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2-groups behaving as automorphism groups of regular 3-polytopes

par Hou, Dong Dong;Feng, Yan Quan;Leemans, Dimitri
Référence Journal of group theroy, 22, 4, page (579-616)
Publication Publié, 2019-01-01

Article révisé par les pairs

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Résumé :

In this paper, we prove that for any positive integers n; s; t such that n ≤ 10, s; t ≤ 2 and n-1 ≤ s C+t , there exists a regular polytope with Schläfli type {2s ; 2} and its automorphism group is of order 2n. Furthermore, we classify regular polytopes with automorphism groups of order 2n and Schläfli types {4; 2n-3}; {4; 2n-4} and {4; 2n-5}, therefore giving a partial answer to a problem proposed by Schulte andWeiss in [Problems on polytopes, their groups, and realizations, Period. Math. Hungar. 53 (2006), no. 1-2, 231-255].