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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.
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