Morgan McGuire had asked me about Goldberg polyhedra. I hadn’t heard of them so I spent some time on Wikipedia and other sites.

- https://en.wikipedia.org/wiki/Goldberg_polyhedron
^{[1]} - https://en.wikipedia.org/wiki/Goldberg%E2%80%93Coxeter_construction
^{[2]}

I don’t understand all the math but it looked cool so I thought I would try it:

Hey, that’s pretty cool. On a cube we can place square tiles that are *not aligned with the cube axes*. Here’s my understanding of how it works:

- We want to place a grid on the cube.
- We
*rotate*the grid a based on the K, L parameters. - We have to rotate it so that the edges line up. To do that, we make the grid N ⨉ N, where N = sqrt(K² + L²).

That’s it!

Wouldn’t it be neat if a roguelike game put tiles on there? Oh, naturally HyperRogue has done this^{[3]}!

I think it would also be fun to:

- Reshape the cube into a sphere. This will distort the squares so that they’re not all the same size. Tradeoffs.
- Try the triangle version of this.

Maybe another day!