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).
