Beauty is highly subjective, but if we are judging by simplicity, then I think an ellipse is perhaps the simplest approximation that might match reasonably well with the side-view of the traditional Japanese bi-convex stone shape, especially for the larger stone sizes that you were particularly interested in.
Of course, I’m sure the masters will say that the ellipse is not quite right and the shape has much more subtlety and nuance, but it looks like an almost exact match when I overlay an ellipse on the size 42 (11.9 mm) stone:
With an ellipse defining the side-view, we’ve reduced the shape of the stone to essentially just one free parameter: the ratio of its height to its width (i.e., length of semi-major vs semi-minor axis). Of course, the rest of the 3D shape is defined by rotating the ellipse around it’s semi-minor axis in 3D space.