The smallest regular polytopes of given rank

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• 作者：Marston Conder ^{m.conder@auckland.ac.nz}
• 关键词：primary ; 52B15 ; secondary ; 05E18 ; 06A11 ; 20B25
• 刊名：Advances in Mathematics
• 出版年：2013
• 出版时间：20 March, 2013
• 年：2013
• 卷：236
• 期：Complete
• 页码：92-110
• 全文大小：279 K

文摘

An abstract polytope is called regular if its automorphism group has a single orbit on flags (maximal chains). In this paper, the regular -polytopes with the smallest number of flags are found, for every rank . With a few small exceptions, the smallest regular -polytopes come from a family of ¡®tight¡¯ polytopes with flags, one for each , with Schl?fli symbol . Also with few exceptions, these have both the smallest number of elements, and the smallest number of edges in their Hasse diagram.