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A convex polyhedron is defined as the set of solutions to a system of linear inequalities mx<=b (i.e., a matrix inequality), where m is a real s×d matrix and b is a real ...

An unfolding is the cutting along edges and flattening out of a polyhedron to form a net. Determining how to unfold a polyhedron into a net is tricky. For example, cuts ...

The cube-octahedron 20-compounds are polyhedron compounds of the cube 20-compound and its dual, the octahedron 20-compound.

The pentagrammic deltohedron (Har'El 1993) is the dual polyhedron of the pentagrammic antiprism U_(79).

The dual polyhedron of the small dodecicosahedron U_(50) and Wenninger dual W_(90).

Generally, a face is a component polygon, polyhedron, or polytope. A two-dimensional face thus has vertices and edges, and can be used to make cells. More formally, a face is ...

Alexandrov's theorem addresses conditions under which a polygon will fold into a convex polyhedron (Malkevitch).

Spherical triangles into which a sphere is divided by the planes of symmetry of a uniform polyhedron.

An assemblage of faces forming a polyhedron of zero volume (Holden 1991, p. 124).

A trapezohedron that is the dual polyhedron of the pentagonal antiprism U_(77). It is also (confusingly) known as the pentagonal deltohedron.