3 problems

Let $Q_{6,\arccos\frac{-1}{2\sqrt7},\frac{4\pi}{3},\arccos\frac{1}{3}}$ be the spherical $4$-gon specified by these parameters, and consider tilings of the sphere by congruent copi…

Brinkmann's three-vertex-type conjecture. There are at most three distinct vertex types in a chart of any spherical monohedral quadrangular tiling.

Convex-tile inverse Grünbaum–Shephard conjecture. For every normal spherical monohedral tiling topologically a Platonic solid, an Archimedean dual, an $n$-gonal bipyramid, or an…