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The (general) icosahedron is a 20-faced polyhedron (where icos- derives from the Greek word for "twenty" and -hedron comes from the Indo-European word for "seat"). Examples ...

The dual polyhedron of the rhombicosahedron U_(56) and Wenninger dual W_(96).

A coordinate system composed of intersecting surfaces. If the intersections are all at right angles, then the curvilinear coordinates are said to form an orthogonal ...

Two lines in two-dimensional Euclidean space are said to be parallel if they do not intersect. In three-dimensional Euclidean space, parallel lines not only fail to ...

If the faces of a convex polyhedron were made of metal plates and the polyhedron edges were replaced by hinges, the polyhedron would be rigid. The theorem was stated by ...

The Dehn invariant is a constant defined using the angles and edge lengths of a three-dimensional polyhedron. It is significant because it remains constant under polyhedron ...

A tiling of regular polygons (in two dimensions), polyhedra (three dimensions), or polytopes (n dimensions) is called a tessellation. Tessellations can be specified using a ...

A polyhedron compound in which the great dodecahedron is interior to its dual small stellated dodecahedron.

A bistable eight-sided polyhedron discovered by Wunderlich and Schwabe (1986).

An equilateral polygon is a polygon whose edges are all of equal length (Williams 1979, pp. 31-32). The most prominent examples of equilateral polygons are the regular ...