Regular and chiral polytopes in low dimensions

Details Regular and chiral polytopes in low dimensions Regular and chiral polytopes in low dimensions

2005-03-18

arxiv.org/abs/math/0503389v1

Mathematics

Metric Geometry

20 pages. In "The Coxeter Legacy -- Reflections and Projections" (eds. C.Davis and E.W.Ellers), Fields Institute Communication

Scientific paper

There are two main thrusts in the theory of regular and chiral polytopes: the abstract, purely combinatorial aspect, and the geometric one of realizations. This brief survey concentrates on the latter. The dimension of a faithful realization of a finite abstract regular polytope in some euclidean space is no smaller than its rank, while that of a chiral polytope must strictly exceed the rank. There are similar restrictions on the dimensions of realizations of regular and chiral apeirotopes. From the viewpoint of realizations in a fixed dimension, the problems are now completely solved in up to three dimensions, while considerable progress has been made on the classification in four dimensions, the finite regular case again having been solved. This article reports on what has been done already, and what might be expected in the near future.

Affiliated with

Also associated with

No associations

Rating

Regular and chiral polytopes in low dimensions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Regular and chiral polytopes in low dimensions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Regular and chiral polytopes in low dimensions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-502497