Hexagon grid on sphere without pentagon

hexagonal-tiles
The Oddler picture The Oddler · Oct 11, 2012 · Viewed 21.9k times · Source

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

Suzan Cioc picture Suzan Cioc · Oct 11, 2012

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

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