Highest rank of a polytope for An. Issue 1 (28th April 2017) - Cameron, Peter J.
Abstract: We prove that the highest rank of a string C‐group constructed from an alternating group A n 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 A n is not a string C‐group. This solves a conjecture made by the last three authors in 2012.