Permuting the vertices of a Platonic solid

Choose a solid and a permutation σ, then press Permute! The vertex labeled i moves to the position where vertex σ(i) started; the edges travel along with their endpoints, so you can see whether σ is a symmetry of the solid. Vertices glide along great circles of the circumscribed sphere. When the move is a genuine rotation, it is animated as one.

Labels follow the dice convention: except on the tetrahedron, opposite vertices always sum to n + 1. Please notify me if you encounter any errors or bugs.

Enter σ in either notation; the other one updates to match. In cycle notation, products are applied right to left, so the cycles need not be disjoint; use e (or leave the box blank) for the identity. Press Enter or Permute! to move the solid. Revert (or Shift+Enter) moves it back to its starting position but keeps σ, so pressing Enter again replays the motion.