Highest rank of a polytope for An
Peter J. Cameron, Maria Elisa Fernandes, Dimitri Leemans, Mark Mixer · Proceedings of the London Mathematical Society · 2017
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.