Polar zonohedra are convex polyhedra bounded by n*(n-1) rhombs, where n is an
integer greater than two. Attached, a zipped archive containing two macros and
a scene file which shows their use.

The two most important parameters or whatever one would call them, are "n" as
defined above, and what I call pitch, a carpentry term applied to the slope of
a rafter. Pitch can be anything from 0 degrees to 90 degrees, although both 0
and 90 give "degenerate" polar zonohedra. It is interesting that when pitch
equals 35.26+ degrees, or arc tan sqrt[ 1/2 ], a polar zonohedron is an
orthogonal and isometric shadow of an n-dimensional cube, a solid shadow, cast
into three dimensions. When pitch is low, polar zonohedra are oblate and like
flying saucers; when pitch is high, polar zonohedra are prolate and like
spindles. If edge length is held fixed and one sends a polar zonohedron through
the whole range of pitch, it has maximal volume if and only if it is an
orthogonal shadow of an n-cube, i.e., when pitch equals arc tan sqrt[ 1/2 ].

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Attachments:
Download 'pov pz macro.zip' (4 KB)