The Grebe triangle is defined and studied here. This page is only a compilation of various cubics and higher degree curves passing through its vertices G1, G2, G3 and other remarkable points.
 Cubics c denotes a circum-cubic, otherwise the three remaining points on the circumcircle (O) are mentioned. Knnn* and Knnn*G denote the isogonal transforms of Knnn with respect to ABC and the Grebe triangle respectively.
 cubic type Xi on the cubic for i = points on (O) remarks K102 c isogonal pK 1, 2, 6, 43, 87, 194, 3224, 15963, 15964, 15965, 15966, 15967, 15968, 39641, 39642, 40139 K138 equilateral 2, 6, 5652, 14898, 14899, 35607, 35608, 35609 Thomson triangle K177 c pK 2, 3, 6, 25, 32, 66, 206, 1676, 1677, 3162, 19615, 41378, 41379, 52041 K141* K281 c spK, nodal 2, 6, 182, 996, 1001, 1344, 1345, 4846, 5967, 10002, 14356, 14609, 18775, 45998, 46023, 46024, 51510 K280* K642 c isog. pK wrt G1G2G3 4, 206, 1676, 1677 K643 c spK, stelloid 4, 6, 4846, 8743, 39641, 39642 see note 2 K644 c pK 2, 4, 6, 83, 251, 1176, 1342, 1343, 8743, 40357, 40358, 40404 K836* K729 c spK 2, 6, 1383, 39162, 39163, 39164, 39165, 51797 K287* K731 c spK 6, 83, 39641, 39642 K835 c spK 3, 4, 6, 32, 1995, 3425, 8743, 14356 K527* K1161 stelloid 3, 6, 40122 CircumTangential triangle K1241 central 3, 5, 182, 206, 5092, 44882, 44883, 44884, 44885 antipodes G1, G2, G3 K644*G K1249 2, 3, 22, 7712, 46264 antipodes of (O) ∩ K006 K1286 focal 2, 3, 23, 110, 182, 187, 353, 9829, 11645, 15080, 39162, 39163, 39164, 39165, 51797, 51798, 51799, 51800 X(110), J1, J2 K1292 stelloid 1, 6, 20, 194, 35237, 46264 antipodes of (O) ∩ K006 K1291*G K1317 c 2, 4, 32, 194, 1340, 1341, 1383, 9463, 14609, 45096, 52672, 52765 K1316 c spK+ 1, 6, 996 see note 2 c spK+ 6, 194, 3224 see note 2
 Note 1 : a pK passes through G1, G2, G3 if and only if its pole, pivot, isopivot lie on K1258 = pK(X251 x X32, X251), K644, K177 respectively. Note 2 : any spK(P, Q = midpoint of X6,P) passes through G1, G2, G3 and X6. It also contains the infinite points of pK(X6, P) and the foci of the inconic with center Q. Its isogonal transform is spK(X6, Q). See CL055. This spK passes through P when P lies on the Grebe cubic K102. This spK is a K+ if and only if P lies on the circular cubic K837 passing through X(1), X(3), X(147), X(194), X(511), X(2930), X(7772). K643 is the most remarkable example obtained with P = X(3). Two other spK+ are listed with P = X(1), X(194), two points on K102.
 Higher degree curves Q019 = Q094*, Q138, Q142, Q144, Q158 = Q157*.