Hexagon grid on sphere without pentagon

Question

I wanted to make a tile-based world on a sphere. I would like to use hexagon-shaped tiles, though as far as I can figure out you need to have pentagons in there too to make it fit.

So, my question is, is it possible to make a hexagon grid on a sphere, without using pentagons? The hexagons don't have to be regular hexagons, if they are all close to regular that's more than enough.

Answer 1

Impossible. This is mathemetical theorem. Only imprecise ways exist I guess.

http://en.wikipedia.org/wiki/Platonic_solid

http://en.wikipedia.org/wiki/Semiregular_polyhedron

Covering Earth with Hexagonal Map Tiles