Existence of regular $3$-hypertopes with $2^n$ chambers

Dong-Dong Hou, Yan-Quan Feng, Dimitri Leemans

Published 2019-01-23Version 1

For any positive integers $n, s, t, l$ such that $n \geq 10$, $s, t \geq 2$, $l \geq 1$ and $n \geq s+t+l$, a new infinite family of regular 3-hypertopes with type $(2^s, 2^t, 2^l)$ and automorphism group of order $2^n$ is constructed.