Those meshes are made by subdividing an octahedron. Approximating an sphere like that has the nice property that the triangles in each subdivision level have th

Those meshes are made by subdividing an octahedron. Approximating an sphere like that has the nice property that the triangles in each subdivision level have the same surface area, and you can use the same underlying texture for all the levels since in the 2D projection the sub triangles are also regular subdivisions of their parents.