From mouse@collatz.mcrcim.mcgill.edu Mon Jan 17 16:23:05 1994 Return-Path: Received: from Collatz.McRCIM.McGill.EDU by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA17923; Mon, 17 Jan 94 16:23:05 EST Received: from localhost (root@localhost) by 5806 on Collatz.McRCIM.McGill.EDU (8.6.4 Mouse 1.0) id QAA05806 for cube-lovers@ai.mit.edu; Mon, 17 Jan 1994 16:22:50 -0500 Date: Mon, 17 Jan 1994 16:22:50 -0500 From: der Mouse Message-Id: <199401172122.QAA05806@Collatz.McRCIM.McGill.EDU> To: cube-lovers@ai.mit.edu Subject: Re: Higher Order Cubes >> Perhaps it would be possible to build a 4-Cube that was internally a >> 5-Cube but for which the middle slice was not actually visible on >> the surface? Or a 2-Cube that's internally a 3-Cube? > Yes, I think you could build such a 4-Cube. Likewise, you could build > a 2-Cube as a 3-Cube with invisible middle slices. But I don't > believe you'd want one: it could get completely jammed much too > easily. > The reason: If you take a 3-Cube and rotate its left and right slices > 45 degrees each, you cannot rotate any of its other faces. Duh, yeah; that never occurred to me. > There may be a way out, though. If you can anchor the place where the > three axes meet to one of the corner cubelets in some way, the > problem is solved: [...]. Yes. I think this may be possible, too...consider a normal 3-Cube, and restrict yourself to R, U, and F turns. Then ignore the center and edge cubies - the ones that get invisibilized. You're left with a 2-Cube. Three edge cubies never move with respect to the center cubies or the corner cubie they surround; glue those together. Presto! The same treatment is not possible for making a 4-Cube out of a 5-Cube, but an alternative occurs to me, that I *think* will work for higher cubes: key three of the (invisible) center cubies to the center six-pronged piece, so that they can't turn. Then half the face turns will cause the invisible center slice to turn with them; non-face slices (which don't exist on the 2/3-Cube) work normally. I notice with this construction for (say) a 4-Cube, the puzzle core turns whenever certain face slices do. With the 4-Cube I owned (and presumably still own, if I could find it), the puzzle core turns whenever certain next-to-center slices do. I suspect the latter would make for a smoother-turning puzzle. Perhaps someone will someday build a 5-Cube-turned-4-Cube and this can be determined. In the (IMO unlikely) event I originated any of the above ideas, I hereby place it/them in the public domain. Go wild, Ishi Press. :-) der Mouse mouse@collatz.mcrcim.mcgill.edu