3 problems

Regular-polytope point-homogeneity conjecture. The vertex set $M$ of any $n$-dimensional regular polytope is $n$-point homogeneous.

Let $X$ be an affinely independent subset of the Hamming cube $H_n=\{0,1\}^n$ with $n+1$ points, and let $D$ be its distance matrix for the Hamming metric. Inverse-distance-sum con…

Let $n$ be the number of points in a finite semi-metric space. The minimum $\ell_1$-dimension is the smallest integer $d$ such that every isometrically $\ell_1$-embeddable semi-met…