Herein I address the current number of plates, the number there should be, and whether there is a pattern in the plate mosaic. Related issues are the optimal sizes and shapes of plates and spacings of ridges, trenches, and transform faults. Similar questions arise in studies of foams, bubble rafts, buckyballs, mudcracks, columnar jointing, the tessellation of spheres, and the planforms of convection. In sphere-covering problems, and in dynamic problems, pentagons replace the familiar hexagons. The “ground” state of plate tectonics on a homogeneous planet may involve ∼12 plates with five nearest and five next-nearest neighbors. The plate mosaic may be a self-organized network of plates and force chains, which are readily reorganized by stress changes. This paper starts with the premise that the mosaic may have simple and surficial explanations rather than convective or plutonic causes. The study of the tessellation of Earth can be called “platonics” to distinguish it from the idea that the lithosphere necessarily mirrors the planform of mantle convection.