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An isosceles tetrahedron is a nonregular tetrahedron in which each pair of opposite polyhedron edges are equal, i.e., a^'=a, b^'=b, and c^'=c, so that all triangular faces ...

A line segment connecting nonadjacent polyhedron vertices sharing a common face in a parallelepiped or other similar solid.

A hexahedron is a polyhedron with six faces. The figure above shows a number of named hexahedra, in particular the acute golden rhombohedron, cube, cuboid, hemicube, ...

The gyrobifastigium is an octahedron with on 8 vertices, 14 edges, and 8 faces. The equilateral gyrobifastigium is Johnson solid J_(26), consisting of two triangular prisms ...

The skeleton graphs of the Johnson solids are polyhedral graphs. The Johnson skeleton graphs J_3 and J_(63) are minimal unit-distance forbidden graphs. The skeleton of the ...

A rotor is a convex figure that can be rotated inside a polygon (or polyhedron) while always touching every side (or face). The least area rotor in a square is the Reuleaux ...

There are several attractive polyhedron compounds consisting of three cubes. The first (left figures) arises by joining three cubes such that each shares two C_2 axes (Holden ...

The (small) rhombicosidodecahedron (Cundy and Rowlett 1989, p. 111), sometimes simply called the rhombicosidodecahedron (Maeder 1997; Wenninger 1989, p. 27; Conway et al. ...

The small triambic icosahedron is the dual polyhedron of the small ditrigonal icosidodecahedron with Maeder index 30 (Maeder 1997), Weinninger index 70 (Wenninger 1971, p. ...

An n-trapezohedron, also called an antidipyramid, antibipyramid, or deltohedron (not to be confused with a deltahedron), is a solid composed of interleaved symmetric ...