4 Jul 2026
For compact convex sets $L,K \subset \mathbb{R}^n$, denote by $λ_K(L)$ the smallest size of a homothet of $K$ that contains $L$. We define a measure of symmetry based on the $n$-simplex $Δ= Δ^n \subset \mathbb{R}^n$ as the ratio \[ ρ_Δ(L):=\frac{λ_{-Δ}(L)}{λ_Δ(L)}.