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Discrete & Computational Geometry

, Volume 37, Issue 4, pp 503–516 | Cite as

f-Vectors of Minkowski Additions of Convex Polytopes

  • Komei FukudaEmail author
  • Christophe WeibelEmail author
Article

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.

Keywords

Normal Cone Discrete Comput Geom Face Lattice Convex Polytopes Moment Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer 2007

Authors and Affiliations

  1. 1.Mathematics Institute, EPFLLausanneSwitzerland

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