We say that a subset A of the sphere r-divides it if r-many rotations of A perfectly tile the sphere's surface. Such divisions were first exhibited by Robinson (47) and developed by Mycielski (55). We discuss a colorful approach to finding these divisions which are Lebesgue measurable or possess the property of Baire.

This includes joint work with J. Grebik, A. Marks, O. Pikhurko, and S. Unger."