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hexagonal-tiles

Hexagon grid on sphere without pentagon

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.

Solution

  • 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