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There’s gifs of hexagons on a planet you can search but you can’t cover a sphere with just hexagons. Even so, I imagine the poles are irrelevant to Uber
by prpl 5y ago
There’s gifs of hexagons on a planet you can search but you can’t cover a sphere with just hexagons. Even so, I imagine the poles are irrelevant to Uber
- xvedejas 5y agoThe image shows a number of pentagons, so it's not just hexagons unless you consider a pentagon some kind of degenerate hexagon. That said, you can indeed cover a sphere with only hexagons, if you relax the requirement that they all be regular hexagons.
- jayd16 5y agoLooks like H3 uses regular hexagons and instead drops the requirement that they can't overlap.
- jacobolus 5y agoAt each tiling level, they have a proper tiling of hexagons with 12 pentagons. The system is based on an icosahedron. But the way the hierarchical division system works, the tile boundaries from one scale don’t precisely match the tile boundaries from another scale.
- ClumsyPilot 5y agoThat can be a deal breaker for some uses
- jacobolus 5y ago> 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.