First, as a comment on the other thread, I think it is safe to say:

If one can solve an (2n+1)^3 cube, then one can solve a (2n)^3 cube.

"Ronnie B. Kon" <ronnie@cisco.com> writes:
>I've had this dream of making cubies which attach (via bars or perhaps
>electromagnets) to their neighbors, with the smarts to detect the torque of
>a turn and release until the turn has been completed. You could then sell
>corner cubies, edge cubies, face cubies, and internal cubies one-at-a-time
>and people could build their own puzzles as large as they wanted.

It would certainly require a very creative design for the corners; your
description seems to say that in the stable state the corners are not
attached by anything!

Perhaps corner cubies could be equipped with buttons that had to be
depressed before a face would turn?
For instance, imagine a cube with three faces that have a button on
the middle, each one triggering a bar on the opposite side. When a button
is pressed, the bar retracts into the cube. This would make a
workable corner cube, although it would be a bit awkward to press the
face that you wanted to turn!

As another aside, I don't understand the rationale behind the canonical
4x4x4 design. It would seem to me that it's better to have two rings of
grooves in each dimension, so that the face pieces could have "fatter"
legs and not break off as easily.

-- 
Wei-Hwa Huang, whuang@cco.caltech.edu, http://www.ugcs.caltech.edu/~whuang/
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Caught Porfiry, Raskolnikov sung his swan Sonia when he went Dounia to Siberia.