The authors consider coupled phase oscillators on finite regular networks that can be thought of as approximating the surface of a sphere. Examples studied include the dodecahedron (20 nodes) and the buckyball (60 nodes) and various generalisations of these. For some networks and some coupling functions the authors can show that rotating wave solutions exist and are stable. Exact synchrony is always a solution as well. The effects of varying the coupling function (making it non-odd, or the local dynamics excitable) are investigated, as are the sizes of basins of attraction for various states. They show that their results generally hold when phase oscillators are replaced by Landau-Stuart or Morris-Lecar oscillators.