By doing this, I not only list which puzzles have been made, but more importantly which puzzles have not. Some of these might be developed, or at least give a few ideas for producing new rotational puzzles. This disqualifies the Domino for example because its sides have order 2 while the top and bottom faces have order 4. Actually this condition implies the first one as well. In each case the axes can go through all the corners, all the faces, or all the edges of the associated Platonic solid.
All axes of rotation go through the centre of a puzzle.
Puzzles with 4 axes of rotation, i.e. the faces or corners of a tetrahedron. Two variations already exist. The standard tetrahedral puzzle is the Pyraminx , a tetrahedron with three pieces to an edge. The corners are fixed on axes. The tips are trivial as they do not interact with other pieces.