From cube-lovers-errors@curry.epilogue.com Thu May 30 18:15:45 1996 Return-Path: cube-lovers-errors@curry.epilogue.com Received: from curry.epilogue.com (localhost [127.0.0.1]) by curry.epilogue.com (8.6.12/8.6.12) with SMTP id SAA05355 for ; Thu, 30 May 1996 18:15:45 -0400 Precedence: bulk Errors-To: cube-lovers-errors@curry.epilogue.com Date: Thu, 30 May 1996 15:23:58 -0400 From: der Mouse Message-Id: <199605301923.PAA18428@Collatz.McRCIM.McGill.EDU> To: cube-lovers@ai.mit.edu Subject: Re: Another subscriber > 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