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Abstract
Within this article we discuss the structure of those polytopes in which are Minkowski sums of de Gua simplexes. A de Gua simplex is the convex hull of the origin and n positive multiples of the unit vectors (see [J.J. Gray, Algebra in geometry from Newton to Plücker (German), Math. Semesterberichte 36 (1989), pp. 175–204.]). We characterize these polytopes by describing the shape of their (outward) faces. Given some notion of ‘nondegeneracy’ or ‘general position’ for our polytopes, we present a recursive procedure that yields all maximal faces. Also, we derive a formula indicating the number of maximal faces, which depends on the dimension and the number of de Gua simplexes involved only.
Acknowledgements
The authors would like to thank Oliver Mayer, University of Karlsruhe (SMW) for a hint in finding the explicit solution of the difference equation (Equation51) and two anonymious referees for their insightful comments on the first draft of this article. Their suggestions led to a substantial improvement of the article.