The Thomson triangle T is defined and studied here. This page is only a compilation of various cubics and higher degree curves passing through its vertices Q1, Q2, Q3 and other remarkable points. See also Table 54, column P = [X2].
 Cubics c denotes a circum-cubic, otherwise the three remaining points on the circumcircle (O) are mentioned. Knnn* and Knnn*T denote the isogonal transforms of Knnn with respect to ABC and T respectively.
 cubic Type Xi on the curve for i = other points on (O) remarks K002 c pK see the page K758*T K078 stelloid 1, 2, 3, 165, 5373, 6194 CircumTangential triangle K003 in T K138 equilateral 2, 6, 5652 Grebe triangle K167 c pK 3, 6, 3167, 8770 K181* K172 c pK 3, 6, 25, 55, 56, 64, 154, 198, 1033, 1035, 1436, 7037 K007* K280 c spK, nodal 2, 6, 262, 378, 995, 1002, 1340, 1341, 5968, 7757 K281* K297 c nodal 3, 6, 183, 956, 1344, 1345, 3445, 5968, 9717 K295* K463 focal 2, 3, 15, 16, 30, 110, 5463, 5464 X110, circular points at ∞ K187 in T K581 c spK, stelloid 2, 3, 4, 262 K1266*T K609 1, 2, 3, 20 see note 1 K615 c spK 2, 3, 4, 64, 154, 3424, 5373 K047* K624 c nK0+ 6, 523, 2574, 2575, 5968, 8105, 8106 K625 c nK0 6, 187, 511, 523, 690, 6137, 6138 K626 c nodal 3, 25, 1073, 1384, 1617, 3167, 3420, 3426, 9717 K616* K703 nK wrt T antipodes of A, B, C K727 2, 3, 7712 CircumTangential triangle K758 central 2, 3, 154, 165, 376, 3576 antipodes of Q1, Q2, Q3 K002*T K759 c spK 2, 3, 4, 3431, 7607, 9716, 9717 K762* K760 c pK 1, 6, 9, 56, 84, 165, 198, 365 K308* K761 c pK 1, 6, 9, 55, 259, 3158, 3445 K365* K764 central 2, 3, 6, 376, 1350, 5373, 9740, 9741 antipodes of Q1, Q2, Q3 K004 in T K765 2, 3, 3524, 5024, 5373, 5646 points on nK0(X6, X14930) K002 in T K804 c spK 2, 3, 4, 3167, 7612 K810 c spK 2, 3, 4, 3426 K851* K833 central stelloid 2, 3, 381 points on nK0(X6, X31489) K834 circular 2, 3, 30, 110, 5373, 10620 X110, circular points at ∞ K001 in T K903 strophoid 3, 23, 110, 187, 6141, 6142 X110, circular points at ∞ K912 focal 3, 15, 16, 23, 110, 5663, 13858, 13859 X110, circular points at ∞ K913 circular 1, 2, 3, 30, 110, 147, 399, 5536 X110, circular points at ∞ K1093 c spK 2, 6, 9741, 21448 K314* K1095 circular 2, 3, 30, 110, 114, 1511 X110, circular points at ∞ K1138 central focal 2, 13, 14, 30, 476, 5463, 5464, 5655 X476, circular points at ∞ K1259 2, 3, 5373, 11472, 39162 ,39163, 39164, 39165 points on nK0(X6, X7736) K006 in T K1260 central 2, 3, 376, 46949, 46950 antipodes of Q1, Q2, Q3 K443 in T K1261 central stelloid 2, 3, 376, 1670, 1671, 7757, 33706, 46948 antipodes of Q1, Q2, Q3 K080 in T K1262 central 1, 2, 3, 40, 376, 5646, 14482, 46943, 46944, 46945, 46946, 46947 antipodes of Q1, Q2, Q3 K047 in T K1263 2, 3, 6, 55, 956, 999, 1001, 1012 points on nK0(X6, X5275) K1264 nodal stelloid 2, 3, 1340, 1341, 5657, 20481, 22712 points on nK0(X6, X7736) K1265*T K1265 nodal 2, 3, 55, 574 CircumTangential triangle K1264*T K1266 2, 3, 154, 3357, 9756 CircumTangential triangle K581*T K1329 2, 3, 61, 62, 15687, 39162, 39163, 39164, 39165, 50859, 50860, 55038, 55039 K1332*T K1330 2, 3, 371, 372, 3167, 3543, 39162, 39163, 39164, 39165, 47391, 55040, 55041 K1331*T K1331 2, 3, 20, 6200, 6396, 13712, 13835, 39162, 39163, 39164, 39165 points on nK0(X6, X7735) K1330*T K1332 2, 3, 550, 10645, 10646, 39162, 39163, 39164, 39165, 49901, 49902 points on nK0(X6, X5306) K1329*T K1333 2, 3, 99, 187, 574, 11676, 39162, 39163, 39164, 39165 points on nK0(X6, X385) = K017 K1334 2, 3, 3098, 5092, 7470, 39162, 39163, 39164, 39165
 Note 1 : K609 meets (O) again at three points (other than X74) on a rectangular hyperbola which is the image of the Jerabek hyperbola under the translation that maps H onto O. Note 2 : Any pK (blue cells) passing through Q1, Q2, Q3 must have its pole on K346, its pivot on K002, its isopivot on K172. Note 3 : spK(P, Q = midpoint of G,P) (yellow cells) passes through Q1, Q2, Q3, G, P*, the infinite points of pK(X6, P), the foci of the inconic with center Q. See CL055. Note 4 : X(39162), X(39163), X(39164), X(39165) are the foci of the Steiner inellipse.
 Higher degree curves Qnnn* is the isogonal transform of Qnnn with respect to ABC.
 curve type Xi on the curve for i = remarks Q002 circular quartic 1, 3, 6, 15, 16, 358, 1135, 1137, 1155, 2574, 2575, 10221 Q003* Q011 symgonal circular quintic 3, 1145, 1312, 1313, 1511, 2028, 2029, 2446, 2447, 5976 Q037 inversible bicircular quintic 1, 3, 15, 16, 30, 36, 5000, 5001 Q030* Q062 quartic 2, 6, 523 Q067 bicircular quintic 1, 3, 15, 16, 30 Q068 circular equilateral quintic 1, 3, 164, 399, 2448, 2449 Q069 circular quintic 1, 3 Q071 bicircular quintic 3, 30, 187, 468, 1155, 1319 Q001* Q076 sextic 1, 2, 6, 13, 14, 15, 16, 110, 523 Q090 nodal quartic 2, 6, 15, 16, 55, 385, 672, 5638, 5639 Q012* Q091 quintic 1, 3, 5373 Q095 quintic 2, 13, 14, 99 Q097 bicircular quintic 3, 15, 16, 36, 55, 187 Q096* Q098 inversible circular quartic 3, 6, 187, 2574, 2575, 3513, 3514, 5000, 5001 Q044* Q101 unicursal quartic 6, 325, 1515, 2574, 2575, 8779 Q113 circular quartic 1, 3, 6, 64, 2574, 2575, 5373 Q063* Q118 circular quartic 2, 376, 3413, 3414, 5000, 5001 Q136 circular quartic 3, 4, 6, 15, 16, 23, 2574, 2575, 7712 Q050* Q137 circular quartic 3, 6, 15, 16, 2574, 2575 Q135* Q178 circular quintic 2, 165, 376, 1113, 1114, 5463, 5464, 11228