From JBRYAN@pstcc.cc.tn.us Wed Dec 20 08:42:45 1995 Return-Path: Received: from PSTCC4.PSTCC.CC.TN.US by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA18095; Wed, 20 Dec 95 08:42:45 EST Resent-From: JBRYAN@pstcc.cc.tn.us Resent-Message-Id: <9512201342.AA18095@life.ai.mit.edu> Received: from pstcc.cc.tn.us by pstcc.cc.tn.us (PMDF V5.0-3 #11457) id <01HZ0VXDUEHS8WY2SC@pstcc.cc.tn.us> for cube-lovers@ai.mit.edu; Wed, 20 Dec 1995 08:44:18 -0400 (EDT) Resent-Date: Wed, 20 Dec 1995 08:44:18 -0400 (EDT) Date: Wed, 20 Dec 1995 08:44:16 -0400 (EDT) From: Jerry Bryan Subject: Re: Physical Cubes and Models Thereof In-Reply-To: <199512201124.GAA04566@Collatz.McRCIM.McGill.EDU> Sender: JBRYAN@pstcc.cc.tn.us To: Cube-Lovers Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Content-Transfer-Encoding: 7BIT On Wed, 20 Dec 1995, der Mouse wrote: > The only facelet for which invisible orientation changes are even > possible is the center facelet on an odd-order cube. Other facelets > always have a fixed orientation with respect to the center of the face > they're on at the moment. (On the 4x4x4, for example, if you mark > every facelet for orientation, you will find that each center facelets > always has the same corner to the face center, regardless of which face > it's on.) I believe Der Mouse is entirely correct for the physical cube case (which is the case I was talking about). Imagine a 99x99x99 or some such large cube, and for each facelet except the face center itself mark the corner closest to the face center. Any slab quarter-turn preserves the fact that all marked corners remain closest to the face center. There are two cases -- a face slab, and any inner slab. But both cases work. In the case of a face slab, the orientations of the facelets on the face of the slab do change, but the orientations change in lock step with the positions of the facelets. In the case of a mathematical model, Evisceration also preserves facelet orientation, if I understand correctly how first Singmaster and then Dan Hoey defined Evisceration. However, Inflection and Exflection do not preserve facelet orientation. Could (or should) the definitions of Inflection and Exflection be broadened to include and preserve facelet orientation? = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) jbryan@pstcc.cc.tn.us