Hunting for 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 $d\ge 3$.

This paper has been withdrawn by the authors. This paper has been superseded by arXiv:1701.08629 (merged from arXiv:1605.06791 and arXiv:1607.08125)