Infinite families of hypertopes from centrally symmetric polytopes

TL;DR

This paper constructs infinite families of regular hypertopes and polytopes using extensions of symmetric polytopes and halving operations, expanding the understanding of their combinatorial structures.

Contribution

It introduces new methods to generate infinite families of hypertopes from symmetric polytopes and explores their properties through halving operations.

Findings

Constructed infinite families of regular polytopes of specific types.

Generated infinite families of locally spherical and toroidal hypertopes.

Demonstrated the application of halving operations to these structures.

Abstract

We construct infinite families of abstract regular polytopes of type $\{4,p_1,\ldots,p_{n-1}\}$ from extensions of centrally symmetric spherical abstract regular $n$-polytopes. In addition, by applying the halving operation, we obtain infinite families of both locally spherical and locally toroidal regular hypertopes of type $\left\{{p_1 \atop p_1},\ldots,p_{n-1}\right\}$.