Thank you for the suggestion! I had not considered that. Thanks, too, for the link to the video. That was quite interesting. I did not know Penrose tilings could be applied to spheres.
A Penrose ball might be a fun project, but to do it justice I would need many more panels than I have been motivated to work with. Even 32 panels is more than I like to work with, and I would probably need at least twice that for a decent Penrose tiling.
Maybe somebody else reading your suggestion will be up to trying it. If anyone does, please reply to this post and let us know, and include a link to a photo of your ball (or email it to me)!