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Abstract: : We use Mathematica to construct zonotopes and display zonohedra. *Work supported in part by NSF grant CCR-9258355 and by matching funds from Xerox corp. Introduction A zonotope is a set of points in d-dimensional space constructed by the sum of scaled vectors a[[i]] v[[i]] where a[[i]] is a scalar between 0 and 1 and v[[i]] is a d-dimensional vector. Alternately it can be viewed as a Minkowski sum of line segments connecting the origin to the endpoint of each vector. It is called a... (Update)
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...then P n i=1 S i is a parallelepiped for n = d, and a zonotope for n d. This is in fact the definition of a zonotope ; see e.g. [6, 8]) The Minkowski sum of line sets above may be written as a linear transformation of a product set, a format which turns out to be both...
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BibTeX entry: (Update)
David Eppstein. Zonohedra and zonotopes. http://www.ics.uci.edu/ eppstein/junkyard/ ukraine/ukraine.html. http://citeseer.ist.psu.edu/254929.html More
@techreport{ eppstein95zonohedra,
author = "David Eppstein",
title = "Zonohedra and Zonotopes",
number = "ICS-TR-95-53",
pages = "22",
year = "1995",
url = "citeseer.ist.psu.edu/254929.html" }
Citations (may not include all citations):97 Lectures on Polytopes - Ziegler - 1995
62 Regular Polytopes (context) - Coxeter - 1973
9 The centroid of points with approximate weights - Bern, Eppstein et al. - 1995
7 The Penguin Dictionary of Curious and Interesting Geometry (context) - Wells - 1995
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