On regular polytopes of order $2^n$

Abstract

For each $d\ge 3$, $n\ge 10$, and $k_1,k_2,\dots ,k_{d-1}\ge 2$ with $k_1+k_2+\dots +k_{d-1}\le n-1$, we construct a regular $d$-polytope whose automorphism group is of order $2^n$ and whose Schläfli type is $\{2^{k_1},2^{k_2},\dots ,2^{k_{d-1}}\}$.

References in corpus (1)

• String C-groups from groups of order 2^m and exponent at least 2^(m - 3)

Cited by in corpus (2)

• Two infinite families of chiral polytopes of type \{4,4,4\} with solvable automorphism groups
• A family of regular polytopes of order $4p^m$ with type $\{p,2p\}$