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The compound of a truncated tetrahedron and its dual, the triakis tetrahedron. The compound can be constructed from a truncated octahedron of unit edge length by midpoint ...

Consider a game, first proposed by Nicolaus Bernoulli, in which a player bets on how many tosses of a coin will be needed before it first turns up heads. The player pays a ...

A cube 12-compound can be constructed from the vertices of the first dodecahedron 2-compound. It will be implemented in a future version of the Wolfram Language as ...

A cube 30-compound can be constructed from the vertices of the first dodecahedron 6-compound. It will be implemented in a future version of the Wolfram Language as ...

A cube 35-compound can be constructed as the dual of the octahedron 35-compound. It will be implemented in a future version of the Wolfram Language as ...

A cube 7-compound can be constructed by combining a cube 6-compound with the original cube used to generate it. It will be implemented in a future version of the Wolfram ...

A number of attractive 10-compounds of the regular dodecahedron can be constructed. The compound illustrated above will be implemented in a future version of the Wolfram ...

A number of attractive 11-compounds of the regular dodecahedron can be constructed. The compound illustrated above will be implemented in a future version of the Wolfram ...

A number of attractive 7-compounds of the regular dodecahedron can be constructed. The compound illustrated above will be implemented in a future version of the Wolfram ...

An (n-1)-dimensional face of an n-dimensional polytope. A procedure for generating facets is known as faceting.