In this post I will explain how to build, subdivide and texture an icosahedron. Look at the ending of the post for eye candy.
So I’ve been following the development of Notch’s new game, 0x10^c, which is looking really exciting. When I saw a screenshot(Can’t find it now) I was reminded of something I read about using icosahedrons to make planets in 3D with minimal distortion when mapping to a texture.
I find this way of attacking the problem of spheres fascinating. Basically you start off with a 20 sided die and split the faces by adding new vertices on a sphere encapsulating the icosahedrons, so in each iteration you get closer to a perfect sphere. You split the faces by adding a point in the middle of each edge in a triangle, you then construct four new triangles using these and the original vertices.