I'm not sure of the shape. May never know. But I can create the same "round" effect as the moon with the INSIDE of a bowl, and a flashlight. I find this same method allows me to make the moon phases more accurately than I could with a convex/ball surface. Try it out. Just use any bowl that is not clear/see-through. Hold the bowl out in front of you, with the inside of the bowl fscing towards you, then shine the flashlight in from an angle at the side of the bowl, and slightly in front of it, and you'll see what I'm talking about. I know this doesn't answer your question, but perhaps it will help with the path to the truth. Good luck, and report back here if you find anything out.