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The 13 Archimedean solids are the convex polyhedra that have a similar arrangement of nonintersecting regular convex polygons of two or more different types arranged in the ...

Any set of n+2 points in R^n can always be partitioned in two subsets V_1 and V_2 such that the convex hulls of V_1 and V_2 intersect.

The small cubicuboctahedron is the uniform polyhedron with Maeder index 13 (Maeder 1997), Wenninger index 69 (Wenninger 1989), Coxeter index 38 (Coxeter et al. 1954), and ...

The dodecahedron-small triambic icosahedron compound is a stellated form of a truncated icosahedron, but a different truncation than in the truncated icosahedron Archimedean ...

The regular dodecahedron, often simply called "the" dodecahedron, is the Platonic solid composed of 20 polyhedron vertices, 30 polyhedron edges, and 12 pentagonal faces, ...

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).

A convex set K is centro-symmetric, sometimes also called centrally symmetric, if it has a center p that bisects every chord of K through p.

A pyramid with a heptagonal base. The heptagonal pyramid is one of the 257 convex octahedra.