Chiral extensions of chiral polytopes

TL;DR

This paper introduces a method to construct higher-dimensional chiral polytopes from lower-dimensional ones with regular facets, providing explicit examples and ensuring finiteness when starting from finite polytopes.

Contribution

It presents a novel construction technique for creating (d+1)-dimensional chiral polytopes from d-dimensional chiral polytopes with regular facets, including explicit examples.

Findings

Constructed chiral 4-polytopes from chiral toroidal maps.

Ensured finiteness of the new polytopes when the original is finite.

Provided explicit examples demonstrating the construction.

Abstract

Given a chiral d-polytope K with regular facets, we describe a construction for a chiral (d + 1)-polytope P with facets isomorphic to K. Furthermore, P is finite whenever K is finite. We provide explicit examples of chiral 4-polytopes constructed in this way from chiral toroidal maps.