Four infinite families of chiral $3$-polytopes of type $\{4,8\}$ with solvable automorphism groups

Dong-Dong Hou, Tian-Tian Zheng, Rui-Rui Guo

We construct four infinite families of chiral $3$-polytopes of type $\{4,8\}$, with $1024m^4$, $2048m^4$, $4096m^4$ and $8192m^4$ automorphisms for every positive integer $m$, res…