A zonotope is a polytope which can be obtained as the Minkowski sum (http://planetmath.org/MinkowskiSum3) of finitely many closed line segments in . 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 -cube is the Minkowski sum of the line segments from the origin to the standard unit vectors for . A hexagon is also a zonotope; for example, the Minkowski sum of the line segments based at the origin with endpoints at , , and is a hexagon. In fact, any projection of an -cube is a zonotope.
- 1 Billera, L., R. Ehrenborg, and M. Readdy, The -index of zonotopes and arrangements, in Mathematical essays in honor of Gian-Carlo Rota, (B. E. Sagan and R. P. Stanley, eds.), BirkhÃÂ¤user, Boston, 1998, pp. 23–40.
- 2 Ziegler, G., Lectures on polytopes, Springer-Verlag, 1997.
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