Every generating polytope is strongly monotypic

TL;DR

This paper proves that polytopes with the generating property are exactly those that are strongly monotypic, confirming a longstanding conjecture and establishing their equivalence.

Contribution

It proves a longstanding conjecture that every generating polytope is strongly monotypic, showing the equivalence of these properties for polytopes.

Findings

Generated polytopes are strongly monotypic.

Strong monotypy and the generating property are equivalent for polytopes.

A criterion for identifying monotypic and strongly monotypic polytopes is provided.

Abstract

We prove an old conjecture of McMullen, Schneider and Shephard that every polytope with the generating property is strongly monotypic. The other direction is already known, which implies that strong monotypy and the generating property for polytopes are the same notion. A criterion for monotypic and strongly monotypic polytopes is also given.