We propose a simple approach to determine all possible wheels that can roll smoothly without slipping on a periodic roadbed, while maintaining the center of mass at a fixed height. We also address the inverse problem that of obtaining the roadbed profile compatible with a specific wheel and all other related “quantized wheels.” The role of symmetry is highlighted, which might preclude the center of mass from remaining at a fixed height. A straightforward consequence of such geometric quantization is that the gravitational potential energy and the moment of inertia are discrete, suggesting a parallelism between macroscopic wheels and nano-systems, such as carbon nanotubes.