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This has a nice visualiser: https://observablehq.com/@four43/h3-index-visualizer
https://observablehq.com/@fil/h3-oddities

also check out the "gnomonic icosahedral" at H0 from the dropdowns, that's the projection the base hexagonal grid is from, it's a perfectly planar hexgrid on an unfolded icosahedron net.

The blog post has a picture showing several layers of hexagons overlapping.
Yes, in the sections under Intro > Comparisons
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
The 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.
> 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

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.

Looks like H3 uses regular hexagons and instead drops the requirement that they can't overlap.
At 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.

That can be a deal breaker for some uses