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A zonohedron is a convex polyhedron where every face is a polygon with point symmetry, or equivalently, symmetry under rotations through 180°. The regular polygons with such symmetry are those with an even number of sides, so the zonohedra with regular polygons for sides are easily enumerated:

Of the Platonic solids, only the cube is a zonohedron
Of the Archimedean solids, only the truncated octahedron, the truncated cuboctahedron and the truncated icosidodecahedron are zonohedra.
Prisms, where the base is a regular polygon with an even number of sides and the sides are squares give an infinite family of vertex-regular zonohedra.

Two other significant zonohedra occur amongst the duals of the Archimedean solids, these being the rhombic dodecahedron and the rhombic triacontahedron.

Mathematically, the zonohedra can be characterised as being the Minkowski sums of line segments, and this characterisation allows the definition to be generalised to higher dimensions, giving zonotopes.

External links

Geometry Junkyard Zonohedron page: http://www.ics.uci.edu/~eppstein/junkyard/zono.html

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