Hunting for reduced polytopes

Abstract

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 $d\ge 3$. Moreover, we prove a novel necessary condition on reduced polytopes in three-dimensional Euclidean space.

This is work is a merger of arXiv:1605.06791 and arXiv:1607.08125