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A planar polygon is convex if it contains all the line segments connecting any pair of its points. Thus, for example, a regular pentagon is convex (left figure), while an ...

The kissing number of a sphere is 12. This led Fejes Tóth (1943) to conjecture that in any unit sphere packing, the volume of any Voronoi cell around any sphere is at least ...

The endodocehedron, also called the concave pyrohedral dodecahedron, is the concave solid corresponding to the interior void formed when each face of a regular dodecahedron ...

The isoperimetric quotient of a closed curve is defined as the ratio of the curve area to the area of a circle (A=pir_A^2) with same perimeter (p=2pir_p) as the curve, Q = ...

The Dejter graph is a weakly regular graph on 112 vertices and 336 edges with regular paremeters (nu,k,lambda,mu)=(112,6,0,(0,1,2)). It can be obtained by deleting a copy of ...

A cube 13-compound can be constructed as the dual of the octahedron 13-compound. It will be implemented in a future version of the Wolfram Language as ...

A cube 9-compound can be constructed from the vertices of the first dodecahedron 2-compound. It will be implemented in a future version of the Wolfram Language as ...

The Ivanov-Ivanov-Faradjev graph is a distance-regular graph on 990 vertices (Brouwer et al. 1989, p. 369). It has intersection array {7,6,4,4,4,1,1,1;1,1,1,2,4,4,6,7} and is ...

The great icosahedron, not to be confused with the great icosidodecahedron orgreat icosicosidodecahedron, is the Kepler-Poinsot polyhedronhose dual is the great stellated ...

The dodecahedron-icosahedron compound is a polyhedron compound consisting of a dodecahedron and its dual the icosahedron. In the compound, the dodecahedron and icosahedron ...