Hunting for reduced polytopes

TL;DR

This paper demonstrates the existence of reduced polytopes in three-dimensional Euclidean space, addressing a longstanding open question about their existence in higher dimensions.

Contribution

It corrects a previous example and proves the existence of reduced polytopes in 3D, partially answering Lassak's question for dimensions three and above.

Findings

Existence of reduced polytopes in 3D confirmed

Corrects a previous example by Polyanskii

Addresses a question about higher-dimensional reduced polytopes

Abstract

By correcting an example by Polyanskii, we show that there exist reduced polytopes in three-dimensional Euclidean space. This partially answers the question posed by Lassak on the existence of reduced polytopes in $d$-dimensional Euclidean space for $d\geq 3$.