  A convex body $R$ in $\mathbb R^d$ is called reduced if the minimal width
$\Delta(R')$ of each convex body $R'\subset R$ different from $R$ is strictly
smaller than the minimal width $\Delta(R)$ of $R$. In this article we construct
a reduced polytope in $\mathbb R^3$, i.e. we answer the following question
posed by Lassak: do there exist reduced polytopes in $\mathbb R^d$,
$d\geqslant3$? Also, we prove some properties of reduced polytopes in $\mathbb
R^3$.

Metric Geometry