Highest rank of a polytope for $A_n$

Peter J. Cameron, Maria Elisa Fernandes, Dimitri Leemans +1

We prove that the highest rank of a string C-group constructed from an alternating group $Al{t}_n$ is 0 if $n=3,4,6,7,8$; 3 if $n=5$; 4 if $n=9$; 5 if $n=10$; 6 if $n=11$; and $\…