Highest rank of a polytope for $A_n$

Abstract

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 $\lfloor \frac{n-1}{2}\rfloor$ if $n\ge 12$. This solves a conjecture made by the last three authors in 2012.

Cited by in corpus (3)

• Regular $3$-polytopes of order $2^{n}p$
• Unravelled Abstract Regular Polytopes
• $2$-groups behaving as automorphism groups of regular $3$-polytopes