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- W2962726478 abstract "Regular polygonal complexes in euclidean $3$-space $mathbb {E}^3$ are discrete polyhedra-like structures with finite or infinite polygons as faces and with finite graphs as vertex-figures, such that their symmetry groups are transitive on the flags. The present paper and its predecessor describe a complete classification of regular polygonal complexes in $mathbb {E}^3$. In Part I we established basic structural results for the symmetry groups, discussed operations on their generators, characterized the complexes with face mirrors as the $2$-skeletons of the regular $4$-apeirotopes in $mathbb {E}^3$, and fully enumerated the simply flag-transitive complexes with mirror vector $(1,2)$. In this paper, we complete the enumeration of all regular polygonal complexes in $mathbb {E}^3$ and in particular describe the simply flag-transitive complexes for the remaining mirror vectors. It is found that, up to similarity, there are precisely 25 regular polygonal complexes which are not regular polyhedra, namely 21 simply flag-transitive complexes and $4$ complexes which are $2$-skeletons of regular $4$-apeirotopes in $mathbb {E}^3$." @default.
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- W2962726478 date "2012-10-31" @default.
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- W2962726478 title "Regular polygonal complexes in space, II" @default.
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- W2962726478 doi "https://doi.org/10.1090/s0002-9947-2012-05684-4" @default.
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