Below are some images showing how some interesting new puzzles would look, if they could be built
The screenshots are taken from my Great Stella program, but I should point out that it won't allow you to actually twist the puzzles, only see where the slicing lines would go.
There was talk recently (started by Bram Cohen) about how a Pentultimate might be built. Well, if one does ever get built, here are some interesting modifications that could be made.
The Rhombicultimate: a rhombic triacontahedron with the Pentultimate mechanism inside. I think this would probably be the best embodiment for the puzzle, with correct orientation of both triangular and pentagonal parts required.
The Cubultimate: a cube with the Pentultimate mechanism inside. This is truly bizarre, and would be extremely disorienting! Any twisting and the puzzle will immediately lose its cube shape. As with the Pentultimate, 1/5th turns are required. The puzzle could be a single colour and still be quite hard. I think a lot of people would even have trouble mixing this one up!
The Octultimate: similar, but now in octahedron shape.
The Pyrultimate: similar again, but now in tetrahedron shape.
Even seeing these strange beasts its hard to imagine how they twist. I might make a cardboard model which twists along only a single plane, just to see how it looks.