I wanted to see if I could make an all quad soccer ball and this is what I came up with.
1. Start with an ico sphere with 1 subdivision.
2. Bevel all vertices (not edges) to create the base tiles.
3. Add a subdivision surface modifier, switch it to simple, set it to 2, and apply it.
4. Add a separate UV sphere object and scale it to match the ico sphere.
5. Add a Shrinkwrap modifier to the ico sphere, select the UV sphere as the target, and apply it.
6. Select the faces that make up a tile of the soccer ball and extrude them a bit along the normal. Repeat this step and make sure to extrude the exact same amount until all tiles are extruded.
Soccer ball mesh:
Soccer ball with bevel and subdivision surface modifiers:
