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A generalization of a solid such as a cube or a sphere to more than three dimensions. A four-dimensional version of a polyhedron is known as a polytope.

Cantellation, also known as (polyhedron) expansion (Stott 1910, not to be confused with general geometric expansion) is the process of radially displacing the edges or faces ...

An n-gonal cupola Q_n is a polyhedron having n obliquely oriented triangular and n rectangular faces separating an {n} and a {2n} regular polygon, each oriented horizontally. ...

A skew polygon such that every two consecutive sides (but no three) belong to a face of a regular polyhedron. Every regular polyhedron can be orthogonally projected onto a ...

A tetradecahedron is a 14-sided polyhedron, sometimes called a tetrakaidecahedron. Examples are illustrated above and summarized in the following table. name family augmented ...

An icositetrahedron is a 24-faced polyhedron. Examples include the deltoidal icositetrahedron, pentagonal icositetrahedron, small triakis octahedron, and tetrakis hexahedron.

The polyhedron resulting from letting each sphere in a sphere packing expand uniformly until it touches its neighbors on flat faces.

A geodesic dome is a triangulation of a Platonic solid or other polyhedron to produce a close approximation to a sphere (or hemisphere). The nth order geodesation operation ...

Johnson solid J_4. The bottom eight polyhedron vertices are (+/-1/2(1+sqrt(2)),+/-1/2,0),(+/-1/2,+/-1/2(1+sqrt(2)),0), and the top four polyhedron vertices are ...

There are a number of attractive polyhedron compounds consisting of five octahedra. The first octahedron 5-compound is a polyhedron compound composed of five octahedra ...