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A number of attractive tetrahedron 10-compounds can be constructed. The first (left figures) can be obtained by combining tetrahedron 5-compounds of opposite chirality ...

There are a number of attractive cube 25-compounds. One can be constructed from the vertices of the second dodecahedron 6-compound (or second tetrahedron 50-compound) and ...

A number of attractive 6-compounds of the regular dodecahedron can be constructed. The first (left figures) can be obtained by combining six dodecahedra, each rotated by 1/10 ...

The insphere of a solid is a sphere that is tangent to all faces of the solid. An insphere does not always exist, but when it does, its radius r is called the inradius and ...

A symbol of the form {p,q,r,...} used to describe regular polygons, polyhedra, and their higher-dimensional counterparts. The symbol {p} denotes a regular polygon for integer ...

A closed three-dimensional figure (which may, according to some terminology conventions, be self-intersecting). Kern and Bland (1948, p. 18) define a solid as any limited ...

A number of attractive 12-compounds of the regular tetrahedron can be constructed. The compounds illustrated above will be implemented in a future version of the Wolfram ...

An attractive compound of three regular tetrahedra can be obtained by taking three tetrahedra with a C_2 axes aligned along the z-axis and rotating them a sixth of a turn ...

The Platonic solids, also called the regular solids or regular polyhedra, are convex polyhedra with equivalent faces composed of congruent convex regular polygons. There are ...

Construct a square equal in area to a circle using only a straightedge and compass. This was one of the three geometric problems of antiquity, and was perhaps first attempted ...