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Given triangle DeltaA_1A_2A_3, let the point of intersection of A_2Omega and A_3Omega^' be B_1, where Omega and Omega^' are the Brocard points, and similarly define B_2 and ...

Given a point P and a triangle DeltaABC, the Cevian triangle DeltaA^'B^'C^' is defined as the triangle composed of the endpoints of the cevians though the Cevian point P. A ...

The cube-octahedron compound is a polyhedron compound composed of a cube and its dual polyhedron, the octahedron. It is implemented in the Wolfram Language as ...

A special case of Apollonius' problem requiring the determination of a circle touching three mutually tangent circles (also called the kissing circles problem). There are two ...

Bezdek and Kuperberg (1991) have constructed packings of identical ellipsoids of densities arbitrarily close to ((24sqrt(2)-6sqrt(3)-2pi)pi)/(72)=0.753355... (OEIS A093824), ...

The locus of the centers of all circumconics that also pass through the orthocenter of a triangle (which, when not degenerate, are rectangular hyperbolas) is a circle through ...

The regular tessellation {6,3} consisting of regular hexagons (i.e., a hexagonal grid). In general, the term honeycomb is used to refer to a tessellation in n dimensions for ...

The hyperbolic octahedron is a hyperbolic version of the Euclidean octahedron, which is a special case of the astroidal ellipsoid with a=b=c=1. It is given by the parametric ...

Given a circle C with center O and radius k, then two points P and Q are inverse with respect to C if OP·OQ=k^2. If P describes a curve C_1, then Q describes a curve C_2 ...

The octahedral equation, by way of analogy with the icosahedral equation, is a set of related equations derived from the projective geometry of the octahedron. Consider an ...