Five-dimensional Perfect Simplices

Mikhail Nevskii, Alexey Ukhalov

Let $Q_n=[0,1{]}^n$ be the unit cube in ${\mathbb{R}}^n$, $n\in \mathbb{N}$. For a nondegenerate simplex $S\subset {\mathbb{R}}^n$, consider the value $ξ(S)=\min \{σ>0: Q_n\subset σS\…