zonotope

A zonotope is a polytope which can be obtained as theMinkowski sum (http://planetmath.org/MinkowskiSum3) of finitely manyclosed line segments in ${ℝ}^n$. Three-dimensional zonotopes are also sometimes called zonohedra. Zonotopes are dual to finite hyperplane arrangements. They are centrally symmetric, compact, convex sets.

For example, the unit $n$-cube is the Minkowski sum ofthe line segments from the origin to the standard unit vectors $e_i$for $1\le i\le n$.A hexagon is also a zonotope; for example, the Minkowskisum of the line segments based at the origin with endpoints at $(1,0)$, $(1,1)$, and $(0,1)$ is a hexagon. In fact, any projection of an $n$-cube is a zonotope.

The prism of a zonotope is always a zonotope, but the pyramid of azonotope need not be. In particular, the$n$-simplex (http://planetmath.org/HomologyTopologicalSpace) is only azonotope for $n\le 1$.