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).
