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Let H be a heptagon with seven vertices given in cyclic order inscribed in a conic. Then the Pascal lines of the seven hexagons obtained by omitting each vertex of H in turn ...

The incentral triangle DeltaI_AI_BI_C is the Cevian triangle of a triangle DeltaABC with respect to its incenter I. It is therefore also the triangle whose vertices are ...

The inner Napoleon triangle is the triangle DeltaN_AN_BN_C formed by the centers of internally erected equilateral triangles DeltaABE_C, DeltaACE_B, and DeltaBCE_A on the ...

Let A^' be the outermost vertex of the regular pentagon erected inwards on side BC of a reference triangle DeltaABC. Similarly, define B^' and C^'. The triangle ...

The Lucas tangents triangle (a term coined here for the first time) is the triangle DeltaT_AT_BT_C formed by the pairwise tangents of the Lucas circles of a given reference ...

The Markström graph is a cubic planar graph on 24 vertices which lacks cycles of length 4 and 8 but contains cycles of length 16. (In particular, it contains cycles of ...

A maximal irredundant set is an irredundant set that cannot be expanded to another irredundant set by addition of any vertex in the graph. Note that a maximal irredundant set ...

The mid-arc triangle is the triangle DeltaA^'B^'C^' whose vertices consist of the intersections of the internal angle bisectors with the incircle, where the points of ...

Consider a convex pentagon and extend the sides to a pentagram. Externally to the pentagon, there are five triangles. Construct the five circumcircles. Each pair of adjacent ...

A noneulerian graph is a graph that is not Eulerian. The numbers of simple noneulerian graphs on n=1, 2, ... nodes are 2, 3, 10, 30, 148, 1007, 12162, 272886, ... (OEIS ...