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The line segment connecting opposite polyhedron vertices (i.e., two polyhedron vertices which do not share a common face) in a parallelepiped or other similar solid. Also ...

A formula relating the number of polyhedron vertices V, faces F, and polyhedron edges E of a simply connected (i.e., genus 0) polyhedron (or polygon). It was discovered ...

A graph G is the edge graph of a polyhedron iff G is a simple planar graph which is 3-connected.

The truncated pentakis dodecahedron is a polyhedron on 180 vertices, 270 edges, and 92 faces. Its canonical polyhedron has edges of three different lengths and faces ...

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 ...

Marsaglia (1972) has given a simple method for selecting points with a uniform distribution on the surface of a 4-sphere. This is accomplished by picking two pairs of points ...

The Schmitt-Conway biprism is a convex polyhedron found to be only aperiodically space-filling by Conway in 1993.

Dini's theorem is a result in real analysis relating pointwise convergence of sequences of functions to uniform convergence on a closed interval. For an increasing sequence ...

Let sum_(n=1)^(infty)u_n(x) be a series of functions all defined for a set E of values of x. If there is a convergent series of constants sum_(n=1)^inftyM_n, such that ...

The elongated dodecahedron, also known as the extended rhombic dodecahedron and rhombo-hexagonal dodecahedron, is a space-filling polyhedron and primary parallelohedron ...