3 problems

Let $P\subset\mathbb{R}^d$ be a polytope and let $q\colon V(G_P)\to\mathbb{R}^e$ be a graph embedding of its edge-graph $G_P$. For each vertex $i\in V(G_P)$, define … Assume that e…

Let $v$ be an inscribed nullspace embedding with circumcenter $0$. Let $w$ be any inscribed embedding whose circumcenter lies in $\operatorname{conv}(w)$ and whose edges are not lo…

Let $v$ be a nullspace embedding of an expansion matrix $M$, and let $c\in\operatorname{conv}\{v_1,\ldots,v_n\}$. Translation conjecture for nullspace embeddings. There is an expan…