are these the kinds of triangles you want to end up with?
That's actually a perfect demonstration of what I am trying to avoid. The method shown in that video is exactly
why cube based spheres get distorted.
Notice the vertex density on the top of the sphere, compared to the vertex density around what would be
the corner of the original cube.
Already there is a big difference: the triangles on top of the sphere are stretched out and the ones near the
original corner point are very small and clustered.
Now if the camera in my planet application was to fly around on ground level, the effect of this distortion
would be easily noticeable. A mountain range around a clustered corner is going to look much better
then a mountain range around the stretched areas on top.
Equilateral triangles is the solution here. They stay the same size all the way around the sphere.