3 problems

Covering product conjecture. One has

Let ${\bf p}=(p_1,\ldots,p_N)$ and ${\bf q}=(q_1,\ldots,q_N)$ be configurations of $N$ points in ${\mathbb E}^d$. The configuration ${\bf q}$ is a contraction of ${\bf p}$ if…

Let $S=\{v_1,\ldots,v_n\}$ be an $(n,k)$-frame spanning $\mathbb{R}^k$, let … and define $P=\operatorname{co}\{\pm v_1,\ldots,\pm v_n\}$ and…