f-vectors of Minkowski additions of convex polytopes

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 the 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.


Published in:
Discrete and Computational Geometry, 37, 4, 503-516
Year:
2007
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 Record created 2006-02-13, last modified 2018-12-03

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