A zonohedron is a convexpolyhedron 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:
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.
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.
Any zonohedron may equivalently be described as the Minkowski sum of a set of line segments in three-dimensional space, or as the three-dimensional projection of a hypercube.
Each edge in a zonohedron is parallel to at least one of the generators, and has length equal to the sum of the lengths of the generators to which it is parallel.
Thus, the edges of the zonohedron can be grouped into zones of parallel edges, which correspond to the segments of a common great circle on the Gauss map, and the 1-skeleton of the zonohedron can be viewed as the planar dual graph to an arrangement of great circles on the sphere.
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