I hope I might be forgiven for posting one question that has been
paining me-- I'd dearly love to know the answer! Is it true that a
physical prototype of the "6" (6 X 6 X 6) has been constructed; [...]
I'm also very curious about the mechanism for a "7"; it seems to me
that locking pins (or the equivalent) would be necessary. I really
wonder whether the mechanical design can be practical.

In my opinion mechanical designs for the 7 and above will have to be
fundamentally different from those for the 6 and below, because that's
the point at which the "buried" corner of a corner cubie extends past
the surface of the face during a face turn and thus it's not possible
to build the thing as rigid pieces connected to a central mechanism, at
least not without cutting away part of some face-center cubies.
(Specifically, that buried corner is at sqrt(2)*(.5-1/N) from the
center, taking the cube side as 1 and N as the order of the cube. The
face is at .5 from the center. The former becomes greater than the
latter at about N=6.83...not that non-integer N make physical sense.)

This is not to say that a 7 is impossible, just that it will have to be
rather drastically different - somehow, when a turn is started, the
corner cubie will have to be mechnically locked to the rest of the face
that's turning with it. I can easily enough imagine possible
mechanisms, but coming up with one simple enough to mass-produce at a
price people are likely to be willing to pay would be a major
challenge.

On the other hand, a straightforward locking mechanism could probably
be put together by a good watchmaking shop at no more than the price of
a high-end watch. A few collectors might go for it, especially since
the result - particularly if made out of metal - would feel much better
than the plastic-on-plastic feel of most cubes.

der Mouse

mouse@collatz.mcrcim.mcgill.edu