5 problems

A centrally symmetric polytope is uniquely determined, up to isometry, by its edge-graph, edge lengths, and vertex-origin distances. Central symmetry reconstruction conjecture. The…

Let $G=(V,E)$ be a graph, and let $r\colon V\to\mathbb{R}_+$ and $\ell\colon E\to\mathbb{R}_+$ be functions. Scaled metric reconstruction conjecture. There is at most one $d\geq 1$…

Let $P,Q\subset\mathbb{R}^d$ be polytopes with isomorphic edge-graphs. Assume that $Q$ contains the origin in its interior, edges in $Q$ are not longer than the corresponding edges…

Let $P\subset\mathbb{R}^d$ and $Q\subset\mathbb{R}^e$ be polytopes with isomorphic edge-graphs. Assume that $0\in\operatorname{int}(Q)$, every edge of $Q$ is at most as long as its…

Let $P\subset\mathbb{R}^d$ and $Q\subset\mathbb{R}^e$ be polytopes with the origin in their respective interiors. Suppose that their edge-graphs are isomorphic, corresponding edges…