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- W1787867404 abstract "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 $ngeq 7$. 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 $ngeq 9$, and nine abstract regular polytopes of rank $n-4$ for each $n geq 11$. Moreover we show that if a transitive permutation group $Gamma$ of degree $n geq 11$ is the automorphism group of an abstract regular polytope of rank at least $n-4$, then $Gammacong S_n$." @default.
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- W1787867404 date "2015-09-03" @default.
- W1787867404 modified "2023-09-23" @default.
- W1787867404 title "An extension of the classification of high rank regular polytopes" @default.
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