1. Select or create a 2-dimensional tiling with 3, 4, or 5-fold rotational symmetry.
2. Divide the 2-dimensional tiling into triangle, square, or pentagon-shaped "faces" to match those on the surface of the platonic solid.
3. Inscribe the faces of the platonic solid on the surface of the sphere.
In the drawings above, the lines on the spheres are great circles that intersect at angles of 60 degrees (tetrahedron), 45 degrees (cube and octahedron), or 36 degrees (dodecahedron and icosahedron).
4. Transfer your 2-dimensional drawing to the surface of the sphere
5. Carve the sphere