If you add an extra side to a Rubik's Cube, you get a Pentagonal Prism. With fudging, 90-degree doctrinaire moves are possible on the square sides (see Oskar's Illegal Cube).

If you add two extra sides to a Face Turning Octahedron, you get a Square Antiprism, but no doctrinaire moves are possible. Can you fudge it like the Illegal Cube to make it functional?

Yes. Just look in Oskar's shop. It's in there somewhere...

I think this is the puzzle you and Tom are talking about:

http://www.shapeways.com/model/139018/anticube.html?gid=sg13603

Carl

Actually I just went through the shop to check before I posted this.

The AntiCube doesn't really fit the analogy of Rubik's Cube : Illegal Cube :: FTO : Illegal Antiprism (as I guess you might as well call it), which is what I originally thought of.