4 problems

Dihedral-angle uniqueness conjecture. A polytope is determined up to congruence by its dihedral angles.

Let $S(t)$ be a differentiable one-parameter family of oriented piecewise-linear surfaces. For each facet $F$, let $n_F$ be its unit normal and $V_F$ its volume, and define the dih…

Let $\ell\in\mathbb{R}$, let $\Delta\in{\mathcal{T}}_{\ell}$, and let $\theta_{ij}$, $1\leq i<j\leq4$, be the dihedral angles of $\Delta$. Set … and let $\Delta'\in{\mathcal{T}}$ b…

Dihedral-angle comparison conjecture. There exist corresponding $(d-2)$-faces $t_1$ of $P_1$ and $t_2$ of $P_2$ such that the dihedral angle of $t_1$ is not greater than the dihedr…