4 problems

Cubical-polytope reconstruction conjecture. Every cubical polytope can be reconstructed from its dual graph.

Let $Q$ be a cubical $d$-polytope, meaning that every proper face of $Q$ is combinatorially a cube. Its cubical $h$-polynomial is written as … and its cubical $g$-vector is…

Let $d$ be a positive integer. For a cubical $d$-polytope $Q$, let $g^c(Q)$ be its cubical $g$-vector, and let $\mathcal{C}_d$ be the minimal closed cone containing all such vector…

Let $K$ be a cubical polytope of dimension $d\geq 3$, with $V$ vertices and $E$ edges. Jockusch's conjecture. … The source attributes this conjecture to Jockusch and discusses part…