Wolfram Library Archive

All Collections Articles Books Conference Proceedings
Courseware Demos MathSource Technical Notes
Title Downloads

Zonohedral Completion

Russell Towle
Old MathSource #

Revision date


Every star of vectors which span a 3-space uniquely determine a zonohedron, and all such zonohedra may be dissected into parallelepipeds. They may just as well be constructed by parallelepipeds, or by combinations of these with parallelogramic dodecahedra, icosahedra, triacontahedra, and so on. The process of "zonohedral completion" illustrates such constructions, using convex polyhedra as input. Examples are provided using the Platonic and Archimedean solids, pyramids, prisms, antiprisms, bipyramids, and polar zonohedra. The algorithm fails at various points, and is slow. Help is needed!

*Mathematica Technology > Programming > 3D Graphics
*Mathematics > Geometry > Solid Geometry

parallelepipeds, parallelogramic dodecahedron, icosahedron, triacontahedron, Platonic and Archimedean solids, pyramids, prisms, antiprisms, bipyramids, polar zonohedron
Related items

*Elect, Bead, and Star Zonohedra   [in MathSource: Packages and Programs]
*Graphics Gallery: Polar Zonohedra   [in Articles]
*Zonohedra and Zonotopes   [in Articles]
*Zonohedrification   [in Articles]
Downloads Download Wolfram CDF Player

Zonohedral_Completion.nb (159.9 KB) - Mathematica notebook

Translate this page: