A zonotope is a set of points in -dimensional space constructed from vectors by taking the sum of , where each is a scalar between 0 and 1. Different choices of scalars give different points, and the zonotope is the set of all such points. 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 (Eppstein 1996).
A three-dimensional zonotope is called a zonohedron.
There is some confusion in the definition of zonotopes (Eppstein 1996). Wells (1991, pp. 274-275) requires the generating vectors to be in general position (all -tuples of vectors must span the whole space), so that all the faces of the zonotope are parallelotopes. Others (Bern et al. 1995; Ziegler 1995, pp. 198-208; Eppstein 1996) do not make this restriction. Coxeter (1973) starts with one definition but soon switches to the other.
The combinatorics of the faces of a zonotope are equivalent to those of an arrangement of hyperplanes in a space of one fewer dimension so, for example, zonohedra correspond to planar line arrangements (Eppstein 1996).