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The polyhedron compound of the truncated icosahedron and its dual, the pentakis dodecahedron. The compound can be constructed from a truncated icosahedron of unit edge length ...

Consider any star of n line segments through one point in space such that no three lines are coplanar. Then there exists a polyhedron, known as a zonohedron, whose faces ...

A decahedron is a polyhedron having 10 faces. Examples include the 5-trapezohedron, augmented pentagonal prism (Johnson solid J_(52)), augmented tridiminished icosahedron ...

A pentahedron is polyhedron having five faces. Because there are two pentahedral graphs, there are two convex pentahedra, corresponding to the topologies of the square ...

The harmonic parameter of a polyhedron is the weighted mean of the distances d_i from a fixed interior point to the faces, where the weights are the areas A_i of the faces, ...

The disdyakis triacontahedron is the dual polyhedron of the Archimedean great rhombicosidodecahedron A_2. It is also known as the hexakis icosahedron (Holden 1971, p. 55). It ...

Shephard's conjecture states that every convex polyhedron admits a self-unoverlapping unfolding (Shephard 1975). This question is still unsettled (Malkevitch), though most ...

The great dodecahedron is the Kepler-Poinsot polyhedron whose dual is the small stellated dodecahedron. It is also uniform polyhedron with Maeder index 35 (Maeder 1997), ...

The ten-of-diamonds decahedron is a stereohedron and space-filling polyhedron on 8 vertices, 16 edges, and 10 faces (8 of which are non-equilateral triangles and two of which ...

The stella octangula is a polyhedron compound composed of a tetrahedron and its dual (a second tetrahedron rotated 180 degrees with respect to the first). The stella ...