Highest rank of a polytope for An

Peter J. Cameron, Maria Elisa Fernandes, Dimitri Leemans, Mark Mixer

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


We prove that the highest rank of a string C-group constructed from an alternating group An is 3 if n=5, 4 if n=9, 5 if n=10, 6 if n=11, and ⌊(n−1)/2⌋ if n⩾12. Moreover, if n=3,4,6,7, or 8, the group An is not a string C-group. This solves a conjecture made by the last three authors in 2012.
Original languageEnglish
Pages (from-to)135-176
Number of pages42
JournalProceedings of the London Mathematical Society
Issue number1
Early online date28 Apr 2017
Publication statusPublished - 4 Jul 2017


  • Abstract regular polytypes
  • String C-groups
  • Alternating groups
  • Permutation groups


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