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Polytopes which are orthogonal projections of regular simplexes

✍ Scribed by Toshio Kawashima

Publisher
Springer
Year
1991
Tongue
English
Weight
422 KB
Volume
38
Category
Article
ISSN
0046-5755

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✦ Synopsis

We consider the polytopes which are certain orthogonal projections of k-dimensional regular simplexes in k-dimensional Euclidean space R k. We call such polytopes r~-polytopes. Every sufficiently symmetric polytope, such as a regular polytope, a quasi-regular polyhedron, etc., belongs to this class. We denote by Pm,~ all n-dimensional n-polytopes with m vertices. We show that there is a one-to-one correspondence between the elements of Pm.n and those of P,n,m-n-1 and that this correspondence preserves the symmetry of 7r-polytopes. Using this duality, we determine some of the Pm,.'s. We also show that a 7r-polytope is an orthogonal projection of a cross polytope if and only if it has central symmetry.

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