How to sew in practice?

TL;DR

This paper presents a theorem and a fast algorithm for sewing even-dimensional neighbourly polytopes, along with a description of their universal faces, advancing practical methods in polytope construction.

Contribution

It introduces a new theorem and an efficient algorithm for sewing neighbourly polytopes, and characterizes their universal faces.

Findings

Theorem on sewing of even-dimensional neighbourly polytopes

Fast algorithm for sewing in practice

Description of universal faces of sewn polytopes

Abstract

In this note we prove a theorem concerning the sewing of even dimensional neighbourly polytopes. The theorem provides a fast algorithm for sewing in practice. We also give a description of the universal faces of a sewn $d$-polytope in terms of the main theorem.