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To: Cube Mailing List <Cube-Lovers@ai.mit.edu>
Subject: d-dimensional cube mechanisms
Date: Mon, 18 Aug 1997 14:32:59 -0700
From: Scott Huddleston <scotth@ichips.intel.com>

Several years ago I worked out a solution to the d-cube 3^d, for d>3.
This is most interesting combinatorially if you assume you're
restricted to only rotating entire (d-1)-faces at a time, so that's
what I assumed in my solution.

But when I thought about building a mechanism for the d-cube, I
came to the surprising (to me) conclusion that any natural extension 
of the 3^3 mechanism to d dimensions would allow you to rotate any 
2-face.  I concluded that any mechanism that would restrict you to 
only rotating entire (d-1)-faces would require some sort of complex 
interlocking mechanism that would have to engage and disengage 
whenever a (d-1)-face was to be rotated.

Has anyone else thought about this problem (d-cube mechanisms)
enough to confirm or refute my conclusions?

Best,
- Scott Huddleston
scotth@ichips.intel.com