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

TL;DR

This paper constructs an infinite family of regular 3-hypertopes with automorphism groups of order 2^n, expanding the understanding of hypertopes with chambers in combinatorial and geometric group theory.

Contribution

It introduces a new infinite family of regular 3-hypertopes with specific types and automorphism group orders, generalizing previous constructions.

Findings

Existence of hypertopes with automorphism groups of order 2^n

Construction valid for n ≥ 10 and specific parameters

Hypertopes have type (2^s, 2^t, 2^l) with n ≥ s+t+l

Abstract

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.