The Hexagonal Tiling Honeycomb

[belter]

https://arxiv.org/abs/2412.00048

[ethbr1]

(Hyper)hexagons are the (hyper)bestagons https://m.youtube.com/watch?v=thOifuHs6eY

[hoseja]

The, sadly not very polished, game Hyperbolica nevertheless really helped me open my mind to hyperbolic spaces.

[erikvanoosten]

I wonder how this compares to H3. Why does H3 has pentagons as well, and this doesn't?

[dragonwriter → erikvanoosten]

H3 is a way of subdividing the (approximated) surface of a sphere into polygons that are (mostly) hexagons of approximately equal size (which requires smaller pentagons at what would can be envisioned as the corners of an icosahedron.)

The hexagon tiling honeycomb this refers to is a way of subdividing a particular 3D non-Euclidean space into polyhedra whose faces are hexagons.

They don’t really compare because they don’t address the same thing at all.

[jsilence → erikvanoosten]

Not an expert, but I think it does not have pentagons because it is in a non-euclidian space. Might be wrong, just a guess.

[awanderingmind]

This is cute, but I don't understand why it's on the arXiv. It's only two pages long, of which almost half is a picture and the bibliography, and as far as I can see contains nothing novel. I love Baez's blog(s) (https://johncarlosbaez.wordpress.com/ and https://math.ucr.edu/home/baez/), and it seems this would have been better served posted there as a post. Am I missing something?

[belter → awanderingmind]

It's in Mathematics -> History and Overview, not Mathematics -> Revolutionary Breakthroughs. It's not claiming novelty, just being very interesting.

[awanderingmind → belter]

Ah missed that, thank you.

[madcaptenor → awanderingmind]

I wonder if Baez put it on the arXiv to make it "citable".