Amazing!

Thanks Dunstan!

What is the license for the data?

Are you referring to the unfoldings.json file? If so, I haven't attached a license but would be happy to attach a permissive license on request. Or, perhaps, you're asking the more general question of a license for data that comes from one of Mathematica's *Data functions? That might be a stickier issue that I'm not sure how to answer. Certainly, the vast majority of the data originated from Netlib, though: http://netlib.org/polyhedra/ As such, it should be public domain.

"polyhedron_data" needs to be removed, otherwise changing the polyhedron will reset the play state (which makes it difficult to compare different polyhedra).

I definitely prefer the animation to always start on change. Of course, any interested party can modify it any number of ways to highlight some aspect that the user is interested in.