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The word polytope is used to mean a number of related, but slightly different mathematical objects. A convex polytope may be defined as the convex hull of a finite set of ...

The necessary condition for the polychoron to be regular (with Schläfli symbol {p,q,r}) and finite is cos(pi/q)<sin(pi/p)sin(pi/r). Sufficiency can be established by ...

The rhombic triacontahedron is a zonohedron which is the dual polyhedron of the icosidodecahedron A_4 (Holden 1971, p. 55). It is Wenninger dual W_(12). It is composed of 30 ...

The detour index omega(G) of a graph G is a graph invariant defined as half the sum of all off-diagonal matrix elements of the detour matrix of G. Unless otherwise stated, ...

The word polyhedron has slightly different meanings in geometry and algebraic geometry. In geometry, a polyhedron is simply a three-dimensional solid which consists of a ...

A general n-gonal antiprism is a polyhedron consisting of identical top and bottom n-gonal faces whose periphery is bounded by a band of 2n triangles with alternating up-down ...

A Heronian triangle is a triangle having rational side lengths and rational area. The triangles are so named because such triangles are related to Heron's formula ...

An n-polyhedral graph (sometimes called a c-net) is a 3-connected simple planar graph on n nodes. Every convex polyhedron can be represented in the plane or on the surface of ...

The rhombic hexecontahedron is a 60-faced polyhedron that can be obtained by stellating the rhombic triacontahedron by placing a plane along each edge which is perpendicular ...

To pick a random point on the surface of a unit sphere, it is incorrect to select spherical coordinates theta and phi from uniform distributions theta in [0,2pi) and phi in ...