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The Eberlein polynomials of degree 2k and variable x are the orthogonal polynomials arising in the Johnson scheme that may be defined by E_k^((n,v))(x) = ...

The augmented tridiminished icosahedron is Johnson solid J_(64), which is formed from augmentation of the triangular face adjecent to all three hexagons of the tridiminished ...

Let O and I be the circumcenter and incenter of a triangle with circumradius R and inradius r. Let d be the distance between O and I. Then d^2=R(R-2r) (Mackay 1886-1887; ...

A geometric construction, also called a verging construction, which allows the classical geometric construction rules to be bent in order to permit sliding of a marked ruler. ...

A bicentric quadrilateral, also called a cyclic-inscriptable quadrilateral, is a four-sided bicentric polygon. The inradius r, circumradius R, and offset x are connected by ...

The biaugmented pentagonal prism is Johnson solid J_(53), which is formed from double augmentation of two nonadjacent lateral faces of the equilateral pentagonal prism by an ...

An n-gonal pyramid adjoined to the top of an n-gonal antiprism. In the 3-gonal gyroelongated pyramid, the pyramid and lateral antiprism are coplanar. However, the 4-gonal and ...

The Simson line is the line containing the feet P_1, P_2, and P_3 of the perpendiculars from an arbitrary point P on the circumcircle of a triangle to the sides or their ...

The geometric centroid (center of mass) of the polygon vertices of a triangle is the point G (sometimes also denoted M) which is also the intersection of the triangle's three ...

The augmented truncated tetrahedron is Johnson solid J_(66) constructed by affixing a square cupola to one of the octagonal faces of a truncated cube such that the cupola's ...