7 problems

Let $Q$ be a cubical $d$-polytope with $n$ vertices, and write $f_k(Q)$ for its number of $k$-dimensional faces. Jockusch's cubical lower bound conjecture. For $1\leq k\leq d-2$, ……

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

Non-polytopality conjecture for $\Psi$. The cubical sphere $\Psi$ is not polytopal.

Hetyei's conjecture. There are cubical $4$-polytopes whose $2$-skeleton is not edge-orientable.

A cubical polytope is a polytope in which every facet is a cube. Its dual graph has one vertex for each facet, with two vertices adjacent when the corresponding facets share a ridg…

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…