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On f-vectors of Minkowski additions of convex polytopes

Komei Fukuda·Christophe Weibel
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Abstract

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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Komei Fukuda, Christophe Weibel. 2006-11-02. On f-vectors of Minkowski additions of convex polytopes. https://doi.org/10.1007/s00454-007-1310-2

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