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A polyhedron dissection (or decomposition) is a dissection of one or more polyhedra into other shapes. Two polyhedra can be dissected into each other iff they have equal Dehn ...

In general, a triakis octahedron is a non-regular icositetrahedron that can be constructed as a positive augmentation of regular octahedron. Such a solid is also known as a ...

The cube is the Platonic solid composed of six square faces that meet each other at right angles and has eight vertices and 12 edges. It is also the uniform polyhedron with ...

There are a number of attractive compounds of two regular tetrahedra. The most symmetrical is the arrangement whose outer hull is the stella octangula (left figure), while ...

Goldberg polyhedra are convex polyhedra first described by Goldberg (1937) and classified in more detail by Hart (2013) for which each face is a regular pentagon or regular ...

An equilateral zonohedron is a zonohedron in which the line segments of the star on which it is based are of equal length (Coxeter 1973, p. 29). Plate II (following p. 32 of ...

The pentagonal gyrocupolarotunda is a convex equilateral solid that is Johnson solid J_(33). The unit pentagonal gyrocupolarotunda has volume V=5/(12)(11+5sqrt(5)) (1) and ...

A polyhedron with extra square faces, given by the Schläfli symbol r{p; q}.

The great ditrigonal dodecicosidodecahedron is the uniform polyhedron with Maeder index 42 (Maeder 1997), Wenninger index 81 (Wenninger 1989), Coxeter index 54 (Coxeter et ...

Stellation is the process of constructing polyhedra by extending the facial planes past the polyhedron edges of a given polyhedron until they intersect (Wenninger 1989). The ...