Random projections of regular polytopes
✍ Scribed by K. Böröczky, Jr.; M. Henk
- Publisher
- Springer
- Year
- 1999
- Tongue
- English
- Weight
- 97 KB
- Volume
- 73
- Category
- Article
- ISSN
- 0003-889X
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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.
Using the technique of Gale diagrams we give a characterization of point sets in (k -1)-dimensional Euclidean space that are obtained by projection of the vertex set of a convex k-polyt0pe of given combinatorial type. This result is also a first step in finding an intrinsic geometric criterion to de