Morgan McGuire had asked me about Goldberg polyhedra. I hadn’t heard of them so I spent some time on Wikipedia and other sites.
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).
Wouldn’t it be neat if a roguelike game put tiles on there? Oh, naturally HyperRogue has done this!
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!