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Polar Zonohedron


PolarZonohedron

A polar zonohedron is a convex zonohedron derived from the star which joins opposite vertices of any right n-gonal prism (for n even) or antiprism (for n odd). The faces of this zonohedron consist of n equal rhombs surrounding one vertex, n rhombs beyond these, and so on, giving n-1 sets of n 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.

As n->infty, the polar zonohedron of order n approaches a solid of revolution created by rotation of a sine curve (Chilton and Coxeter 1963, Towle 1996).


See also

Cube, Equilateral Zonohedron, Isozonohedron, Rhombic Dodecahedron, Rhombic Icosahedron, Zonohedron

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References

Coxeter, H. S. M. Regular Polytopes, 3rd ed. New York: Dover, p. 29, 1973.Chilton, B. L. and Coxeter, H. S. M. "Polar Zonohedra." Amer. Math. Monthly 70, 946-951, 1963.Franklin, C. H. H. "Hypersolid Concepts, and the Completeness of Things and Phenomena." Math. Gaz. 21, 360-364, 1937.Towle, R. "Graphics Gallery: Polar Zonohedra." Mathematica J. 6, 8-12, 1996. http://library.wolfram.com/infocenter/Articles/3335/.

Referenced on Wolfram|Alpha

Polar Zonohedron

Cite this as:

Weisstein, Eric W. "Polar Zonohedron." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PolarZonohedron.html

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