Polytopality criteria for the mix of polytopes and maniplexes

TL;DR

This paper establishes a general criterion to determine when the mix of two maniplexes, especially involving polytopes, results in a structure that retains polytopality, extending previous criteria.

Contribution

It introduces a unified, generalized criterion for polytopality of the mix of maniplexes, broadening the understanding of their structural properties.

Findings

Provides a new criterion for polytopality of maniplex mixes

Generalizes several previously known polytopality criteria

Facilitates identification of minimal regular covers in maniplexes

Abstract

The mix of two maniplexes is the minimal maniplex that covers both. This construction has many important applications, such as finding the smallest regular cover of a maniplex. If one of the maniplexes is an abstract polytope, a natural question to ask is whether the mix is also a polytope. We describe here a general criterion for the polytopality of the mix which generalizes several previously-known polytopality criteria.