On f-vectors of Minkowski additions of convex polytopes

Details On f-vectors of Minkowski additions of convex polytopes On f-vectors of Minkowski additions of convex polytopes

2005-10-21

arxiv.org/abs/math/0510470v4

Discrete & Computational Geometry, vol. 37 (2007), pp. 503-516

Mathematics

Combinatorics

13 pages, submitted to Discrete & Computational Geometry

Scientific paper

10.1007/s00454-007-1310-2

The objective of this paper is to present two types of results on Minkowski sums of convex polytopes. The first is about a special class of polytopes we call perfectly centered and the combinatorial properties of the Minkowski sum with their own dual. In particular, we have a characterization of face lattice of the sum in terms of the face lattice of a given perfectly centered polytope. Exact face counting formulas are then obtained for perfectly centered simplices and hypercubes. The second type of results concerns tight upper bounds for the f-vectors of Minkowski sums of several polytopes.

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