# An extension of the classification of high rank regular polytopes

@article{Fernandes2015AnEO,
title={An extension of the classification of high rank regular polytopes},
author={Maria Elisa Fernandes and D. Leemans and M. Mixer},
journal={arXiv: Combinatorics},
year={2015}
}
• Published 2015
• Mathematics
• arXiv: Combinatorics
Up to isomorphism and duality, there are exactly two non-degenerate abstract regular polytopes of rank greater than $n-3$, one of rank $n-1$ and one of rank $n-2$, with automorphism groups that are transitive permutation groups of degree $n\geq 7$. In this paper we extend this classification of high rank regular polytopes to include the ranks $n-3$ and $n-4$. The result is, up to a isomorphism and duality, seven abstract regular polytopes of rank $n-3$ for each $n\geq 9$, and nine abstract… Expand
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