@MISC{Eppstein95zonohedraand, author = {David Eppstein}, title = {Zonohedra and Zonotopes}, year = {1995} }

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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 zonotope because the faces parallel to each vector form a so-called zone wrapping around the polytope. A zonohedron is just a three-dimensional zonotope. This notebook contains code for constructing zonotopes and displaying zonohedra. There is some confusion in the definition of zonotopes; Wells [W91] requires the generating vectors to be in general position (all d-tuples of vectors must span the whole space), so that all the faces of the zonotope are parallelotopes. Others [BEG95,Z95] do not make this ...