[lodi]

> Hexagons are all equidistant from their neighbors and all share the same size edge with all neighbors.

Technically, in spherical geometry this isn't true. It's actually not possible to tile the sphere with regular hexagons (even after including those 12 pentagons). Unlike a planar tiling, some hexagons end up bigger or smaller than others, the internal angles aren't all equal to each other, and the internal angles sum to more than 360 degrees.

This page has some good diagrams where this effect is readily visible: https://en.wikipedia.org/wiki/Goldberg_polyhedron