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 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.
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Fukuda, K., Weibel, C. f-Vectors of Minkowski Additions of Convex Polytopes. Discrete Comput Geom 37, 503–516 (2007). https://doi.org/10.1007/s00454-007-1310-2
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DOI: https://doi.org/10.1007/s00454-007-1310-2