If you search for "fibonacci grid sphere," you'll find the grid used for research. It's less regular and a lot more work, with a few regions of five or seven sides, but it might look more natural, and it's used because it has fewer sharp corners than the icosohedron. Just another option.
The surface geometry is not very important in this task. You can easily push out a million triangles or more, so you're going to get a pretty round shape in the end, no matter which primitive you take as a starting point.
The hard part is texturing and area distortions. Ideally you wouldn't have texture boundaries crossing the triangle boundaries. Since textures are rectangular, using the "cube sphere" is a very popular choice for planet rendering.
Things get more difficult if you have to use real-life imagery (satellite images and aerial photography), because then you're going to have to stitch several layers of textures on top of each other. There are texture splatting techniques and other tricks that need to be done to get proper texturing on the planet.