> you can indeed cover a sphere with only hexagons, if you relax the requirement that they all be regular hexagons More precisely, what you need to relax is th

> you can indeed cover a sphere with only hexagons, if you relax the requirement that they all be regular hexagons More precisely, what you need to relax is the requirement that 3 hexagons always meet at every vertex. See https://en.wikipedia.org/wiki/Euler_characteristic#Polyhedra https://en.wikipedia.org/wiki/Euler_characteristic#Polyhedra If you have only hexagons, you end up with 6 vertices on the sphere where only 2 hexagons meet (whether you still consider these to be "hexagons" when they have two adjacent sides is a matter of definitions). But what many spacial indices do instead is include 12 pentagons among the hexagons.