Discrete & Computational Geometry

, Volume 32, Issue 1, pp 1–35

Regular Polytopes of Full Rank


DOI: 10.1007/s00454-004-0848-5

Cite this article as:
McMullen, P. Discrete Comput Geom (2004) 32: 1. doi:10.1007/s00454-004-0848-5


The dimension of a faithful realization of a finite abstract regular polytope in some euclidean space is no smaller than its rank. Similarly, that of a discrete faithful realization of a regular apeirotope is at least one fewer than the rank. Realizations which attain the minimum are said to be of full rank. The regular polytopes and apeirotopes of full rank in two and three dimensions were classified in an earlier paper. In this paper these polytopes and apeirotopes are classified in all dimensions. Moreover, it is also shown that there are no chiral polytopes of full rank.

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Department of Mathematics, University College London, Gower Street, London WC1E 6BTEngland

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