Cephoids: Minkowski sums of de Gua simplexes
Within this article we discuss the structure of those polytopes in [image omitted] 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 Plucker (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.
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