}, {30450, 892}, {37778, 317}, {41586, 52032}, {44102, 571}, {44146, 7763}, {55250, 69477}, {55553, 18023}, {56395, 5961}, {56891, 6091}, {57716, 46277}, {57898, 57999}, {60428, 24}, {60501, 14908}, {65176, 691}

X(70183) = X(4)X(54)∩X(23)X(19189)

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

X(70183) lies on these lines: {4, 54}, {23, 19189}, {95, 10603}, {97, 7493}, {421, 2501}, {468, 23200}, {933, 40118}, {3091, 63668}, {3292, 44146}, {5169, 23295}, {7527, 19172}, {7530, 19173}, {7556, 19185}, {8794, 61379}, {8795, 43697}, {8901, 37981}, {11061, 32258}, {14567, 60428}, {18020, 41203}, {19180, 34117}, {23286, 47249}, {44893, 51458}, {52300, 59183}

X(70183) = X(i)-isoconjugate of X(j) for these (i,j): {343, 36060}, {418, 46277}, {895, 44706}, {897, 5562}, {923, 52347}, {14908, 18695}, {17434, 36085}, {23181, 69477}, {30786, 62266}, {36142, 60597}, {44088, 57999}
X(70183) = X(i)-Dao conjugate of X(j) for these (i,j): {1560, 343}, {1649, 35442}, {2482, 52347}, {6593, 5562}, {23992, 60597}, {38988, 17434}, {48317, 6368}
X(70183) = cevapoint of X(44102) and X(60428)
X(70183) = crossdifference of every pair of points on line {5562, 17434}
X(70183) = barycentric product X(i)*X(j) for these {i,j}: {54, 37778}, {95, 60428}, {187, 8795}, {275, 468}, {276, 44102}, {351, 42405}, {524, 8884}, {690, 16813}, {3266, 61362}, {3292, 8794}, {4235, 66300}, {5468, 15422}, {8882, 44146}, {14273, 18831}, {14567, 57844}, {19174, 52898}
X(70183) = barycentric quotient X(i)/X(j) for these {i,j}: {187, 5562}, {275, 30786}, {351, 17434}, {468, 343}, {524, 52347}, {690, 60597}, {933, 65321}, {1648, 35442}, {8794, 46111}, {8795, 18023}, {8882, 895}, {8884, 671}, {14273, 6368}, {14567, 418}, {15422, 5466}, {16813, 892}, {19174, 31125}, {37778, 311}, {42405, 53080}, {44102, 216}, {44146, 28706}, {52779, 59762}, {58756, 10097}, {60428, 5}, {61207, 23181}, {61362, 111}, {62268, 36060}, {62271, 14908}, {66300, 14977}
X(70183) = {X(275),X(61362)}-harmonic conjugate of X(19174)

X(70184) = X(4)X(67)∩X(24)X(935)

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

X(70184) lies on the cubic K620 and these lines: {4, 67}, {5, 60590}, {24, 935}, {76, 18020}, {107, 36833}, {235, 67086}, {468, 14357}, {1995, 57476}, {2493, 60507}, {2501, 23105}, {3767, 8791}, {8262, 44146}, {10512, 18027}, {10603, 18019}, {37458, 46338}, {54412, 65269}, {58087, 67809}, {59422, 60502}

X(70184) = polar conjugate of X(57481)
X(70184) = polar conjugate of the isotomic conjugate of X(57496)
X(70184) = X(i)-isoconjugate of X(j) for these (i,j): {48, 57481}, {255, 14246}, {326, 52142}, {897, 58357}, {923, 68654}, {22151, 36060}, {52430, 52551}
X(70184) = X(i)-Dao conjugate of X(j) for these (i,j): {1249, 57481}, {1560, 22151}, {2482, 68654}, {6523, 14246}, {6593, 58357}, {14357, 51253}, {15259, 52142}, {48317, 9517}, {65725, 394}
X(70184) = barycentric product X(i)*X(j) for these {i,j}: {4, 57496}, {67, 37778}, {468, 46105}, {524, 68634}, {690, 65356}, {2052, 14357}, {4235, 66943}, {8791, 44146}, {14273, 65269}, {14618, 60503}, {18019, 60428}, {18027, 59175}, {39269, 51823}, {52628, 66950}
X(70184) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 57481}, {187, 58357}, {393, 14246}, {468, 22151}, {524, 68654}, {935, 65321}, {2052, 52551}, {2207, 52142}, {8791, 895}, {14273, 9517}, {14357, 394}, {37778, 316}, {44102, 10317}, {44146, 37804}, {46105, 30786}, {57496, 69}, {58757, 10561}, {59175, 577}, {60428, 23}, {60503, 4558}, {65356, 892}, {65725, 51253}, {66943, 14977}, {66950, 66929}, {68634, 671}
X(70184) = {X(4),X(46105)}-harmonic conjugate of X(39269)

X(70185) = X(6)X(1344)∩X(32)X(23109)

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

X(70185) lies on these lines: {6, 1344}, {32, 23109}, {249, 8115}, {512, 44126}, {598, 2592}, {690, 5095}, {843, 1114}, {1992, 50945}, {3569, 66357}, {6787, 8427}, {15165, 35146}, {16070, 41518}, {32741, 44124}, {39240, 66298}

X(70185) = reflection of X(66876) in X(6)
X(70185) = X(i)-isoconjugate of X(j) for these (i,j): {671, 1822}, {691, 2583}, {892, 2579}, {895, 2580}, {897, 8115}, {923, 46813}, {2575, 36085}, {2576, 30786}, {2585, 65350}, {2589, 65321}, {15164, 36060}, {22340, 36142}, {36128, 68658}, {39298, 69477}, {46277, 57026}
X(70185) = X(i)-Dao conjugate of X(j) for these (i,j): {1313, 671}, {1560, 15164}, {2482, 46813}, {6593, 8115}, {15166, 30786}, {21905, 66876}, {23992, 22340}, {38988, 2575}, {48317, 2593}
X(70185) = crosssum of X(35607) and X(35608)
X(70185) = crossdifference of every pair of points on line {895, 2105}
X(70185) = X(249)-line conjugate of X(8115)
X(70185) = barycentric product X(i)*X(j) for these {i,j}: {187, 2592}, {351, 15165}, {468, 2574}, {524, 8105}, {690, 1114}, {896, 2588}, {1648, 39299}, {2581, 2642}, {3292, 68636}, {4235, 66877}, {5467, 39240}, {8116, 14273}, {22105, 46167}, {22339, 44102}, {35522, 44124}, {42668, 44146}, {44068, 51479}, {46814, 60428}
X(70185) = barycentric quotient X(i)/X(j) for these {i,j}: {187, 8115}, {351, 2575}, {468, 15164}, {524, 46813}, {690, 22340}, {922, 1822}, {1114, 892}, {2574, 30786}, {2577, 36085}, {2588, 46277}, {2592, 18023}, {2642, 2583}, {3292, 68658}, {8105, 671}, {14273, 2593}, {14567, 57026}, {15165, 53080}, {21906, 66876}, {23200, 68657}, {39240, 52632}, {39299, 52940}, {42668, 895}, {44102, 1113}, {44124, 691}, {46812, 59762}, {57025, 65321}, {60428, 46815}, {61207, 39298}, {66877, 14977}, {68636, 46111}

X(70186) = X(6)X(1345)∩X(32)X(23110)

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

X(70186) lies on these lines: {6, 1345}, {32, 23110}, {249, 8116}, {512, 44125}, {598, 2593}, {690, 5095}, {843, 1113}, {1992, 50944}, {3569, 66358}, {6787, 8426}, {15164, 35146}, {16071, 41519}, {32741, 44123}, {39241, 66298}

X(70186) = reflection of X(66877) in X(6)
X(70186) = X(i)-isoconjugate of X(j) for these (i,j): {671, 1823}, {691, 2582}, {892, 2578}, {895, 2581}, {897, 8116}, {923, 46810}, {2574, 36085}, {2577, 30786}, {2584, 65350}, {2588, 65321}, {15165, 36060}, {22339, 36142}, {36128, 68656}, {39299, 69477}, {46277, 57025}
X(70186) = X(i)-Dao conjugate of X(j) for these (i,j): {1312, 671}, {1560, 15165}, {2482, 46810}, {6593, 8116}, {15167, 30786}, {21905, 66877}, {23992, 22339}, {38988, 2574}, {48317, 2592}
X(70186) = crosssum of X(14899) and X(35609)
X(70186) = crossdifference of every pair of points on line {895, 2104}
X(70186) = X(249)-line conjugate of X(8116)
X(70186) = barycentric product X(i)*X(j) for these {i,j}: {187, 2593}, {351, 15164}, {468, 2575}, {524, 8106}, {690, 1113}, {896, 2589}, {1648, 39298}, {2580, 2642}, {3292, 68635}, {4235, 66876}, {5467, 39241}, {8115, 14273}, {22105, 46166}, {22340, 44102}, {35522, 44123}, {42667, 44146}, {44067, 51479}, {46811, 60428}
X(70186) = barycentric quotient X(i)/X(j) for these {i,j}: {187, 8116}, {351, 2574}, {468, 15165}, {524, 46810}, {690, 22339}, {922, 1823}, {1113, 892}, {2575, 30786}, {2576, 36085}, {2589, 46277}, {2593, 18023}, {2642, 2582}, {3292, 68656}, {8106, 671}, {14273, 2592}, {14567, 57025}, {15164, 53080}, {21906, 66877}, {23200, 68655}, {39241, 52632}, {39298, 52940}, {42667, 895}, {44102, 1114}, {44123, 691}, {46815, 59762}, {57026, 65321}, {60428, 46812}, {61207, 39299}, {66876, 14977}, {68635, 46111}

X(70187) = X(4)X(525)∩X(125)X(2501)

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

X(70187) lies on these lines: {4, 525}, {114, 60590}, {125, 2501}, {468, 14417}, {690, 60428}, {1297, 36166}, {2409, 66084}, {2419, 10603}, {3154, 65759}, {4563, 18020}, {5099, 52475}, {9209, 34212}, {14120, 69782}, {32649, 46619}, {32687, 35907}, {44146, 45807}, {51937, 56967}

X(70187) = X(51429)-cross conjugate of X(468)
X(70187) = X(i)-isoconjugate of X(j) for these (i,j): {163, 36894}, {441, 36142}, {691, 8766}, {2312, 65321}, {8779, 36085}, {34211, 36060}
X(70187) = X(i)-Dao conjugate of X(j) for these (i,j): {115, 36894}, {1560, 34211}, {1649, 68791}, {23992, 441}, {38988, 8779}, {48317, 1503}
X(70187) = barycentric product X(i)*X(j) for these {i,j}: {468, 43673}, {523, 56601}, {524, 68640}, {690, 6330}, {2419, 60428}, {2435, 37778}, {14273, 35140}, {34212, 44146}, {35522, 43717}, {44770, 52628}, {47105, 50942}, {52485, 66126}
X(70187) = barycentric quotient X(i)/X(j) for these {i,j}: {351, 8779}, {468, 34211}, {523, 36894}, {690, 441}, {1297, 65321}, {1648, 68791}, {2642, 8766}, {6330, 892}, {8767, 36085}, {14273, 1503}, {34212, 895}, {43673, 30786}, {43717, 691}, {44770, 66929}, {47105, 50941}, {52038, 34156}, {52475, 63856}, {56601, 99}, {58780, 35282}, {60428, 2409}, {68640, 671}

X(70188) = X(4)X(64)∩X(25)X(62545)

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

X(70188) lies on these lines: {4, 64}, {25, 62545}, {253, 10603}, {1301, 40118}, {2501, 65478}, {5159, 60590}, {13157, 44212}, {14572, 30769}, {15384, 18020}, {40126, 41489}

X(70188) = X(i)-isoconjugate of X(j) for these (i,j): {897, 35602}, {20580, 36142}, {36060, 37669}, {36085, 58796}
X(70188) = X(i)-Dao conjugate of X(j) for these (i,j): {1560, 37669}, {1649, 122}, {6593, 35602}, {23992, 20580}, {38988, 58796}, {40839, 30786}, {48317, 8057}
X(70188) = crossdifference of every pair of points on line {35602, 58796}
X(70188) = barycentric product X(i)*X(j) for these {i,j}: {64, 37778}, {253, 60428}, {459, 468}, {524, 6526}, {690, 65181}, {1648, 44181}, {3266, 61349}, {14273, 53639}, {15384, 52628}, {33919, 55268}, {41489, 44146}, {44102, 52581}
X(70188) = barycentric quotient X(i)/X(j) for these {i,j}: {187, 35602}, {351, 58796}, {459, 30786}, {468, 37669}, {690, 20580}, {1301, 65321}, {1648, 122}, {6526, 671}, {14273, 8057}, {15384, 66929}, {33919, 55269}, {37778, 14615}, {41489, 895}, {44102, 15905}, {44181, 52940}, {55268, 64460}, {60428, 20}, {61349, 111}, {65181, 892}

X(70189) = X(4)X(74)∩X(25)X(12079)

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

X(70189) lies on these lines: {2, 35908}, {4, 74}, {24, 56686}, {25, 12079}, {69, 18020}, {393, 2433}, {403, 52488}, {468, 9717}, {868, 47147}, {1304, 6353}, {1494, 10603}, {1552, 6623}, {1637, 66168}, {1648, 60428}, {2052, 54495}, {2394, 36191}, {2409, 11657}, {3089, 52646}, {3147, 14385}, {3542, 14264}, {3580, 4240}, {4232, 17986}, {7417, 65980}, {7735, 8749}, {14052, 68701}, {14380, 47252}, {18533, 34150}, {26255, 46808}, {32225, 36890}, {38282, 57487}, {47152, 62551}, {52493, 62961}, {56601, 62594}

X(70189) = X(2682)-cross conjugate of X(14273)
X(70189) = X(i)-isoconjugate of X(j) for these (i,j): {255, 9214}, {897, 51394}, {1636, 36085}, {2631, 65321}, {4575, 66124}, {11064, 36060}, {36142, 41077}
X(70189) = X(i)-Dao conjugate of X(j) for these (i,j): {136, 66124}, {1560, 11064}, {1649, 1650}, {6523, 9214}, {6593, 51394}, {23992, 41077}, {38988, 1636}, {48317, 9033}
X(70189) = cevapoint of X(i) and X(j) for these (i,j): {468, 12828}, {2682, 14273}
X(70189) = trilinear pole of line {14273, 52475}
X(70189) = crossdifference of every pair of points on line {1636, 51394}
X(70189) = barycentric product X(i)*X(j) for these {i,j}: {74, 37778}, {107, 66126}, {393, 36890}, {468, 16080}, {524, 68642}, {648, 52475}, {690, 15459}, {1494, 60428}, {1648, 42308}, {2052, 9717}, {2682, 57570}, {4235, 18808}, {8749, 44146}, {14273, 16077}, {32695, 35522}
X(70189) = barycentric quotient X(i)/X(j) for these {i,j}: {187, 51394}, {351, 1636}, {393, 9214}, {468, 11064}, {690, 41077}, {1304, 65321}, {1648, 1650}, {2501, 66124}, {2682, 39008}, {8749, 895}, {9717, 394}, {12828, 62569}, {14273, 9033}, {15459, 892}, {16080, 30786}, {17986, 51405}, {18808, 14977}, {32695, 691}, {36890, 3926}, {37778, 3260}, {40354, 14908}, {42308, 52940}, {44102, 3284}, {51479, 18557}, {52475, 525}, {52476, 65758}, {56395, 51254}, {60428, 30}, {60499, 51253}, {66126, 3265}, {68642, 671}
X(70189) = {X(6353),X(36875)}-harmonic conjugate of X(1304)

X(70190) = X(4)X(3414)∩X(468)X(52723)

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

X(70190) lies on these lines: {4, 3414}, {468, 52723}, {690, 5095}, {1379, 40118}, {2501, 13722}, {4232, 30508}, {4235, 66626}, {5094, 13636}, {18020, 57013}, {46463, 52475}

X(70190) = polar conjugate of the isotomic conjugate of X(52723)
X(70190) = X(6189)-isoconjugate of X(36060)
X(70190) = X(i)-Dao conjugate of X(j) for these (i,j): {1560, 6189}, {13636, 14977}, {39022, 30786}, {39067, 895}, {48317, 3413}
X(70190) = trilinear pole of line {14273, 46463}
X(70190) = barycentric product X(i)*X(j) for these {i,j}: {4, 52723}, {468, 3414}, {524, 68643}, {648, 46463}, {690, 57014}, {2501, 66625}, {4235, 13722}, {5639, 44146}, {6190, 14273}, {52475, 67691}
X(70190) = barycentric quotient X(i)/X(j) for these {i,j}: {468, 6189}, {1379, 65321}, {3414, 30786}, {5095, 66626}, {5639, 895}, {13722, 14977}, {14273, 3413}, {44102, 1380}, {46463, 525}, {52723, 69}, {57014, 892}, {58780, 52722}, {60428, 57013}, {66187, 51258}, {66625, 4563}, {66884, 10097}, {68643, 671}

X(70191) = X(4)X(3413)∩X(468)X(52722)

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

X(70191) lies on these lines: {4, 3413}, {468, 52722}, {690, 5095}, {1380, 40118}, {2501, 13636}, {4232, 30509}, {4235, 66625}, {5094, 13722}, {18020, 57014}, {46462, 52475}

X(70191) = polar conjugate of the isotomic conjugate of X(52722)
X(70191) = X(6190)-isoconjugate of X(36060)
X(70191) = X(i)-Dao conjugate of X(j) for these (i,j): {1560, 6190}, {13722, 14977}, {39023, 30786}, {39068, 895}, {48317, 3414}
X(70191) = trilinear pole of line {14273, 46462}
X(70191) = barycentric product X(i)*X(j) for these {i,j}: {4, 52722}, {468, 3413}, {524, 68644}, {648, 46462}, {690, 57013}, {2501, 66626}, {4235, 13636}, {5638, 44146}, {6189, 14273}, {52475, 67680}
X(70191) = barycentric quotient X(i)/X(j) for these {i,j}: {468, 6190}, {1380, 65321}, {3413, 30786}, {5095, 66625}, {5638, 895}, {13636, 14977}, {14273, 3414}, {44102, 1379}, {46462, 525}, {52722, 69}, {57013, 892}, {58780, 52723}, {60428, 57014}, {66186, 51258}, {66626, 4563}, {66885, 10097}, {68644, 671}

X(70192) = X(4)X(850)∩X(338)X(2501)

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

X(70192) lies on these lines: {4, 850}, {338, 2501}, {468, 35522}, {647, 60040}, {670, 18020}, {2373, 40118}, {3265, 34336}, {10561, 14618}, {57496, 65612}, {60428, 65611}

X(70192) = polar conjugate of the isogonal conjugate of X(65611)
X(70192) = X(65268)-Ceva conjugate of X(44146)
X(70192) = X(i)-cross conjugate of X(j) for these (i,j): {125, 57496}, {690, 60040}, {5099, 37778}
X(70192) = X(i)-isoconjugate of X(j) for these (i,j): {662, 34158}, {4575, 57485}, {4592, 51962}, {14961, 36142}, {32676, 51253}, {36060, 61198}
X(70192) = X(i)-Dao conjugate of X(j) for these (i,j): {136, 57485}, {1084, 34158}, {1560, 61198}, {1649, 42665}, {5139, 51962}, {15526, 51253}, {23992, 14961}, {48317, 2393}
X(70192) = trilinear pole of line {14273, 52628}
X(70192) = barycentric product X(i)*X(j) for these {i,j}: {264, 65611}, {523, 58078}, {850, 51823}, {14273, 46140}, {14618, 65712}, {35522, 60133}, {44146, 60040}, {52628, 65268}, {53784, 66299}
X(70192) = barycentric quotient X(i)/X(j) for these {i,j}: {468, 61198}, {512, 34158}, {525, 51253}, {690, 14961}, {1648, 42665}, {2373, 65321}, {2489, 51962}, {2501, 57485}, {2970, 65609}, {14273, 2393}, {14618, 59422}, {35522, 62382}, {37778, 61181}, {51823, 110}, {52475, 60499}, {58078, 99}, {58757, 64619}, {58780, 47426}, {60040, 895}, {60133, 691}, {60428, 46592}, {65268, 66929}, {65611, 3}, {65712, 4558}

X(70193) = X(2)X(18020)∩X(4)X(32)

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

X(70193) lies on these lines: {2, 18020}, {4, 32}, {6, 35912}, {25, 669}, {69, 67008}, {111, 53155}, {183, 50437}, {187, 4235}, {193, 17932}, {230, 54380}, {232, 65764}, {287, 10603}, {385, 877}, {393, 20031}, {427, 14052}, {468, 1648}, {685, 4232}, {879, 47502}, {1383, 16081}, {1560, 66128}, {1843, 15630}, {1976, 44080}, {2715, 36472}, {2966, 40890}, {2967, 12829}, {3053, 53783}, {3552, 56362}, {5970, 22456}, {6353, 40820}, {6388, 60506}, {6394, 32985}, {6403, 13137}, {6792, 34761}, {7473, 35606}, {10418, 65776}, {10986, 52491}, {14273, 53156}, {14602, 44893}, {27369, 32540}, {40825, 41175}, {41936, 52301}, {51404, 51963}, {52038, 52475}, {53173, 65612}, {60184, 60199}

X(70193) = polar conjugate of the isotomic conjugate of X(5967)
X(70193) = X(i)-isoconjugate of X(j) for these (i,j): {63, 5968}, {304, 51980}, {325, 36060}, {684, 36085}, {895, 1959}, {897, 36212}, {923, 6393}, {1755, 30786}, {2421, 69477}, {3289, 46277}, {4575, 62629}, {4592, 8430}, {6333, 36142}, {14908, 46238}, {14977, 23997}, {23894, 68648}, {36128, 51386}
X(70193) = X(i)-Dao conjugate of X(j) for these (i,j): {136, 62629}, {1560, 325}, {2482, 6393}, {3162, 5968}, {5139, 8430}, {6593, 36212}, {21905, 41172}, {23992, 6333}, {36899, 30786}, {38988, 684}, {48317, 2799}, {62562, 14977}
X(70193) = cevapoint of X(187) and X(5477)
X(70193) = trilinear pole of line {14273, 33919}
X(70193) = crossdifference of every pair of points on line {684, 36212}
X(70193) = barycentric product X(i)*X(j) for these {i,j}: {4, 5967}, {25, 52145}, {98, 468}, {187, 16081}, {248, 37778}, {287, 60428}, {290, 44102}, {351, 22456}, {524, 6531}, {648, 52038}, {685, 690}, {896, 36120}, {1648, 60179}, {1976, 44146}, {2395, 4235}, {2966, 14273}, {3266, 57260}, {5095, 9154}, {5467, 68624}, {5468, 53149}, {14417, 20031}, {14567, 60199}, {21906, 41174}, {32696, 35522}, {34761, 53156}, {43665, 61207}, {51823, 52672}, {51963, 56601}, {52076, 60503}, {52475, 65776}
X(70193) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 5968}, {98, 30786}, {187, 36212}, {351, 684}, {468, 325}, {524, 6393}, {685, 892}, {690, 6333}, {1974, 51980}, {1976, 895}, {2395, 14977}, {2422, 10097}, {2489, 8430}, {2501, 62629}, {2715, 65321}, {3292, 51386}, {4235, 2396}, {5095, 50567}, {5467, 68648}, {5477, 62590}, {5967, 69}, {6531, 671}, {14273, 2799}, {14567, 3289}, {14601, 14908}, {15471, 51438}, {16081, 18023}, {20031, 65350}, {21906, 41172}, {22456, 53080}, {32696, 691}, {34369, 51405}, {36104, 36085}, {36120, 46277}, {37778, 44132}, {44102, 511}, {44146, 69963}, {51441, 51258}, {51963, 36894}, {52038, 525}, {52145, 305}, {52475, 65973}, {53149, 5466}, {53156, 34765}, {57260, 111}, {60179, 52940}, {60428, 297}, {61207, 2421}, {64724, 51371}, {68624, 52632}
X(70193) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2715, 52451, 65726}, {41200, 41201, 35906}

X(70194) = X(4)X(14)∩X(463)X(2501)

Barycentrics   (2*a^2 - b^2 - c^2)*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^4 + a^2*b^2 - 2*b^4 + a^2*c^2 + 4*b^2*c^2 - 2*c^4 - 2*Sqrt[3]*a^2*S)::

X(70194) lies on these lines: {4, 14}, {25, 8015}, {463, 2501}, {468, 52040}, {470, 18020}, {1843, 54473}, {4232, 21467}, {5994, 40118}, {6756, 11556}, {10603, 40710}, {10642, 46343}, {30455, 52477}, {44102, 56395}, {57585, 60590}

X(70194) = polar conjugate of the isotomic conjugate of X(52040)
X(70194) = X(i)-isoconjugate of X(j) for these (i,j): {63, 66873}, {299, 36060}, {895, 65570}, {897, 44719}, {2152, 30786}, {17403, 69477}, {36085, 60009}, {46113, 46277}
X(70194) = X(i)-Dao conjugate of X(j) for these (i,j): {1560, 299}, {3162, 66873}, {6593, 44719}, {38988, 60009}, {40579, 30786}, {48317, 23871}
X(70194) = crossdifference of every pair of points on line {44719, 60009}
X(70194) = barycentric product X(i)*X(j) for these {i,j}: {4, 52040}, {14, 468}, {301, 44102}, {470, 56395}, {524, 8738}, {690, 36309}, {3458, 44146}, {4235, 20579}, {5095, 36310}, {8739, 43084}, {14273, 23896}, {17983, 30455}, {36297, 37778}, {40710, 60428}
X(70194) = barycentric quotient X(i)/X(j) for these {i,j}: {14, 30786}, {25, 66873}, {187, 44719}, {351, 60009}, {463, 52750}, {468, 299}, {3458, 895}, {5994, 65321}, {8738, 671}, {9204, 45792}, {14273, 23871}, {14567, 46113}, {18384, 36307}, {20579, 14977}, {30453, 51258}, {30455, 6390}, {36309, 892}, {44102, 16}, {52040, 69}, {56395, 40709}, {58780, 9205}, {60428, 471}, {61207, 17403}

X(70195) = X(4)X(13)∩X(462)X(2501)

Barycentrics   (2*a^2 - b^2 - c^2)*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^4 + a^2*b^2 - 2*b^4 + a^2*c^2 + 4*b^2*c^2 - 2*c^4 + 2*Sqrt[3]*a^2*S)::

X(70195) lies on these lines: {4, 13}, {25, 8014}, {462, 2501}, {468, 52039}, {471, 18020}, {1843, 54472}, {4232, 21466}, {5995, 40118}, {6756, 11555}, {10603, 40709}, {10641, 46342}, {30454, 52477}, {44102, 56395}, {57593, 60590}

X(70195) = polar conjugate of the isotomic conjugate of X(52039)
X(70195) = X(i)-isoconjugate of X(j) for these (i,j): {63, 66872}, {298, 36060}, {895, 65569}, {897, 44718}, {2151, 30786}, {17402, 69477}, {36085, 60010}, {46112, 46277}
X(70195) = X(i)-Dao conjugate of X(j) for these (i,j): {1560, 298}, {3162, 66872}, {6593, 44718}, {38988, 60010}, {40578, 30786}, {48317, 23870}
X(70195) = crossdifference of every pair of points on line {44718, 60010}
X(70195) = barycentric product X(i)*X(j) for these {i,j}: {4, 52039}, {13, 468}, {300, 44102}, {471, 56395}, {524, 8737}, {690, 36306}, {3457, 44146}, {4235, 20578}, {5095, 36307}, {8740, 43084}, {14273, 23895}, {17983, 30454}, {36296, 37778}, {40709, 60428}
X(70195) = barycentric quotient X(i)/X(j) for these {i,j}: {13, 30786}, {25, 66872}, {187, 44718}, {351, 60010}, {462, 52751}, {468, 298}, {3457, 895}, {5995, 65321}, {8737, 671}, {9205, 45792}, {14273, 23870}, {14567, 46112}, {18384, 36310}, {20578, 14977}, {30452, 51258}, {30454, 6390}, {36306, 892}, {44102, 15}, {52039, 69}, {56395, 40710}, {58780, 9204}, {60428, 470}, {61207, 17402}

X(70196) = X(4)X(3096)∩X(420)X(2501)

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

X(70196) lies on these lines: {4, 3096}, {419, 14052}, {420, 2501}, {468, 31068}, {3108, 38282}, {6353, 61418}, {7953, 40118}, {10603, 57852}, {18020, 65960}, {37943, 60590}

X(70196) = polar conjugate of the isotomic conjugate of X(31068)
X(70196) = X(i)-isoconjugate of X(j) for these (i,j): {895, 17469}, {897, 22352}, {923, 7767}, {3589, 36060}, {61211, 69477}
X(70196) = X(i)-Dao conjugate of X(j) for these (i,j): {1560, 3589}, {2482, 7767}, {6593, 22352}, {48317, 7927}
X(70196) = cevapoint of X(468) and X(64724)
X(70196) = barycentric product X(i)*X(j) for these {i,j}: {4, 31068}, {468, 10159}, {3108, 44146}, {4235, 31065}, {14273, 35137}, {37778, 41435}, {40425, 64724}, {57852, 60428}
X(70196) = barycentric quotient X(i)/X(j) for these {i,j}: {187, 22352}, {468, 3589}, {524, 7767}, {3108, 895}, {4235, 10330}, {7953, 65321}, {10159, 30786}, {14273, 7927}, {31065, 14977}, {31068, 69}, {37778, 44142}, {44102, 5007}, {44146, 39998}, {60428, 428}, {61207, 61211}, {64724, 6292}

X(70197) = X(4)X(110)∩X(6)X(2501)

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

X(70197) lies on the cubic K1301 and these lines: {2, 10420}, {4, 110}, {5, 53788}, {6, 2501}, {25, 3233}, {317, 18020}, {378, 39986}, {403, 39371}, {421, 61181}, {427, 16933}, {468, 5467}, {974, 59291}, {1007, 10603}, {1316, 15421}, {1560, 66128}, {1593, 51895}, {2434, 52477}, {4240, 44084}, {5094, 51456}, {5468, 44146}, {9717, 52475}, {10311, 10418}, {10419, 52488}, {11064, 35235}, {11185, 18878}, {11744, 39372}, {32708, 41370}, {35138, 65267}, {39379, 45088}, {40388, 62213}, {44438, 52219}, {47230, 66082}, {52449, 63082}, {60428, 61207}, {65586, 65770}

X(70197) = X(5642)-cross conjugate of X(468)
X(70197) = X(i)-isoconjugate of X(j) for these (i,j): {63, 60498}, {671, 2315}, {686, 36085}, {895, 1725}, {897, 13754}, {923, 62338}, {3580, 36060}, {6334, 36142}, {15329, 69477}
X(70197) = X(i)-Dao conjugate of X(j) for these (i,j): {468, 12827}, {1560, 3580}, {2482, 62338}, {3162, 60498}, {6593, 13754}, {23992, 6334}, {38988, 686}, {48317, 55121}, {66127, 62569}
X(70197) = trilinear pole of line {187, 14273}
X(70197) = crossdifference of every pair of points on line {686, 13754}
X(70197) = barycentric product X(i)*X(j) for these {i,j}: {187, 65267}, {351, 57932}, {468, 2986}, {524, 1300}, {687, 690}, {4235, 15328}, {5504, 37778}, {14273, 18878}, {14910, 44146}, {18020, 66128}, {32708, 35522}, {36890, 51965}, {38936, 43084}, {40832, 44102}, {57829, 60428}
X(70197) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 60498}, {187, 13754}, {351, 686}, {468, 3580}, {524, 62338}, {687, 892}, {690, 6334}, {922, 2315}, {1300, 671}, {1560, 12827}, {2986, 30786}, {4235, 61188}, {5642, 62569}, {10420, 65321}, {14273, 55121}, {14910, 895}, {15328, 14977}, {32708, 691}, {36114, 36085}, {37778, 44138}, {40388, 9139}, {44102, 3003}, {51456, 51405}, {51965, 9214}, {52475, 65614}, {56395, 39170}, {57932, 53080}, {60428, 403}, {61207, 15329}, {65267, 18023}, {65615, 66124}, {66128, 125}
X(70197) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 38936, 15454}, {427, 16933, 66167}

X(70198) = X(3)X(60590)∩X(4)X(1177)

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

X(70198) lies on these lines: {3, 60590}, {4, 1177}, {107, 14246}, {315, 18020}, {468, 51823}, {2207, 2501}, {2373, 10603}, {3542, 10423}, {4232, 10422}, {5489, 60040}, {6353, 10424}, {7493, 60002}, {36823, 44492}, {41616, 58080}, {44146, 53777}, {56685, 65268}

X(70198) = isogonal conjugate of X(51253)
X(70198) = polar conjugate of the isotomic conjugate of X(51823)
X(70198) = X(60133)-Ceva conjugate of X(60428)
X(70198) = X(1648)-cross conjugate of X(60040)
X(70198) = X(i)-isoconjugate of X(j) for these (i,j): {1, 51253}, {255, 59422}, {304, 34158}, {326, 57485}, {1102, 64619}, {36060, 62382}
X(70198) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 51253}, {1560, 62382}, {6523, 59422}, {15259, 57485}
X(70198) = cevapoint of X(468) and X(41616)
X(70198) = barycentric product X(i)*X(j) for these {i,j}: {4, 51823}, {25, 58078}, {107, 65611}, {393, 65712}, {468, 60133}, {1177, 37778}, {2373, 60428}, {6524, 53784}, {14273, 65268}
X(70198) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 51253}, {393, 59422}, {468, 62382}, {1974, 34158}, {2207, 57485}, {10423, 65321}, {36417, 51962}, {37778, 1236}, {44102, 14961}, {51823, 69}, {52439, 64619}, {53784, 4176}, {58078, 305}, {58757, 65609}, {60133, 30786}, {60428, 858}, {65611, 3265}, {65712, 3926}

X(70199) = X(2)X(2501)∩X(4)X(99)

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

X(70199) lies on these lines: {2, 2501}, {4, 99}, {25, 14052}, {69, 10425}, {193, 68088}, {468, 5468}, {2418, 52477}, {2987, 37645}, {3618, 64618}, {4235, 32459}, {5094, 62672}, {5203, 6390}, {6353, 18020}, {6720, 32970}, {7736, 69986}, {9170, 52290}, {10603, 57872}, {14356, 34803}, {14376, 32969}, {14912, 70035}, {18440, 56572}, {32817, 65277}, {32829, 58083}, {32985, 69778}, {36875, 40428}, {36890, 46986}, {37188, 40812}, {37690, 38970}, {37880, 38282}, {47108, 69424}, {52091, 60590}, {52094, 53156}, {54380, 66084}, {56689, 69418}

X(70199) = polar conjugate of X(52450)
X(70199) = X(i)-cross conjugate of X(j) for these (i,j): {5967, 56601}, {50567, 44146}
X(70199) = X(i)-isoconjugate of X(j) for these (i,j): {48, 52450}, {230, 36060}, {810, 52035}, {895, 8772}, {897, 52144}, {923, 3564}, {1733, 14908}, {23894, 56389}, {61213, 69477}
X(70199) = X(i)-Dao conjugate of X(j) for these (i,j): {1249, 52450}, {1560, 230}, {2482, 3564}, {6593, 52144}, {39062, 52035}, {48317, 55122}
X(70199) = cevapoint of X(14417) and X(51429)
X(70199) = trilinear pole of line {524, 14273}
X(70199) = barycentric product X(i)*X(j) for these {i,j}: {468, 8781}, {524, 35142}, {690, 65354}, {2987, 44146}, {3266, 3563}, {4235, 62645}, {4563, 52476}, {5203, 70049}, {5468, 60338}, {14273, 65277}, {32697, 35522}, {37778, 43705}, {52145, 57493}, {53156, 67101}, {56572, 56601}, {57872, 60428}
X(70199) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 52450}, {187, 52144}, {468, 230}, {524, 3564}, {648, 52035}, {2987, 895}, {3563, 111}, {4235, 4226}, {5095, 5477}, {5203, 70020}, {5467, 56389}, {5967, 65726}, {8781, 30786}, {9155, 47406}, {10425, 65321}, {14273, 55122}, {32654, 14908}, {32697, 691}, {35142, 671}, {35364, 10097}, {36051, 36060}, {36105, 36085}, {37778, 44145}, {44102, 1692}, {44146, 51481}, {47736, 60863}, {50567, 62590}, {51429, 41181}, {52476, 2501}, {56572, 36894}, {56601, 56687}, {56604, 59423}, {57493, 5968}, {60338, 5466}, {60428, 460}, {61207, 61213}, {62645, 14977}, {65354, 892}, {65758, 66124}, {66162, 51258}, {69778, 6091}
X(70199) = {X(8781),X(63613)}-harmonic conjugate of X(3563)

X(70200) = X(4)X(575)∩X(468)X(51541)

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

X(70200) lies on these lines: {4, 575}, {468, 51541}, {1235, 40826}, {1383, 4232}, {2501, 8599}, {5094, 23297}, {5095, 44146}, {6353, 61345}, {8744, 17983}, {10295, 52692}, {10511, 60133}, {10603, 52290}, {11636, 40118}, {15471, 20380}, {23287, 52475}

X(70200) = polar conjugate of X(42008)
X(70200) = polar conjugate of the isotomic conjugate of X(51541)
X(70200) = X(i)-isoconjugate of X(j) for these (i,j): {48, 42008}, {63, 42007}, {599, 36060}, {656, 32583}, {895, 36263}, {923, 69437}, {4575, 23288}, {9145, 69477}
X(70200) = X(i)-Dao conjugate of X(j) for these (i,j): {136, 23288}, {468, 19510}, {1249, 42008}, {1560, 599}, {2482, 69437}, {3162, 42007}, {40596, 32583}, {48317, 3906}
X(70200) = cevapoint of X(468) and X(15471)
X(70200) = trilinear pole of line {14273, 23287}
X(70200) = barycentric product X(i)*X(j) for these {i,j}: {4, 51541}, {112, 65008}, {468, 598}, {524, 68566}, {648, 23287}, {1383, 44146}, {4235, 8599}, {5095, 18818}, {14273, 35138}, {17983, 20380}, {37778, 43697}, {40826, 44102}, {52477, 61345}, {58078, 65007}, {60428, 64982}
X(70200) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 42008}, {25, 42007}, {112, 32583}, {468, 599}, {524, 69437}, {598, 30786}, {1383, 895}, {1560, 19510}, {2501, 23288}, {4235, 9146}, {5095, 39785}, {8599, 14977}, {11636, 65321}, {14273, 3906}, {15471, 11165}, {20380, 6390}, {23287, 525}, {44102, 574}, {44146, 9464}, {46001, 10097}, {51541, 69}, {60428, 5094}, {61207, 9145}, {65008, 3267}, {68566, 671}
X(70200) = {X(598),X(68566)}-harmonic conjugate of X(4)

X(70201) = X(4)X(155)∩X(924)X(2501)

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

X(70201) lies on these lines: {4, 155}, {235, 60835}, {858, 13398}, {924, 2501}, {1995, 57484}, {6748, 60775}, {10297, 21268}, {10603, 63155}, {40678, 67237}, {47309, 59497}, {52582, 54913}

X(70201) = X(3292)-cross conjugate of X(468)
X(70201) = X(i)-isoconjugate of X(j) for these (i,j): {111, 64455}, {155, 897}, {895, 920}, {923, 40697}, {6503, 36128}, {6515, 36060}, {14908, 33808}
X(70201) = X(i)-Dao conjugate of X(j) for these (i,j): {1560, 6515}, {2482, 40697}, {6593, 155}, {48317, 65694}
X(70201) = X(4)-line conjugate of X(155)
X(70201) = barycentric product X(i)*X(j) for these {i,j}: {187, 46746}, {254, 524}, {468, 6504}, {3266, 39109}, {6390, 67189}, {15316, 37778}, {44146, 60775}
X(70201) = barycentric quotient X(i)/X(j) for these {i,j}: {187, 155}, {254, 671}, {468, 6515}, {524, 40697}, {896, 64455}, {3292, 6503}, {6504, 30786}, {13398, 65321}, {14273, 65694}, {39109, 111}, {44102, 1609}, {46746, 18023}, {60428, 3542}, {60775, 895}, {60779, 8753}, {67189, 17983}

X(70202) = X(4)X(290)∩X(25)X(16083)

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

X(70202) lies on these lines: {4, 290}, {25, 16083}, {264, 36183}, {468, 52145}, {2052, 2501}, {7418, 16089}, {9306, 18020}, {10603, 18024}, {16081, 52672}, {22456, 40118}

X(70202) = X(i)-isoconjugate of X(j) for these (i,j): {255, 51980}, {3289, 36060}, {5968, 52430}
X(70202) = X(i)-Dao conjugate of X(j) for these (i,j): {1560, 3289}, {6523, 51980}, {48317, 39469}
X(70202) = trilinear pole of line {14273, 37778}
X(70202) = barycentric product X(i)*X(j) for these {i,j}: {290, 37778}, {468, 60199}, {2052, 52145}, {5967, 18027}, {14273, 65272}, {16081, 44146}, {18024, 60428}
X(70202) = barycentric quotient X(i)/X(j) for these {i,j}: {393, 51980}, {468, 3289}, {2052, 5968}, {3266, 51386}, {4235, 68647}, {5967, 577}, {6531, 14908}, {14273, 39469}, {16081, 895}, {20031, 32729}, {22456, 65321}, {36120, 36060}, {36874, 53782}, {37778, 511}, {44146, 36212}, {52038, 39201}, {52145, 394}, {60199, 30786}, {60428, 237}, {66299, 8430}, {68624, 10097}

X(70203) = X(4)X(39)∩X(2501)X(3005)

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

X(70203) lies on these lines: {4, 39}, {263, 44084}, {2501, 3005}, {7813, 44146}, {7824, 26224}, {10603, 42313}, {18020, 26276}, {23297, 46106}, {26714, 40118}, {51543, 60590}

X(70203) = X(i)-isoconjugate of X(j) for these (i,j): {183, 36060}, {895, 52134}, {3403, 14908}
X(70203) = X(i)-Dao conjugate of X(j) for these (i,j): {1560, 183}, {48317, 23878}, {67187, 30786}
X(70203) = barycentric product X(i)*X(j) for these {i,j}: {262, 468}, {263, 44146}, {327, 44102}, {524, 68572}, {690, 65349}, {4235, 66291}, {14273, 65271}, {36885, 53156}, {37778, 43718}, {42299, 64724}, {42313, 60428}
X(70203) = barycentric quotient X(i)/X(j) for these {i,j}: {262, 30786}, {263, 895}, {468, 183}, {3402, 36060}, {14273, 23878}, {26714, 65321}, {37778, 44144}, {44102, 182}, {44146, 20023}, {46319, 14908}, {52631, 10097}, {60428, 458}, {64724, 14994}, {65349, 892}, {66291, 14977}, {68572, 671}

X(70204) = X(4)X(3414)∩X(30)X(115)

Barycentrics   2*(a^2 - b^2 - c^2)*(b^2 - c^2)^2*(a^6*b^2 - a^4*b^4 - a^2*b^6 + b^8 + a^6*c^2 - 2*a^4*b^2*c^2 + 2*a^2*b^4*c^2 - 3*b^6*c^2 - a^4*c^4 + 2*a^2*b^2*c^4 + 4*b^4*c^4 - a^2*c^6 - 3*b^2*c^6 + c^8)*(a^2*b^2 - b^4 + a^2*c^2 - c^4 - (a^2 - b^2 - c^2)*Sqrt[a^4 - a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + c^4]) - (a^2 - c^2)*(a^2 + b^2 - c^2)*(-a^2 + c^2)*(a^2 - b^2 + c^2)*(2*a^6 - 5*a^4*b^2 + 4*a^2*b^4 - b^6 + a^4*c^2 - 3*a^2*b^2*c^2 + 4*b^4*c^2 + a^2*c^4 - 5*b^2*c^4 + 2*c^6)*(-a^4 + a^2*b^2 + b^2*c^2 - c^4 - (-a^2 + b^2 - c^2)*Sqrt[a^4 - a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + c^4]) + (a^2 - b^2)^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(2*a^6 + a^4*b^2 + a^2*b^4 + 2*b^6 - 5*a^4*c^2 - 3*a^2*b^2*c^2 - 5*b^4*c^2 + 4*a^2*c^4 + 4*b^2*c^4 - c^6)*(-a^4 - b^4 + a^2*c^2 + b^2*c^2 - (-a^2 - b^2 + c^2)*Sqrt[a^4 - a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + c^4])::
X(70204) = 3 X[3545] - 2 X[67692], 3 X[3839] - X[67694], X[6040] - 3 X[14639]

X(70204) lies on the cubic K955 and these lines: {4, 3414}, {30, 115}, {99, 67681}, {148, 67683}, {193, 67695}, {671, 3413}, {2039, 66626}, {2549, 57630}, {3545, 67692}, {3839, 67694}, {6040, 14639}, {7790, 67689}, {7841, 67677}, {8370, 67678}, {11185, 67688}, {11317, 46024}, {11632, 64482}, {13636, 52450}, {13722, 53161}, {19660, 47617}, {31862, 43448}, {44518, 47365}, {54395, 67680}

X(70204) = midpoint of X(i) and X(j) for these {i,j}: {148, 67683}, {11632, 64482}
X(70204) = reflection of X(i) in X(j) for these {i,j}: {99, 67681}, {66626, 2039}, {67679, 115}

X(70205) = X(4)X(3413)∩X(30)X(115)

Barycentrics   2*(a^2 - b^2 - c^2)*(b^2 - c^2)^2*(a^6*b^2 - a^4*b^4 - a^2*b^6 + b^8 + a^6*c^2 - 2*a^4*b^2*c^2 + 2*a^2*b^4*c^2 - 3*b^6*c^2 - a^4*c^4 + 2*a^2*b^2*c^4 + 4*b^4*c^4 - a^2*c^6 - 3*b^2*c^6 + c^8)*(a^2*b^2 - b^4 + a^2*c^2 - c^4 + (a^2 - b^2 - c^2)*Sqrt[a^4 - a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + c^4]) - (a^2 - c^2)*(a^2 + b^2 - c^2)*(-a^2 + c^2)*(a^2 - b^2 + c^2)*(2*a^6 - 5*a^4*b^2 + 4*a^2*b^4 - b^6 + a^4*c^2 - 3*a^2*b^2*c^2 + 4*b^4*c^2 + a^2*c^4 - 5*b^2*c^4 + 2*c^6)*(-a^4 + a^2*b^2 + b^2*c^2 - c^4 + (-a^2 + b^2 - c^2)*Sqrt[a^4 - a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + c^4]) + (a^2 - b^2)^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(2*a^6 + a^4*b^2 + a^2*b^4 + 2*b^6 - 5*a^4*c^2 - 3*a^2*b^2*c^2 - 5*b^4*c^2 + 4*a^2*c^4 + 4*b^2*c^4 - c^6)*(-a^4 - b^4 + a^2*c^2 + b^2*c^2 + (-a^2 - b^2 + c^2)*Sqrt[a^4 - a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + c^4])::
X(70205) = 3 X[3545] - 2 X[67681], 3 X[3839] - X[67683], X[6039] - 3 X[14639]

X(70205) lies on the cubic K955 and these lines: {4, 3413}, {30, 115}, {99, 67692}, {148, 67694}, {193, 67684}, {671, 3414}, {2040, 66625}, {2549, 57631}, {3545, 67681}, {3839, 67683}, {6039, 14639}, {7790, 67678}, {7841, 67688}, {8370, 67689}, {11185, 67677}, {11317, 46023}, {11632, 64483}, {13636, 53161}, {13722, 52450}, {19659, 47617}, {31863, 43448}, {44518, 47366}, {54395, 67691}

X(70205) = midpoint of X(i) and X(j) for these {i,j}: {148, 67694}, {11632, 64483}
X(70205) = reflection of X(i) in X(j) for these {i,j}: {99, 67692}, {66625, 2040}, {67690, 115}

X(70206) = X(1)X(514)∩X(516)X(1025)

Barycentrics   (a^2 + b^2 - a*c - b*c)*(a^2 - a*b - b*c + c^2)*(a^7*b - 3*a^6*b^2 + 2*a^5*b^3 + 2*a^4*b^4 - 3*a^3*b^5 + a^2*b^6 + a^7*c + a^5*b^2*c - 6*a^4*b^3*c + 2*a^3*b^4*c + 3*a^2*b^5*c - b^7*c - 3*a^6*c^2 + a^5*b*c^2 + 6*a^4*b^2*c^2 + a^3*b^3*c^2 - 3*a^2*b^4*c^2 - 4*a*b^5*c^2 + 2*b^6*c^2 + 2*a^5*c^3 - 6*a^4*b*c^3 + a^3*b^2*c^3 - 2*a^2*b^3*c^3 + 4*a*b^4*c^3 + b^5*c^3 + 2*a^4*c^4 + 2*a^3*b*c^4 - 3*a^2*b^2*c^4 + 4*a*b^3*c^4 - 4*b^4*c^4 - 3*a^3*c^5 + 3*a^2*b*c^5 - 4*a*b^2*c^5 + b^3*c^5 + a^2*c^6 + 2*b^2*c^6 - b*c^7) : :

X(70206) lies on these lines: {1, 514}, {516, 1025}, {927, 2717}, {2801, 14942}, {11019, 56850}, {28132, 70172}, {57494, 66632}, {67658, 68917}.

X(70207) = X(1)X(4)∩X(63)X(53151)

Barycentrics   (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^8 - 2*a^7*b - a^6*b^2 + 4*a^5*b^3 - a^4*b^4 - 2*a^3*b^5 + a^2*b^6 - 2*a^7*c + 9*a^6*b*c - 7*a^5*b^2*c - 7*a^4*b^3*c + 10*a^3*b^4*c - 3*a^2*b^5*c - a*b^6*c + b^7*c - a^6*c^2 - 7*a^5*b*c^2 + 18*a^4*b^2*c^2 - 8*a^3*b^3*c^2 - 7*a^2*b^4*c^2 + 7*a*b^5*c^2 - 2*b^6*c^2 + 4*a^5*c^3 - 7*a^4*b*c^3 - 8*a^3*b^2*c^3 + 18*a^2*b^3*c^3 - 6*a*b^4*c^3 - b^5*c^3 - a^4*c^4 + 10*a^3*b*c^4 - 7*a^2*b^2*c^4 - 6*a*b^3*c^4 + 4*b^4*c^4 - 2*a^3*c^5 - 3*a^2*b*c^5 + 7*a*b^2*c^5 - b^3*c^5 + a^2*c^6 - a*b*c^6 - 2*b^2*c^6 + b*c^7) : :

X(70207) lies on these lines: {1, 4}, {63, 53151}, {92, 1309}, {281, 70172}, {522, 1709}, {1768, 61178}, {1897, 2801}, {4242, 64211}, {19541, 60062}, {37805, 44425}, {41013, 67725}, {53008, 67628}.

X(70208) = X(1)X(104)∩X(2717)X(35011)

Barycentrics   a*(a^3 - a^2*b - a*b^2 + b^3 + 2*a*b*c - a*c^2 - b*c^2)*(a^3 - a*b^2 - a^2*c + 2*a*b*c - b^2*c - a*c^2 + c^3)*(2*a^8 - 6*a^7*b + a^6*b^2 + 12*a^5*b^3 - 9*a^4*b^4 - 6*a^3*b^5 + 7*a^2*b^6 - b^8 - 6*a^7*c + 22*a^6*b*c - 22*a^5*b^2*c - 15*a^4*b^3*c + 36*a^3*b^4*c - 10*a^2*b^5*c - 8*a*b^6*c + 3*b^7*c + a^6*c^2 - 22*a^5*b*c^2 + 54*a^4*b^2*c^2 - 30*a^3*b^3*c^2 - 21*a^2*b^4*c^2 + 20*a*b^5*c^2 - 2*b^6*c^2 + 12*a^5*c^3 - 15*a^4*b*c^3 - 30*a^3*b^2*c^3 + 48*a^2*b^3*c^3 - 12*a*b^4*c^3 - 3*b^5*c^3 - 9*a^4*c^4 + 36*a^3*b*c^4 - 21*a^2*b^2*c^4 - 12*a*b^3*c^4 + 6*b^4*c^4 - 6*a^3*c^5 - 10*a^2*b*c^5 + 20*a*b^2*c^5 - 3*b^3*c^5 + 7*a^2*c^6 - 8*a*b*c^6 - 2*b^2*c^6 + 3*b*c^7 - c^8) : :

X(70208) lies on these lines: {1, 104}, {2717, 35011}, {2801, 36037}, {3738, 44425}, {44055, 61080}, {52663, 70172}.

X(70209) = X(1)X(84)∩X(521)X(1750)

Barycentrics   a*(a^3 - a^2*b - a*b^2 + b^3 + a^2*c + 2*a*b*c + b^2*c - a*c^2 - b*c^2 - c^3)*(a^3 + a^2*b - a*b^2 - b^3 - a^2*c + 2*a*b*c - b^2*c - a*c^2 + b*c^2 + c^3)*(a^8 - 4*a^7*b + 2*a^6*b^2 + 8*a^5*b^3 - 8*a^4*b^4 - 4*a^3*b^5 + 6*a^2*b^6 - b^8 - 4*a^7*c + 13*a^6*b*c - 15*a^5*b^2*c - 8*a^4*b^3*c + 26*a^3*b^4*c - 7*a^2*b^5*c - 7*a*b^6*c + 2*b^7*c + 2*a^6*c^2 - 15*a^5*b*c^2 + 36*a^4*b^2*c^2 - 22*a^3*b^3*c^2 - 14*a^2*b^4*c^2 + 13*a*b^5*c^2 + 8*a^5*c^3 - 8*a^4*b*c^3 - 22*a^3*b^2*c^3 + 30*a^2*b^3*c^3 - 6*a*b^4*c^3 - 2*b^5*c^3 - 8*a^4*c^4 + 26*a^3*b*c^4 - 14*a^2*b^2*c^4 - 6*a*b^3*c^4 + 2*b^4*c^4 - 4*a^3*c^5 - 7*a^2*b*c^5 + 13*a*b^2*c^5 - 2*b^3*c^5 + 6*a^2*c^6 - 7*a*b*c^6 + 2*b*c^7 - c^8) : :

X(70209) lies on these lines: {1, 84}, {282, 70172}, {521, 1750}, {1768, 8059}, {2717, 6081}, {2801, 13138}.

X(70210) = X(4)X(69)∩X(5)X(99)

Barycentrics   a^4 - b^4 + 3*b^2*c^2 - c^4 : :
X(70210) = 3 X[5] - 2 X[42788], 6 X[597] - 5 X[5038], X[7905] - 4 X[39590], 2 X[1506] - 3 X[33013], X[7783] - 3 X[33013], 5 X[5116] - 7 X[47355].

X(70210) lies on the cubic K1401 and these lines: {2, 7748}, {3, 69387}, {4, 69}, {5, 99}, {20, 7771}, {23, 11056}, {26, 21395}, {30, 1078}, {32, 11361}, {39, 148}, {83, 597}, {115, 384}, {141, 7911}, {183, 382}, {187, 6658}, {192, 9650}, {194, 5475}, {230, 19687}, {274, 5046}, {290, 3521}, {305, 7394}, {325, 546}, {330, 9665}, {350, 3585}, {376, 52718}, {381, 1975}, {385, 7747}, {428, 33651}, {491, 42269}, {492, 42268}, {538, 7785}, {543, 1506}, {550, 37688}, {574, 16921}, {598, 2996}, {618, 11304}, {619, 11303}, {620, 32967}, {625, 7836}, {626, 14041}, {631, 53127}, {668, 52367}, {754, 17129}, {801, 37873}, {1003, 7857}, {1007, 3855}, {1479, 64133}, {1799, 34603}, {1909, 3583}, {1995, 37803}, {2475, 18140}, {2548, 7757}, {2549, 7786}, {2552, 46810}, {2553, 46813}, {2896, 7842}, {3090, 69450}, {3091, 7763}, {3096, 7841}, {3146, 14907}, {3266, 7533}, {3267, 68328}, {3314, 7825}, {3329, 7765}, {3363, 31406}, {3398, 52034}, {3522, 32838}, {3523, 69407}, {3529, 34229}, {3543, 3785}, {3544, 34803}, {3545, 6337}, {3552, 7746}, {3627, 7750}, {3629, 43676}, {3734, 5025}, {3760, 18513}, {3761, 18514}, {3767, 3972}, {3788, 18424}, {3830, 7811}, {3832, 3926}, {3839, 7871}, {3843, 7773}, {3845, 3933}, {3850, 6390}, {3851, 69413}, {3853, 7767}, {3854, 32831}, {3858, 32820}, {3861, 7917}, {3934, 6655}, {3978, 62949}, {4027, 62356}, {4045, 68522}, {4366, 69175}, {4857, 25303}, {5007, 32457}, {5013, 44543}, {5023, 66387}, {5056, 69424}, {5066, 59634}, {5068, 32829}, {5071, 69442}, {5076, 69417}, {5080, 17143}, {5116, 7770}, {5133, 16276}, {5169, 37804}, {5189, 26235}, {5206, 17004}, {5286, 7878}, {5305, 12150}, {5309, 7787}, {5395, 60209}, {5485, 53107}, {5976, 22515}, {5989, 38732}, {5999, 34885}, {6179, 7737}, {6292, 7924}, {6392, 63061}, {6393, 67865}, {6528, 62274}, {6645, 69259}, {6656, 34573}, {6661, 63543}, {6683, 33020}, {6722, 33245}, {6761, 59528}, {6781, 19696}, {6997, 57518}, {7391, 40022}, {7603, 20094}, {7610, 66395}, {7615, 26613}, {7617, 33274}, {7738, 32983}, {7745, 7760}, {7749, 13586}, {7751, 7823}, {7753, 7839}, {7754, 7812}, {7756, 7824}, {7758, 7926}, {7759, 20081}, {7761, 31276}, {7762, 53418}, {7764, 43457}, {7775, 7906}, {7776, 61984}, {7777, 7781}, {7779, 7843}, {7780, 14712}, {7788, 14269}, {7789, 7899}, {7793, 51224}, {7794, 7885}, {7795, 7934}, {7797, 7804}, {7798, 7921}, {7800, 7910}, {7801, 7912}, {7803, 32971}, {7805, 14537}, {7806, 14034}, {7807, 14061}, {7808, 7864}, {7810, 8597}, {7813, 7941}, {7815, 7833}, {7817, 10583}, {7819, 7919}, {7820, 7901}, {7822, 7933}, {7830, 33256}, {7834, 68525}, {7835, 7887}, {7844, 7892}, {7846, 7851}, {7852, 19689}, {7853, 46226}, {7854, 7898}, {7855, 7900}, {7862, 7891}, {7863, 7925}, {7870, 33006}, {7872, 7876}, {7873, 63044}, {7875, 7902}, {7877, 63933}, {7882, 14711}, {7883, 8352}, {7884, 69209}, {7886, 33225}, {7889, 7923}, {7893, 17131}, {7895, 31173}, {7907, 69171}, {7913, 16895}, {7920, 66410}, {7922, 32996}, {7930, 14064}, {7931, 14045}, {7935, 16986}, {7936, 16990}, {7937, 32974}, {7940, 32961}, {7942, 14001}, {7943, 16898}, {7944, 33184}, {8024, 37349}, {8182, 66398}, {8369, 9166}, {8550, 45018}, {8556, 66396}, {8588, 33268}, {8859, 53144}, {9818, 14558}, {9855, 34506}, {10159, 53106}, {11059, 62937}, {11132, 22832}, {11133, 22831}, {11168, 66424}, {11257, 37348}, {11285, 44526}, {11324, 63541}, {11591, 51440}, {12215, 19130}, {12243, 52088}, {13111, 39093}, {13335, 14651}, {13468, 66423}, {14360, 67591}, {14382, 34175}, {14928, 25555}, {14929, 62006}, {14957, 60707}, {15022, 32839}, {15048, 55085}, {15271, 33234}, {15513, 33265}, {15515, 33015}, {15589, 50688}, {15682, 69384}, {15683, 32885}, {15687, 37671}, {15717, 32867}, {16275, 39998}, {16589, 33030}, {16808, 69157}, {16809, 69165}, {16925, 43620}, {16988, 67269}, {17006, 33276}, {17008, 33280}, {17503, 18840}, {17578, 32834}, {17686, 63537}, {17941, 57598}, {18121, 65713}, {18122, 33799}, {18145, 62969}, {18354, 57805}, {18358, 51374}, {18362, 33246}, {18843, 60626}, {18845, 60228}, {19569, 63952}, {19925, 69038}, {20065, 63955}, {20099, 23297}, {20112, 41134}, {20394, 36251}, {20395, 36252}, {20398, 35950}, {21734, 32897}, {21843, 33244}, {23698, 37334}, {24275, 33834}, {26233, 62963}, {27356, 39286}, {28706, 66766}, {29317, 60702}, {29479, 33839}, {30737, 50009}, {31168, 66392}, {31239, 33021}, {31392, 46139}, {31400, 32991}, {31401, 32962}, {31415, 32995}, {31455, 33002}, {32448, 35705}, {32450, 63018}, {32456, 33259}, {32532, 60644}, {32533, 54124}, {32817, 61964}, {32818, 41099}, {32821, 61970}, {32823, 69419}, {32824, 63098}, {32825, 69452}, {32827, 32830}, {32835, 69402}, {32836, 61985}, {32837, 61954}, {32869, 61992}, {32870, 50693}, {32872, 50690}, {32874, 62005}, {32883, 61820}, {32893, 62032}, {32965, 43619}, {32980, 53033}, {32992, 63548}, {33189, 39143}, {33192, 55164}, {33198, 63536}, {33232, 63121}, {33235, 37637}, {33239, 62992}, {33249, 59545}, {33251, 47005}, {33698, 60210}, {33703, 69386}, {35007, 50570}, {35139, 58733}, {35930, 38907}, {37668, 61982}, {38259, 43527}, {38734, 43157}, {39113, 54105}, {40236, 52854}, {40279, 43460}, {40344, 68504}, {40853, 59197}, {41106, 69434}, {41895, 60278}, {43291, 68177}, {44267, 67606}, {44535, 68516}, {45103, 60250}, {45201, 52285}, {46138, 65284}, {46951, 50687}, {47101, 66420}, {47287, 59546}, {50248, 63925}, {51371, 67884}, {53102, 60219}, {54493, 60639}, {54494, 60636}, {55470, 67880}, {55958, 57829}, {57275, 61749}, {61339, 66145}, {61945, 69443}, {61967, 69445}, {61975, 69437}, {61980, 69447}, {61988, 69439}, {61989, 69433}, {62310, 67238}, {63538, 68719}, {63556, 67630}, {64687, 66837}, {69409, 69453}.

X(70210) = reflection of X(i) in X(j) for these {i,j}: {1078, 59635}, {7783, 1506}, {7785, 39590}, {7905, 7785}
X(70210) = isotomic conjugate of X(13622)
X(70210) = anticomplement of X(37512)
X(70210) = anticomplement of the isogonal conjugate of X(53109)
X(70210) = isotomic conjugate of the isogonal conjugate of X(13595)
X(70210) = X(53109)-anticomplementary conjugate of X(8)
X(70210) = X(i)-cross conjugate of X(j) for these (i,j): {41578, 67117}, {41579, 13595}
X(70210) = X(31)-isoconjugate of X(13622)
X(70210) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 13622}, {45161, 512}
X(70210) = cevapoint of X(3629) and X(68085)
X(70210) = barycentric product X(i)*X(j) for these {i,j}: {76, 13595}, {308, 41579}, {311, 67117}, {1502, 56918}, {40633, 62278}, {41578, 57903}
X(70210) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 13622}, {13595, 6}, {40633, 54034}, {41578, 570}, {41579, 39}, {56918, 32}, {67117, 54}
X(70210) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 7748, 7847}, {4, 76, 316}, {4, 11185, 76}, {4, 52713, 32006}, {4, 69378, 315}, {4, 69428, 7860}, {5, 99, 7769}, {5, 32819, 99}, {20, 32832, 7771}, {20, 69382, 32832}, {39, 63922, 148}, {69, 69378, 69449}, {69, 69428, 76}, {76, 316, 7768}, {76, 7850, 69410}, {76, 7860, 69}, {83, 671, 5254}, {83, 5254, 7827}, {99, 15031, 5}, {115, 384, 7828}, {141, 33229, 7911}, {148, 16044, 39}, {183, 382, 7802}, {194, 5475, 7858}, {194, 33018, 5475}, {315, 11185, 69378}, {315, 69378, 76}, {381, 1975, 7752}, {385, 14042, 7747}, {550, 37688, 43459}, {598, 7894, 69208}, {621, 622, 43150}, {671, 8370, 7827}, {1003, 13881, 7857}, {1007, 32822, 69451}, {1975, 7752, 7799}, {2549, 16924, 7786}, {3091, 32815, 7763}, {3091, 69425, 69408}, {3146, 32828, 14907}, {3314, 14062, 7825}, {3543, 69383, 3785}, {3545, 6337, 69430}, {3627, 64093, 7750}, {3734, 5025, 7832}, {3734, 69141, 5025}, {3767, 14035, 3972}, {3788, 18424, 32966}, {3839, 32833, 48913}, {3839, 69379, 32816}, {3843, 69380, 7773}, {3855, 32822, 1007}, {3934, 6655, 7831}, {5254, 8370, 83}, {7620, 69208, 2996}, {7745, 47286, 7760}, {7747, 63924, 385}, {7751, 62203, 7823}, {7754, 11317, 65630}, {7754, 65630, 7812}, {7770, 7790, 7859}, {7770, 44518, 7790}, {7773, 69380, 7796}, {7783, 33013, 1506}, {7789, 33228, 7899}, {7795, 14063, 7934}, {7800, 33017, 7910}, {7803, 32971, 60855}, {7805, 14537, 20088}, {7806, 14034, 69172}, {7807, 63534, 14061}, {7808, 11648, 7864}, {7812, 34505, 11054}, {7815, 65633, 7833}, {7816, 39565, 2}, {7816, 47617, 39565}, {7823, 14066, 62203}, {7825, 17130, 3314}, {7836, 32993, 625}, {7841, 69139, 3096}, {7842, 9466, 2896}, {7851, 11286, 7846}, {7855, 63956, 7900}, {7864, 66413, 7808}, {7871, 48913, 32816}, {11317, 34505, 7812}, {11361, 18546, 14568}, {14041, 17128, 626}, {15031, 32819, 7769}, {17004, 33257, 5206}, {17131, 63931, 7893}, {17578, 32834, 64018}, {19570, 20088, 7805}, {31276, 33019, 7761}, {32006, 52713, 69410}, {32006, 69410, 7850}, {32815, 69408, 69425}, {32816, 32833, 7871}, {32816, 69379, 32833}, {32830, 50689, 32827}, {32961, 69206, 7940}, {32971, 43448, 7803}, {34505, 65630, 7754}, {37647, 62362, 7769}, {38228, 64089, 5}, {39998, 62967, 16275}, {43676, 53109, 3629}, {52713, 69410, 76}, {53418, 63923, 7762}, {69162, 69172, 7806}, {69378, 69449, 69428}, {69408, 69425, 7763}

X(70211) = X(23)X(110)∩X(1173)X(35909)

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

X(70211) lies on the cubic K1401 and these lines: {23, 110}, {1173, 35909}, {3470, 6140}, {5966, 64775}, {6034, 52199}, {13582, 54554}, {34174, 38664}, {40604, 47053}.

X(70211) = X(54554)-Ceva conjugate of X(842)
X(70211) = X(i)-isoconjugate of X(j) for these (i,j): {542, 51804}, {2247, 13582}
X(70211) = trilinear pole of line {8562, 11063}
X(70211) = barycentric product X(i)*X(j) for these {i,j}: {842, 37779}, {3470, 51228}, {5641, 11063}, {5649, 45147}, {6035, 6140}, {14223, 47053}, {23969, 45790}, {37943, 65308}, {40604, 54554}, {46751, 48453}
X(70211) = barycentric quotient X(i)/X(j) for these {i,j}: {842, 13582}, {2914, 68694}, {3470, 51227}, {5649, 65279}, {6140, 1640}, {11063, 542}, {14998, 64935}, {35909, 64938}, {37943, 60502}, {45147, 18312}, {47053, 14999}, {48453, 3471}, {50461, 65722}, {52199, 64936}, {56404, 43087}

X(70212) = X(5)X(38394)∩X(511)X(1263)

Barycentrics   (a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10 + a^8*c^2 - 3*a^6*b^2*c^2 + 6*a^2*b^6*c^2 - 4*b^8*c^2 - a^6*c^4 + a^4*b^2*c^4 + 6*b^6*c^4 - a^4*c^6 - 3*a^2*b^2*c^6 - 4*b^4*c^6 + a^2*c^8 + b^2*c^8)*(a^8*b^2 - a^6*b^4 - a^4*b^6 + a^2*b^8 + a^8*c^2 - 3*a^6*b^2*c^2 + a^4*b^4*c^2 - 3*a^2*b^6*c^2 + b^8*c^2 - 4*a^6*c^4 - 4*b^6*c^4 + 6*a^4*c^6 + 6*a^2*b^2*c^6 + 6*b^4*c^6 - 4*a^2*c^8 - 4*b^2*c^8 + c^10) : :
X(70212) = 3 X[25147] - 2 X[39506].

X(70212) lies on the circumconic {{A, B, C, X(4), X(5)}}, the cubic K1401, and these lines: {5, 38394}, {137, 3613}, {511, 1263}, {8266, 11671}, {11063, 60517}, {14627, 40449}, {22335, 67861}, {25147, 39506}, {25149, 60037}, {45147, 61196}

X(70212) = midpoint of X(8266) and X(11671)
X(70212) = reflection of X(3613) in X(137)
X(70212) = antigonal image of X(3613)
X(70212) = trilinear pole of line {1506, 12077}

X(70213) = X(3)X(5965)∩X(25)X(7747)

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

X(70213) lies on the cubic K947 and these lines: {3, 5965}, {25, 7747}, {39, 14908}, {98, 3520}, {184, 5206}, {187, 10547}, {574, 40319}, {682, 3455}, {1799, 3266}, {3425, 32534}, {12038, 42065}, {13595, 53109}, {14671, 38228}, {16042, 23297}, {32366, 37512}, {35007, 41593}, {42288, 70203}, {44879, 67311}, {54072, 62362}

X(70213) = isogonal conjugate of the anticomplement of X(37512)
X(70213) = isogonal conjugate of the isotomic conjugate of X(13622)
X(70213) = X(i)-isoconjugate of X(j) for these (i,j): {75, 13595}, {561, 56918}, {3112, 41579}, {14213, 67117}, {40633, 62272}
X(70213) = X(i)-Dao conjugate of X(j) for these (i,j): {206, 13595}, {34452, 41579}, {40368, 56918}
X(70213) = crosssum of X(3629) and X(68085)
X(70213) = barycentric product X(6)*X(13622)
X(70213) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 13595}, {1501, 56918}, {3051, 41579}, {13622, 76}, {14573, 40633}, {54034, 67117}

X(70214) = X(3)X(54)∩X(98)X(1291)

Barycentrics   a^2*(a^10 - 4*a^8*b^2 + 6*a^6*b^4 - 4*a^4*b^6 + a^2*b^8 - 4*a^8*c^2 + 6*a^6*b^2*c^2 - 3*a^2*b^6*c^2 + b^8*c^2 + 6*a^6*c^4 + a^2*b^4*c^4 - b^6*c^4 - 4*a^4*c^6 - 3*a^2*b^2*c^6 - b^4*c^6 + a^2*c^8 + b^2*c^8) : :

X(70214) lies on the cubic K947 and these lines: {3, 54}, {50, 41724}, {98, 1291}, {110, 61300}, {511, 14652}, {1510, 3005}, {3060, 56308}, {6032, 37637}, {9380, 36830}, {13558, 15107}, {14979, 58948}, {15787, 21230}, {16336, 40393}, {16337, 66766}, {19165, 62291}, {19552, 50138}, {27866, 68741}, {32744, 33332}, {41586, 47053}

X(70214) = reflection of X(14652) in the Lemoine axis
X(70214) = circumcircle-inverse of X(5012)
X(70214) = crossdifference of every pair of points on line {1506, 12077}

X(70215) = X(98)X(1291)∩X(140)X(523)

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

X(70215) lies on the cubic K947 and these lines: {3, 15554}, {67, 5965}, {98, 1291}, {140, 523}, {231, 1989}, {1117, 34365}, {1273, 1494}, {7570, 52192}, {15246, 70024}, {17983, 68638}, {38539, 45943}

X(70215) = circumcircle-inverse of X(15554)
X(70215) = X(i)-isoconjugate of X(j) for these (i,j): {842, 1749}, {8562, 36096}, {51802, 54554}
X(70215) = X(i)-Dao conjugate of X(j) for these (i,j): {23967, 37779}, {42426, 37943}, {65728, 45147}
X(70215) = crossdifference of every pair of points on line {8562, 11063}
X(70215) = X(i)-line conjugate of X(j) for these (i,j): {140, 8562}, {231, 11063}
X(70215) = barycentric product X(i)*X(j) for these {i,j}: {542, 13582}, {1291, 18312}, {1640, 65279}, {3471, 51227}, {7473, 64938}, {14999, 64935}, {15392, 68694}, {43704, 60502}, {46786, 64936}, {65722, 68638}
X(70215) = barycentric quotient X(i)/X(j) for these {i,j}: {542, 37779}, {1291, 5649}, {1640, 45147}, {2247, 1749}, {3471, 51228}, {5191, 11063}, {6041, 6140}, {6103, 37943}, {11071, 54554}, {13582, 5641}, {14579, 842}, {43704, 65308}, {48451, 3470}, {51227, 46751}, {51428, 10413}, {64935, 14223}, {64936, 46787}, {64937, 14998}, {65279, 6035}

X(70216) = X(5)X(112)∩X(54)X(67)

Barycentrics   (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^16 - 4*a^14*b^2 + 6*a^12*b^4 - 3*a^10*b^6 - 3*a^8*b^8 + 6*a^6*b^10 - 4*a^4*b^12 + a^2*b^14 - 4*a^14*c^2 + 14*a^12*b^2*c^2 - 19*a^10*b^4*c^2 + 14*a^8*b^6*c^2 - 9*a^6*b^8*c^2 + 7*a^4*b^10*c^2 - 4*a^2*b^12*c^2 + b^14*c^2 + 6*a^12*c^4 - 19*a^10*b^2*c^4 + 15*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 - 2*b^12*c^4 - 3*a^10*c^6 + 14*a^8*b^2*c^6 - 3*a^6*b^4*c^6 - 8*a^4*b^6*c^6 + a^2*b^8*c^6 - b^10*c^6 - 3*a^8*c^8 - 9*a^6*b^2*c^8 + a^4*b^4*c^8 + a^2*b^6*c^8 + 4*b^8*c^8 + 6*a^6*c^10 + 7*a^4*b^2*c^10 + 2*a^2*b^4*c^10 - b^6*c^10 - 4*a^4*c^12 - 4*a^2*b^2*c^12 - 2*b^4*c^12 + a^2*c^14 + b^2*c^14) : :

X(70216) lies on these lines: {3, 66175}, {5, 112}, {24, 2453}, {54, 67}, {98, 3520}, {1235, 22467}, {1352, 14591}, {6143, 33695}. on K947.

X(70216) = circumcircle-inverse of X(66175),

X(70217) = EXCENTRAL-POLAR-CIRCLE-INVERSE OF X(23)

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

The Gibert-Burek-Moses-concurrent-circles image of a point P (see X(5524)) is actually the polar-circle-of-excentral-triangle-inverse of P
The points X(70217)-X(70228) are examples

X(70217) lies on these lines: {1, 23}, {40, 5524}, {43, 484}, {46, 17779}, {57, 985}, {1763, 3465}, {3219, 32778}, {6210, 21381}, {7291, 29676}, {41319, 52679}

X(70217) = Bevan-circle-inverse of X(5524)
X(70217) = excentral-polar-circle-inverse of X(23)

X(70218) = EXCENTRAL-POLAR-CIRCLE-INVERSE OF X(37)

Barycentrics   a*(a^3 - 3*a^2*b + a*b^2 + b^3 - 3*a^2*c - a*b*c + b^2*c + a*c^2 + b*c^2 + c^3) : :
3 X[5525] - 4 X[41391], 3 X[5526] - 2 X[41391]

X(70218) lies on these lines: {1, 6}, {41, 6763}, {169, 3901}, {191, 4251}, {239, 17484}, {484, 3684}, {672, 69275}, {758, 5540}, {910, 4880}, {2748, 8700}, {3309, 47948}, {3894, 40131}, {4051, 11280}, {4067, 33950}, {4253, 69274}, {4384, 31019}, {5030, 15015}, {5131, 35342}, {5134, 50016}, {5164, 13146}, {5538, 58036}, {5902, 37658}, {9359, 34996}, {16126, 17451}, {16833, 31164}, {18206, 37783}, {20109, 30133}

X(70218) = reflection of X(i) in X(j) for these {i,j}: {5525, 5526}, {5540, 63087}
X(70218) = Conway-circle-inverse of X(64546)
X(70218) = excentral-polar-circle-inverse of X(37)
X(70218) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 5692, 56532}, {6, 69281, 1}, {218, 5904, 17744}, {16973, 54981, 1}, {51194, 54330, 1}

X(70219) = EXCENTRAL-POLAR-CIRCLE-INVERSE OF X(42)

Barycentrics   a^3 + a^2*b - a*b^2 + a^2*c + 3*a*b*c - 2*b^2*c - a*c^2 - 2*b*c^2 : :
X(70219) = 7 X[5121] - 8 X[60380], X[5524] + 2 X[38473], 3 X[5529] - 4 X[6789]

X(70219) lies on these lines: {1, 2}, {11, 32846}, {171, 49484}, {312, 32913}, {536, 18201}, {740, 1054}, {742, 24398}, {846, 14829}, {982, 49453}, {1155, 4693}, {1757, 4358}, {2748, 9110}, {3306, 49474}, {3416, 24217}, {3667, 4932}, {3706, 17122}, {3711, 49689}, {3750, 4891}, {3816, 32861}, {3886, 56010}, {3923, 37684}, {3936, 20546}, {3980, 70152}, {3993, 24627}, {3994, 24821}, {4009, 49712}, {4011, 37683}, {4038, 44417}, {4365, 27003}, {4387, 4650}, {4413, 49459}, {4434, 68969}, {4519, 37520}, {4649, 30818}, {4716, 16610}, {4851, 17717}, {4860, 49493}, {4892, 17297}, {4966, 17719}, {4974, 25531}, {5087, 17374}, {5143, 15571}, {5241, 42334}, {6682, 34064}, {7321, 48641}, {9282, 17731}, {11814, 63002}, {16560, 34997}, {17300, 25385}, {17593, 49462}, {17595, 49452}, {17596, 32915}, {17720, 33087}, {17728, 32855}, {17770, 17777}, {17889, 18141}, {18149, 30940}, {18326, 31828}, {18743, 32853}, {24210, 33085}, {24342, 37633}, {24593, 32845}, {24727, 61234}, {25079, 56018}, {26842, 48642}, {28522, 62300}, {28581, 56009}, {31035, 51294}, {32863, 69173}, {32930, 37639}, {32944, 69632}, {33135, 69092}, {33158, 37646}, {33160, 37634}, {34379, 62297}, {37759, 49676}, {44908, 68839}, {50122, 69025}

X(70219) = midpoint of X(i) and X(j) for these {i,j}: {5205, 38473}, {38476, 68482}
X(70219) = reflection of X(i) in X(j) for these {i,j}: {1, 47626}, {5212, 50535}, {5524, 5205}, {63002, 11814}
X(70219) = Conway-circle-inverse of X(3741)
X(70219) = excentral-polar-circle-inverse of X(42)
X(70219) = psi-transform of X(24342)
X(70219) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 49488, 17779}, {1647, 49995, 32842}, {1999, 3840, 29821}, {3912, 33140, 29862}, {3994, 62235, 24821}, {4358, 32919, 1757}, {7081, 42057, 3979}, {10453, 29649, 3961}, {11269, 29674, 29861}, {17763, 29824, 1}, {26015, 49990, 32847}, {30567, 39594, 43}, {50001, 62659, 3935}

X(70220) = EXCENTRAL-POLAR-CIRCLE-INVERSE OF X(44)

Barycentrics   a*(3*a^3 - 5*a^2*b + 3*a*b^2 - b^3 - 5*a^2*c + 5*a*b*c - b^2*c + 3*a*c^2 - b*c^2 - c^3) : :
X[1] - 4 X[1083], X[1] + 2 X[67385], 2 X[9] + X[70173], 2 X[1083] + X[67385], X[5525] + 2 X[5526], X[5525] - 4 X[41391], X[5526] + 2 X[41391], X[40] + 2 X[14661], 2 X[644] + X[5540], 5 X[1698] - 2 X[18343], 5 X[7987] - 2 X[67724], 3 X[25055] - 2 X[68377]

X(70220) lies on these lines: {1, 6}, {40, 14661}, {57, 60059}, {63, 40215}, {101, 14439}, {144, 4089}, {165, 3309}, {200, 6065}, {346, 49998}, {644, 2802}, {1026, 35258}, {1698, 18343}, {2246, 4752}, {2384, 2748}, {2718, 6078}, {2725, 6017}, {2751, 59068}, {3161, 6790}, {3573, 63961}, {3632, 4530}, {3679, 61730}, {4370, 16554}, {5091, 61686}, {6172, 38941}, {6544, 68827}, {7280, 34877}, {7987, 67724}, {16820, 17350}, {24036, 57192}, {25055, 68377}, {26074, 59419}, {30731, 67343}, {46917, 68768}, {59413, 67583}, {62669, 67576}, {64112, 69717}, {68137, 68833}

X(70220) = excentral-polar-circle-inverse of X(44)
X(70220) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 1023, 1}, {44, 59239, 9}, {101, 14439, 15015}, {1023, 67385, 70173}, {1083, 67385, 1}, {2246, 4752, 5541}, {5526, 41391, 5525}, {67386, 67387, 1}

X(70221) = EXCENTRAL-POLAR-CIRCLE-INVERSE OF X(45)

Barycentrics   a*(3*a^3 - 7*a^2*b + 3*a*b^2 + b^3 - 7*a^2*c + a*b*c + b^2*c + 3*a*c^2 + b*c^2 + c^3) : :
X(70221) = X[5525] - 4 X[5526], 5 X[5525] - 8 X[41391], 5 X[5526] - 2 X[41391]

X(70221) lies on these lines: {1, 6}, {672, 15015}, {2748, 28310}, {2802, 63087}, {3309, 47777}, {3679, 61706}, {4089, 20072}, {14439, 69275}, {16833, 27479}, {30727, 47626}

X(70221) = excentral-polar-circle-inverse of X(45)

X(70222) = EXCENTRAL-POLAR-CIRCLE-INVERSE OF X(63)

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

X(70222) lies on these lines: {1, 21}, {3, 5197}, {6, 63304}, {11, 238}, {35, 22076}, {36, 26884}, {43, 212}, {55, 22139}, {105, 5536}, {109, 1758}, {110, 3724}, {162, 68801}, {171, 6690}, {323, 902}, {511, 1283}, {580, 31870}, {582, 24174}, {601, 63291}, {602, 21214}, {605, 63298}, {606, 63299}, {643, 740}, {692, 5143}, {727, 65886}, {739, 65885}, {741, 6083}, {748, 31204}, {750, 63344}, {978, 51281}, {985, 29657}, {1054, 13329}, {1331, 1757}, {1362, 2078}, {1399, 60682}, {1460, 63311}, {1711, 7070}, {1724, 37702}, {1754, 17889}, {1756, 61221}, {1914, 2323}, {2006, 39136}, {2175, 7015}, {2195, 61434}, {2254, 6003}, {2342, 7281}, {3011, 5985}, {3072, 13408}, {3073, 63318}, {3286, 53324}, {3750, 63393}, {3939, 5524}, {4123, 59674}, {4252, 63316}, {4331, 18625}, {4588, 65875}, {5060, 42669}, {5078, 51235}, {5150, 35992}, {5247, 37730}, {5255, 63360}, {5264, 63319}, {5266, 63396}, {5348, 63327}, {5901, 63307}, {6187, 56878}, {8758, 65524}, {10902, 48893}, {11012, 49118}, {11269, 17127}, {17126, 37635}, {17735, 20741}, {21059, 68585}, {21189, 47176}, {21381, 44661}, {24161, 33592}, {29675, 36482}, {29820, 55086}, {30652, 41819}, {33295, 68996}, {34172, 56419}, {37652, 49168}, {39137, 68779}, {39258, 69894}, {49736, 61661}, {59016, 65883}, {59019, 65882}

X(70222) = reflection of X(1283) in the Lemoine axis
X(70222) = circumcircle-inverse of X(5197)
X(70222) = incircle-inverse of X(62852)
X(70222) = excentral-polar-circle-inverse of X(63)
X(70222) = crossdifference of every pair of points on line {661, 17451}
X(70222) = {X(238),X(1936)}-harmonic conjugate of X(33140)

X(70223) = EXCENTRAL-POLAR-CIRCLE-INVERSE OF X(72)

Barycentrics   a*(a^5 - a^4*b - a*b^4 + b^5 - a^4*c - 3*a^3*b*c + a*b^3*c - b^4*c + 4*a*b^2*c^2 + a*b*c^3 - a*c^4 - b*c^4 + c^5) : :
X(70223) = 3 X[165] - 4 X[51622]

X(70223) lies on these lines: {1, 6}, {4, 24779}, {21, 25065}, {165, 7298}, {200, 33156}, {614, 33143}, {990, 4859}, {1040, 23511}, {1054, 37959}, {1718, 11809}, {1781, 4223}, {2074, 52680}, {2725, 8687}, {2957, 5538}, {3008, 3100}, {3216, 24933}, {3309, 7655}, {3465, 49997}, {4021, 5262}, {4383, 61718}, {4656, 7191}, {5131, 54095}, {5142, 65128}, {5272, 7988}, {5540, 44661}, {7070, 10900}, {8226, 37887}, {13221, 32116}, {14017, 15803}, {16566, 17522}, {18343, 18865}, {20445, 32922}, {24773, 36652}, {25101, 34772}, {29820, 68377}, {30447, 37718}, {41327, 60353}

X(70223) = incircle-inverse of X(68604)
X(70223) = excentral-polar-circle-inverse of X(72)
X(70223) = {X(4223),X(32118)}-harmonic conjugate of X(1781)

X(70224) = EXCENTRAL-POLAR-CIRCLE-INVERSE OF X(78)

Barycentrics   a^4 - a^3*b + a^2*b^2 + 2*a*b^3 - b^4 - a^3*c + a^2*b*c - 3*a*b^2*c + a^2*c^2 - 3*a*b*c^2 + 2*b^2*c^2 + 2*a*c^3 - c^4 : :
X(70224) = 3 X[3582] - 2 X[67348], X[5524] + 2 X[53614], 2 X[50535] - 3 X[60409]

X(70224) lies on these lines: {1, 2}, {65, 33096}, {80, 1739}, {125, 68946}, {238, 40663}, {242, 1877}, {244, 5176}, {355, 24174}, {515, 1054}, {517, 26727}, {529, 18201}, {726, 36926}, {1283, 2077}, {1459, 4147}, {1463, 18838}, {1772, 56825}, {1837, 24440}, {2726, 8685}, {3421, 62865}, {3445, 66240}, {3551, 30513}, {3583, 4674}, {3667, 21186}, {3753, 33109}, {3756, 38455}, {3976, 64087}, {3987, 37702}, {5080, 32857}, {5123, 17719}, {5193, 14027}, {5247, 52407}, {5252, 17063}, {5440, 66643}, {5587, 17889}, {5657, 8616}, {5722, 64176}, {5724, 17122}, {5855, 51415}, {5881, 11512}, {7613, 54448}, {8056, 37712}, {8256, 37588}, {9956, 24161}, {11113, 69025}, {11236, 33103}, {18326, 45631}, {24175, 38155}, {31141, 33101}, {33141, 61717}, {33147, 37716}, {33152, 54315}, {44669, 56009}, {44848, 59593}, {49609, 56311}, {63460, 68904}

X(70224) = midpoint of X(38471) and X(53614)
X(70224) = reflection of X(i) in X(j) for these {i,j}: {5524, 38471}, {47623, 5121}, {53619, 6788}, {68245, 10}
X(70224) = complement of X(47624)
X(70224) = excentral-polar-circle-inverse of X(78)
X(70224) = orthoptic-circle-of-the-Steiner-inellipse inverse of X(66632)
X(70224) = psi-transform of X(3944)
X(70224) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 28074, 1}, {1737, 60353, 33140}, {3753, 37717, 33109}

X(70225) = EXCENTRAL-POLAR-CIRCLE-INVERSE OF X(145)

Barycentrics   a*(a^3 - 2*a^2*b - 2*a*b^2 + b^3 - 2*a^2*c + 13*a*b*c - 4*b^2*c - 2*a*c^2 - 4*b*c^2 + c^3) : :
X(70225) = 4 X[1] - X[5524], 3 X[1] - X[5529], 5 X[1] - 2 X[45763], 3 X[1] - 2 X[47622], 3 X[5524] - 4 X[5529], 5 X[5524] - 8 X[45763], 3 X[5524] - 8 X[47622], 5 X[5529] - 6 X[45763], 2 X[5529] - 3 X[47623], 3 X[45763] - 5 X[47622], 4 X[45763] - 5 X[47623], 4 X[47622] - 3 X[47623]

X(70225) lies on these lines: {1, 2}, {484, 2718}, {517, 13541}, {518, 9282}, {758, 10700}, {846, 5919}, {1054, 3880}, {3667, 4449}, {3756, 32426}, {4342, 33099}, {4694, 41702}, {5048, 49675}, {7262, 12513}, {7962, 62865}, {17460, 54391}, {33096, 34749}, {33103, 34640}, {33109, 66228}, {39969, 56113}, {46190, 64201}

X(70225) = reflection of X(i) in X(j) for these {i,j}: {484, 2718}, {5121, 60374}, {5524, 47623}, {5529, 47622}, {47623, 1}, {68482, 47626}
X(70225) = excentral-polar-circle-inverse of X(145)
X(70225) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3241, 3979}, {1, 3872, 29820}, {1, 5529, 47622}, {1, 6048, 54319}, {1, 11519, 56630}, {1, 12629, 21214}, {5529, 47622, 47623}

X(70226) = EXCENTRAL-POLAR-CIRCLE-INVERSE OF X(5525)

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

X(70226) lies on the Evans circle (see X(10190) and these lines: {1, 187}, {9, 484}, {40, 5525}, {46, 56532}, {1018, 65589}, {1100, 28607}, {1759, 41322}, {3218, 16834}, {3496, 6205}, {5011, 68480}, {9093, 29179}, {11010, 36643}, {16777, 21338}, {39586, 69226}

X(70226) = Bevan-circle-inverse of X(5525)
X(70226) = excentral-polar-circle-inverse of X(187)

X(70227) = EXCENTRAL-POLAR-CIRCLE-INVERSE OF X(214)

Barycentrics   a*(a^3 + 2*a^2*b - 2*a*b^2 - 3*b^3 + 2*a^2*c - 7*a*b*c + 6*b^2*c - 2*a*c^2 + 6*b*c^2 - 3*c^3) : :
X(70227) = 3 X[1] - 4 X[106], 5 X[1] - 4 X[10700], 7 X[1] - 8 X[11717], 3 X[1] - 2 X[13541], X[1] - 4 X[64234], 2 X[106] - 3 X[1054], 5 X[106] - 3 X[10700], 7 X[106] - 6 X[11717], X[106] - 3 X[64234], 2 X[214] - 3 X[14193], 5 X[1054] - 2 X[10700], 7 X[1054] - 4 X[11717], 3 X[1054] - X[13541], 7 X[10700] - 10 X[11717], 6 X[10700] - 5 X[13541], and others

X(70227) lies on these lines: {1, 88}, {6, 21888}, {10, 17777}, {40, 14663}, {45, 21885}, {121, 19875}, {148, 1654}, {165, 38620}, {484, 62393}, {517, 5529}, {519, 20098}, {528, 26727}, {545, 52871}, {902, 60353}, {970, 3030}, {1018, 3731}, {1145, 24715}, {1168, 19653}, {1276, 39151}, {1277, 39150}, {1293, 10563}, {1357, 3339}, {1647, 9802}, {1698, 11814}, {1739, 16489}, {1757, 3245}, {1766, 3973}, {2093, 2810}, {2163, 49494}, {2827, 12767}, {2832, 13259}, {2841, 59294}, {2842, 41329}, {3125, 3247}, {3654, 32865}, {3753, 16484}, {3919, 3979}, {3987, 5315}, {4668, 50914}, {4695, 37680}, {4730, 53411}, {4738, 24821}, {4919, 8649}, {5119, 15485}, {6018, 9819}, {6085, 21385}, {6154, 66643}, {6715, 50915}, {7280, 34139}, {7982, 38576}, {8056, 56795}, {9355, 64189}, {9589, 34548}, {9624, 61568}, {10713, 51066}, {10744, 37714}, {11010, 54296}, {11512, 52183}, {14664, 16192}, {15522, 50865}, {16189, 51531}, {16483, 24440}, {16485, 63138}, {16486, 24174}, {16496, 63137}, {16499, 17596}, {16676, 21821}, {17601, 40587}, {20092, 62666}, {21041, 30578}, {22313, 67416}, {24161, 32157}, {28228, 38471}, {30315, 61582}, {30389, 38604}, {38671, 52182}, {39586, 48443}, {50581, 61220}, {58423, 64850}

X(70227) = reflection of X(i) in X(j) for these {i,j}: {1, 1054}, {1054, 64234}, {5541, 68246}, {7982, 38576}, {9589, 34548}, {13541, 106}, {17777, 10}
X(70227) = excentral-polar-circle-inverse of X(214)
X(70227) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {106, 13541, 1}, {1054, 9324, 14193}, {1054, 13541, 106}, {4674, 5541, 1}, {4792, 9324, 1}

X(70228) = EXCENTRAL-POLAR-CIRCLE-INVERSE OF X(239)

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

X(70228) lies on these lines: {1, 2}, {9, 9282}, {55, 51634}, {87, 4076}, {609, 1023}, {984, 67428}, {1054, 14839}, {1083, 8616}, {1742, 3667}, {2108, 3799}, {2726, 7220}, {2748, 9111}, {3550, 3573}, {3675, 62865}, {4069, 9359}, {4517, 40730}, {5091, 56010}, {16283, 51321}, {33099, 67570}, {36814, 59486}, {53967, 65886}

X(70228) = excentral-polar-circle-inverse of X(239)
X(70228) = psi-transform of X(2108)
X(70228) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1026, 43}, {1, 16569, 27846}

X(70229) = INTOUCH-ISOGONAL CONJUGATE FO X(4)

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

Contributed by Jean-Louis Ayme, October 15, 2025. X(70229) is not the same point as X(21) = isogonal conjugate of X(4)-of-intouch-triangle = isogonal conjugate of X(65)

X(70229) lies on these lines: {1, 19904}, {4, 65}, {56, 269}, {57, 2956}, {208, 221}, {354, 30493}, {1071, 59816}, {1361, 2817}, {1426, 42448}, {1854, 68059}, {2099, 35671}, {3485, 37054}, {6610, 52218}, {7066, 64723}, {11415, 62402}, {16596, 25917}, {17114, 37566}, {21746, 58906}, {28097, 28109}, {38357, 40953}, {40933, 51660}, {51490, 51616}

X(70229) = X(i)-isoconjugate of X(j) for these (i,j): {271, 40396}, {280, 947}, {282, 55987}, {285, 56195}, {2192, 40417}
X(70229) = X(i)-Dao conjugate of X(j) for these (i,j): {57, 40417}, {946, 8}, {20262, 44189}, {40943, 34404}
X(70229) = crosspoint of X(7) and X(223)
X(70229) = crosssum of X(55) and X(282)
X(70229) = crossdifference of every pair of points on line {4130, 36054}
X(70229) = intouch-isogonal conjugate of X(4)
X(70229) = barycentric product X(i)*X(j) for these {i,j}: {7, 40943}, {196, 17102}, {223, 946}, {278, 52097}, {342, 22063}, {347, 2262}, {6611, 23528}, {47372, 59178}
X(70229) = barycentric quotient X(i)/X(j) for these {i,j}: {221, 55987}, {223, 40417}, {946, 34404}, {2199, 947}, {2262, 280}, {3209, 40396}, {17102, 44189}, {22063, 271}, {40943, 8}, {52097, 345}
X(70229) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1875, 67011, 65}, {4295, 46017, 65}

X(70230) = ISOGONAL CONJUGATE OF X(18239)

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

X(70230) lies on these lines: {40, 8602}, {57, 57422}, {223, 1167}, {329, 10309}, {14256, 63185}

X(70230) = isogonal conjugate of X(18239)
X(70230) = isogonal conjugate of the anticomplement of X(18238)
X(70230) = isogonal conjugate of the complement of X(67992)
X(70230) = X(56)-cross conjugate of X(1167)
X(70230) = X(i)-isoconjugate of X(j) for these (i,j): {1, 18239}, {1108, 56545}, {1210, 10310}, {2057, 37566}, {30201, 61227}
X(70230) = barycentric product X(i)*X(j) for these {i,j}: {8602, 40424}, {10309, 40399}, {57422, 63876}
X(70230) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 18239}, {1167, 56545}, {8602, 1210}, {10309, 17862}





leftri   Points associated with P-Brocard triangles: X(70231) - X(70236)  rightri

Contributed by Peter Moses and Clark Kimberling, October 17, 2025.

The P-Brocard triangle is defined at X(5642) as follows:

Let O = X(3) and suppose that P is a point other than O. Let OP be the circle with segment PO as diameter. Let A' be the point of intersection, other than O, of OP and the perpendicular bisector of segment BC, and define B' and C' cyclically. Triangle A'B'C' is called the P-Brocard triangle, and X(5642) is X(23)-of-the-X(2)-Brocard triangle. (Randy Hutson, June 16-17, 2014)

Subsequently, P-Brocard triangles have been mentioned in properties of points X(i) for i = 110, 146, 147, 153, 599, and others.

In October 2025, Peter Moses found barycentric coordinates for the P-Brocard triangle of a point P = p : q : r, as follows:

A-vertex = 2*a^2*p : (-b^2 + c^2)*p + a^2*(q + r) : (b^2 - c^2)*p + a^2*(q + r)
B-vertex = (c^2 - a^2)*q + b^2*(r + p) : 2*b^2*q : (-c^2 + a^2)*q + b^2*(r + p)
C-vertex = (-a^2 + b^2)*r + c^2*(p + q) : (a^2 - b^2)*r + c^2*(p + q) : 2*c^2*r

The following triangles are perspective, with perspector X(3), for every point P:

medial (TCCT 6.2)
tangential (TCCT 6.5)
1st circumperp (TCCT 6.21)
2nd circumperp (TCCT 6.22)
outer Napoleon (TCCT 6.31)
inner Napoleon (TCCT 6.32)
outer Fermat (TCCT p178)
inner Fermat (TCCT p178)
inner Vecten (MathWorld)
outer Vecten (MathWorld)
1st Neuberg (MathWorld)
2nd Neuberg (MathWorld)
Fuhrmann (TCCT 8.25)
1st Brocard (CTC)
Kosnita (see ETC X(1658))
McCay (see ETC X(7606))
Trinh (see ETC X(7688))
Carnot / Johnson (reflection of ABC about X(5). MathWorld)
2nd Euler (see ETC X(3758))
Ara (see ETC X(5594) / excentral of tangential
1st EhrmannT (see ETC (8537))
Ascella (see ETC X(8726))
reflected 1st Brocard (CTC table 32)
Ae, (CTC K798)
Ai, (CTC K798)
infinite altitude
anti-Hutson intouch (see X(11363))
anti-incircle-circles (see X(11363))
orthic-of-medial / anti-6th-mixtilinear (see X(11363))
Ehrmann side-triangle
2nd Fuhrmann
Bankoff equilateral triangle (see X(34551))
anti-Ehrmann-mid

If P lies on the Stammler hyperbola (SH, the Feuerbach circumhyperbola of the tangential triangle), then the P-Brocard triangle is perspective to ABC, and the perspector lies on the cubic K028. The appearance of (i,j) in the following list means that the lies on SH, and the X(i)-Brocard triangle is perspective to ABC with perspector X(j)
(1,8), (3,3), (6,76), (155,847), (159,8743), (195,25043), (399,14254), (610,14256), (1498,14249), (2574,4), (2575,4), (2916,14247), (2917,58079), (2930,14246), (2931,38936), (2935,38937), (2948,58076), (3216,58073), (3511,14251), (5898,38539), (8053,3730), (9937,34756), (15141,39269), (19588,14248), (23361,10571), (31521,14259), (35237,39263), (46373,39268), (53406,14266), (57012,70041), (64214,58080), (1740,70231), (3499,70232), (8925,70233), (2509,70234), (44196,70235), (44199,70236),

underbar



X(70231) = X(8)X(291)∩X(10)X(87)

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

X(70231) lies on the cubic K028 and these lines: {1, 56142}, {2, 3223}, {3, 932}, {4, 4645}, {8, 291}, {10, 87}, {76, 4014}, {171, 7121}, {350, 33789}, {519, 52573}, {1575, 25273}, {1740, 25311}, {2053, 4598}, {3494, 29674}, {3501, 14199}, {3661, 7093}, {3730, 65167}, {6376, 49537}, {6384, 10453}, {7153, 10106}, {7346, 69912}, {8817, 56928}, {10449, 42027}, {16606, 59296}, {17105, 37603}, {17750, 21759}, {18149, 23497}, {19567, 20537}, {20350, 52043}, {20532, 53146}, {20691, 40881}, {20917, 52211}, {24524, 53679}, {26135, 51575}, {27424, 56164}, {32937, 56931}, {34252, 39976}, {39914, 50289}, {40720, 50302}

X(70231) = isogonal conjugate of X(57505)
X(70231) = anticomplement of X(14823)
X(70231) = X(18830)-Ceva conjugate of X(21438)
X(70231) = X(17786)-cross conjugate of X(32937)
X(70231) = X(i)-isoconjugate of X(j) for these (i,j): {1, 57505}, {239, 67005}, {2176, 3500}, {2209, 54128}
X(70231) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 57505}, {982, 41886}, {5518, 4083}, {62574, 54128}
X(70231) = crosssum of X(8640) and X(40610)
X(70231) = barycentric product X(i)*X(j) for these {i,j}: {87, 17786}, {291, 70079}, {330, 32937}, {334, 70075}, {335, 14199}, {932, 21438}, {3501, 6384}, {4598, 17072}, {5383, 23772}, {6383, 34247}, {13588, 60244}, {18830, 21348}, {21958, 56053}
X(70231) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 57505}, {87, 3500}, {330, 54128}, {1911, 67005}, {3501, 43}, {13588, 27644}, {14199, 239}, {17072, 3835}, {17786, 6376}, {21300, 27527}, {21348, 4083}, {21438, 20906}, {21958, 21051}, {22229, 50491}, {22443, 22090}, {23655, 20979}, {23772, 21138}, {32937, 192}, {34247, 2176}, {51840, 33890}, {51949, 2209}, {52657, 41886}, {56557, 56806}, {56931, 20284}, {67001, 904}, {70075, 238}, {70079, 350}

:

X(70232) = X(2)X(39953)∩X(3)X(689)

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

X(70232) lies on the cubic K028 and these lines: {2, 39953}, {3, 689}, {4, 18022}, {76, 14970}, {83, 3114}, {194, 9495}, {308, 2998}, {384, 69953}, {871, 18833}, {881, 44165}, {1031, 1502}, {7770, 40362}, {8743, 44161}, {14603, 59249}

X(70232) = isogonal conjugate of X(57503)
X(70232) = isotomic conjugate of X(69928)
X(70232) = isotomic conjugate of the isogonal conjugate of X(69953)
X(70232) = X(i)-cross conjugate of X(j) for these (i,j): {9230, 69953}, {37890, 384}
X(70232) = X(i)-isoconjugate of X(j) for these (i,j): {1, 57503}, {31, 69928}, {39, 9236}, {560, 67165}, {695, 1923}, {1964, 51948}, {2236, 67000}, {3051, 9288}, {9285, 41331}, {56915, 70059}
X(70232) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 69928}, {3, 57503}, {6374, 67165}, {35971, 688}, {37895, 3051}, {41884, 51948}
X(70232) = crosssum of X(9494) and X(55050)
X(70232) = trilinear pole of line {35558, 68787}
X(70232) = barycentric product X(i)*X(j) for these {i,j}: {76, 69953}, {308, 9230}, {384, 40016}, {1925, 3112}, {1965, 18833}, {37894, 68630}, {42371, 68787}
X(70232) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 69928}, {6, 57503}, {76, 67165}, {82, 9236}, {83, 51948}, {308, 695}, {384, 3051}, {733, 67000}, {1582, 1923}, {1915, 41331}, {1925, 38}, {1965, 1964}, {3112, 9288}, {4074, 59994}, {9230, 39}, {14970, 14946}, {16985, 56915}, {18833, 9285}, {35558, 62454}, {37893, 68651}, {37894, 20775}, {40016, 9229}, {68630, 37892}, {68787, 688}, {69953, 6}, {69999, 70059}

:

X(70233) = X(3)X(6037)∩X(4)X(263)

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

X(70233) lies on the cubic K028 and these lines: {3, 6037}, {4, 263}, {76, 53196}, {262, 14251}, {290, 69771}, {327, 9473}, {13860, 34536}, {14252, 64625}, {39265, 70041}, {67179, 69780}

X(70233) = X(67171)-Dao conjugate of X(52658)
X(70233) = crosssum of X(9420) and X(39009)
X(70233) = trilinear pole of line {54267, 70026}
X(70233) = barycentric product X(i)*X(j) for these {i,j}: {290, 70026}, {327, 47737}, {18024, 57259}, {53196, 54267}
X(70233) = barycentric quotient X(i)/X(j) for these {i,j}: {47737, 182}, {57259, 237}, {70026, 511}

:

X(70234) = X(3)X(36066)∩X(4)X(811)

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

X(70234) lies on the cubic K028 and these lines: {2, 9510}, {3, 36066}, {4, 811}, {6, 57554}, {8, 4589}, {76, 65285}, {3730, 4584}, {18827, 49488}, {20158, 37128}

X(70234) = barycentric product X(19308)*X(40017)
X(70234) = barycentric quotient X(19308)/X(2238)

:

X(70235) = X(3)X(13030)∩X(4)X(371)

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

X(70235) lies on the cubic K028 and these lines: {3, 13030}, {4, 371}, {6, 8825}, {76, 54031}, {372, 53060}, {6423, 44192}, {8577, 45515}, {9733, 10665}, {10960, 24246}, {13045, 13882}, {39384, 60501}

X(70235) = X(5062)-Dao conjugate of X(641)
X(70235) = {X(13440),X(45511)}-harmonic conjugate of X(485)

:

X(70236) = X(3)X(13032)∩X(4)X(372)

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

X(70236) lies on the cubic K028 and these lines: {3, 13032}, {4, 372}, {76, 54030}, {371, 53061}, {6424, 44193}, {8576, 45514}, {9732, 10666}, {10962, 24245}, {13048, 13934}, {26922, 45499}, {39383, 60501}

X(70236) = X(5058)-Dao conjugate of X(642)
X(70236) = {X(13429),X(45510)}-harmonic conjugate of X(486)

: (Part 37 will be started in the future.)

This is the end of PART 36: Centers X(70001) - X(72000)

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)