A polar zonohedron is a convex zonohedron derived from the star which joins opposite vertices of any right -gonal prism (for even) or antiprism (for odd). The faces of this zonohedron consist of equal rhombs surrounding one vertex, rhombs beyond these, and so on, giving sets of rhombs altogether that end with those surrounding the opposite vertex (Franklin 1937; Coxeter 1973, p. 29).
The following table summarizes the first few polar zonohedra.
polar zonohedron | |
3 | cube |
4 | rhombic dodecahedron |
5 | rhombic icosahedron |
As , the polar zonohedron of order approaches a solid of revolution created by rotation of a sine curve (Chilton and Coxeter 1963, Towle 1996).