4 problems

Let $B_1^n=\operatorname{conv}\{\pm e_1,\ldots,\pm e_n\}$ be the cross-polytope, and let … For $a\in\mathcal{M}$, consider the central hyperplane section $B_1^n\cap a^\perp$. Maxim…

Let $n\ge 4$, and consider exotic flexible cross-polytopes in the sphere $\mathbb{S}^n$. These are flexible cross-polytopes whose dihedral-angle tangents have the exotic parametriz…

Let $\Diamond^n$ be the standard cross-polytope in $\mathbb{R}^n$, let $H_k$ be a $k$-dimensional subspace of $\mathbb{R}^n$, and let $\Diamond^n|H_k$ denote the orthogonal project…

Cross-polytope conjecture. Then $A_1,\ldots,A_{2n}$ are the vertices of an $n$-dimensional cross-polytope.