Goldberg-Coxeter Construction

 from Red Blob Games
10 Jan 2019

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:

Wrapped on cube

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:

  1. We want to place a grid on the cube.
  2. We rotate the grid a based on the K, L parameters.
  3. 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:

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

Maybe another day!

Goldberg-Coxeter pattern

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