There are only two dimensions available. Easiest way to think of a wheel is in cylindrical coordinates, the axis of which system is running through the axle of the wheel. Each point on the rim you want at a constant radius (length from the axis) and height (which is displacement along the axis). The third dimension is theta, angular displacement around the axis. Since we have the constraint of spokes, theta is going to be fixed for a given height and radius. In other words, it is a 3d system, like typical newtonian physical systems, with one constraint. That leaves two free dimensions.