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Zonohedral Completion

Russell Towle
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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!

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

parallelepipeds, parallelogramic dodecahedron, icosahedron, triacontahedron, Platonic and Archimedean solids, pyramids, prisms, antiprisms, bipyramids, polar zonohedron
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*Elect, Bead, and Star Zonohedra   [in MathSource: Packages and Programs]
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*Zonohedrification   [in Articles]
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Zonohedral_Completion.nb (159.9 KB) - Mathematica notebook