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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(11868)∩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}
on K777, K1325

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(3)X(8694)∩X(84)X(165)

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 K and K 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}
on K150, K222

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}
on K523, K639

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(511)

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}
on K863, K991

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}
on K863, K991

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}
on K961, K983

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)
vX(51973)-cross conjugate of X(1911)
vX(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}
on K224, K532

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(2)X(66974)∩X(183)X(1350)

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(2)X(2501)∩X(4)X(99)

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(1281)

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) = EXTERNAL-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(70230) 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) = EXTERNAL-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) = EXTERNAL-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) = EXTERNAL-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) = EXTERNAL-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) = EXTERNAL-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) = EXTERNAL-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) = EXTERNAL-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) = EXTERNAL-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) = EXTERNAL-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) = EXTERNAL-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) = EXTERNAL-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}

(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)