For the research on my planet renderer I have been looking into how icospheres are constructed. The process is rather simple:

- Define the triangle edges with three intersecting planes that use the golden ratio (1+sqrt(5))/2 : 1
- Create 20 triangles between the vertices of those planes:
- Subdivide those triangles and keep them in the shape of a sphere by making sure the distance from the center is the radius of the sphere:

There is barely a noticable difference from how icospheres look like when adding them via the Add Mesh menu in Blender:

The nice thing about icosahedrons is that they use equilateral triangles of the same scale everywhere, so they have a nicely distributed amount of surface detail, so it might be quite ideal for rendering of planets.

Hi! I love all the work you’ve done and am very appreciative of the detailed explanation. I was wondering if you could elaborate on why you eventually chose to go with Icosahedrons instead of a Spherified Cube. The only reasoning I can find is that there is a more even distribution of triangles on the sphere. This is driving my decision too, but I was wondering if you really found that it was the correct choice or if you had any other reasoning to stick with an Icosahedron? Any further elaboration would be much appreciated! Thanks!