   A cubic is a member of the Steiner net when it is a circum-cubic passing through the (four) foci of the Steiner inscribed ellipse, the in-conic with center the centroid G of ABC. These foci are X{39162, 39163, 39164, 39165} in ETC. Any such cubic is a spK(P, G) for some P. See CL055 for general properties of these cubics and their construction. The following table gives a selection of spK(P, G) according to P.  P spK(P, G) type centers and/or remark X(2) K002 pK the only pK of the net X(524) K018 nK0 focal orthopivotal cubic X(519) K086 nK strophoid X(30) K187 nK focal cubic X(538) K248 nK focal cubic X(6) K287 K0 central cubic, center G, isogonal transform of K729 X(527) K352 nK focal cubic X(385) K353 K0 isogonal transform of K705 X(3) K358 - stelloid, the only K60 of the net X(7840) K705 K0 isogonal transform of K353 X(3543) K706 - central cubic, center O, isogonal transform of K847 X(599) K729 K0 isogonal transform of K287 X(3524) K812 - X(3), X(4), X(3531), X(3545) X(20) K847 - isogonal transform of K706 X(323) K0 X(2), X(6), X(186), X(381), X(1989) X(381) - isogonal transform of K358, a circumnormal cubic X(671) nK X(99), X(187), X(1379), X(1380) X(1121) nK X(101), X(664), X(1055), X(1323)   Notes : • spK(P, G) is circular if and only if P lies at infinity, giving a pencil of focal nKs with root G, focus F on (O), see yellow lines. • spK(P, G) is also a nK when P lies on the Steiner (circum) ellipse in which case its root lies on this same ellipse and the pole on K229. Two examples are given in the pink lines. • spK(P, G) is a K0 if and only if P lies on the line GK in which case it contains G and K, see red points P in the table. These cubics are in a same pencil of K0s, stable under isogonal conjugation, generated by K002 and K018 which are the only two self-isogonal cubics. • if P1 and P2 are symmetric about G, then the cubics spK(P1, G) and spK(P2, G) are swapped under isogonal conjugation. They meet again at two isogonal conjugate points on K002 hence collinear with G.    Other cubics passing through the foci of the Steiner inscribed ellipse These cubics are not circum-cubics of ABC but, in some cases, they are circum-cubics of some other triangle. Those in the orange cells are circum-cubics of the Thomson triangle (T) and pass through G and K. They form a pencil which contains the Thomson cubic K002. The remaining points on (O) lie on a nK0(X6, R on GK) and the tangents at these points concur on a hyperbola passing through {2, 6, 110}. Those in the blue cells are focal cubics with singular focus F on the circle passing through {2, 3, 110, 842, 8724, 14649, 14685, 34291, 35911}, with center X(44814), which is the (O)-inverse of the line {23,110} ans the Psi-image of the line {3,74}. These cubics are in a same pencil of circular cubics passing through X(2), X(3), X(110). They are Psi-invariant, see at the bottom of Table 60. Every such focal cubic meets the circumcircle (O) again at three points on an isogonal pK with pivot on the line GK. Those in the green cells are focal cubics with singular focus F on the Fermat axis and same orthic line, namely the Euler line. These cubics are in a same pencil of circular cubics passing through X(30), X(31862), X(31863). The latter two points lie on the Fermat axis. The red cubics are also in a same pencil of focal cubics with singular focus F on the line {3, 74, 110, 156, 246, 399, 1511, 1614, 2972, 3470, 5191, 5609, etc} which contains the circum-cubic K187 and the decomposed cubic, union of the line at infinity and the rectangular hyperbola with center G, passing through {3, 6, 381, 599, 2574, 2575} and the four foci of inSteiner. This hyperbola is the polar conic of X(30) in K003, of X(3) in K005 , of X(6) in K018. Every cubic of the pencil passes through X(30) and O, with tangent the line {3, 74, etc}, and orthic line the Euler line, except K038 which has a node at O. The blue cubics are in a same pencil of stelloids with radial center X on the Euler line, which also contains the decomposed cubic above and the circum-cubic K358. Every cubic contains O, X(381) and the infinite points of the McCay cubic K003.  cubic type centers 39162, 39163, 39164, 39165 and ... / remark K038 strophoid, F = X(14685) 3, 30, 36, 131, 187, 1511, 2482, 3184, 6150, 6592, 12095, 12096, 17729, 35204, 39987, 47077, 47078, 47079, 47080, 47081, 47082, 47083, 47084, 47085, 47086, 47087, 47088, 47089, 50388, 50389, midpoints of ABC K463 focal, F = X(110) 2, 3, 15, 16, 30, 110, 5463, 5464 / K187 of (T) / (O) ∩ K002 K727 pK in CircumTangential triangle 2, 3, 7712, antipoints see Table 77 / isogonal transform of K833 wrt (T) K758 central, center O 2, 3, 154, 165, 376, 3576, 10606, midpoints of (T) / isogonal transform of K002 wrt (T) K800 focal, F = X(399) 1, 3, 5, 30, 191, 399, 5127, 5535, 6326, 7701, 13513, 18865, 31862, 31863, 39229, 39230, 40851, 40852, excenters of ABC K816 focal, F = X(14685) 2, 3, 4, 74, 110, 125, 131, 541, 11472, 14685 / (O) ∩ K1169 K833 central stelloid, X = X(2) 2, 3, 381, 39641, 39642 / isogonal transform of K727 wrt (T) / (L∞) ∩ K003 K893 focal, F = X(3) 2, 3, 6, 110, 111, 542, 2482, 14916 / (O) ∩ K1156 K911 stelloid, X = X(5054) 1, 3, 381, 1340, 1341, 3576, excenters of ABC / (L∞) ∩ K003 K1092 focal, F = X(6) 6, 30, 1379, 1380, 5000, 5001, 11472, 13872, 16303, 31862, 31863 K1259 K006 of (T) 2, 3, 5373, 11472 K1275 strophoid, F = X(28662) 6, 115, 187, 524, 5526, 9721, 16303, 28662, 44909, 48653, 48654, 48721, 50536 K1286 focal, F = X(51800) 2, 3, 23, 110, 182, 187, 353, 9829, 11645, 15080, 51797, 51798, 51799, 51800 / (O) ∩ K102 K1288 focal, F = X(113) 30, 113, 2043, 2044, 31862, 31863, 47084 K1289 central focal, F = X(381) 30, 381, 31862, 31863, 51825, 51826 K1293 central, center O 1, 3, 40, 2043, 2044, 11472, 35237, 45633, 52050, 52051, 52052, 52053, 52054, excenters of ABC / (L∞) ∩ K243 K1294 central, center O 3, 30, 1379, 1380 / (L∞) ∩ K001 K1295 focal, F = X(8724) 2, 3, 110, 352, 511, 574, 599, 7998, 8724, 10717, 10989, 11178 / (O) ∩ pK(X6, X599) K1296 focal, F = Psi(X399) 2, 3, 5, 13, 14, 110, 399, 3448, 6592 / (O) ∩ pK(X6, X37779)    