From @mitvma.mit.edu,@WVNVM.WVNET.EDU:BRYAN@WVNVM.WVNET.EDU Thu Dec 9 04:56:35 1993 Return-Path: <@mitvma.mit.edu,@WVNVM.WVNET.EDU:BRYAN@WVNVM.WVNET.EDU> Received: from mitvma.mit.edu by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA22759; Thu, 9 Dec 93 04:56:35 EST Message-Id: <9312090956.AA22759@life.ai.mit.edu> Received: from MITVMA.MIT.EDU by mitvma.mit.edu (IBM VM SMTP V2R2) with BSMTP id 2770; Thu, 09 Dec 93 03:39:11 EST Received: from WVNVM.WVNET.EDU (NJE origin MAILER@WVNVM) by MITVMA.MIT.EDU (LMail V1.1d/1.7f) with BSMTP id 1322; Thu, 9 Dec 1993 03:39:11 -0500 Received: from WVNVM.WVNET.EDU (NJE origin BRYAN@WVNVM) by WVNVM.WVNET.EDU (LMail V1.1d/1.7f) with BSMTP id 7496; Wed, 8 Dec 1993 23:39:35 -0500 X-Acknowledge-To: Date: Wed, 8 Dec 1993 23:39:35 EST From: "Jerry Bryan" To: "Cube Lovers List" Subject: That's all the 48-Fold Symmetries The two patterns I just posted are the only two for which the size of the equivalence class is 48. The next size up is 72, and there are twelve patterns whose equivalence class size is 72. Things become less interesting as the equivalence class size increases because they are less symmetrical overall. Also, there are more patterns. Finally, these things take a good deal of time to chase down. Therefore, I am going to stop chasing down "pretty patterns" for now unless somebody is just dying to see the patterns whose equivalence class size is 72. Finally, nobody really answered an earlier question, but is the following true: 1) Mirror-Image-of-Start is 12 q-turns from Start, and a sequence is known (Dan Hoey sent me a well-known sequence), 2) All-Edges-Flipped is 9 q-turns from Start, and a sequence is known, and 3) Mirror-Image-of-Start-and-All-Edges-Flipped (the antipodal of Start) is 15 q-turns from Start, and a sequence is *not* known? If this is true, then I will start working on the 15 move sequence. = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) (304) 293-5192 Associate Director, WVNET (304) 293-5540 fax 837 Chestnut Ridge Road BRYAN@WVNVM Morgantown, WV 26505 BRYAN@WVNVM.WVNET.EDU If you don't have time to do it right today, what makes you think you are going to have time to do it over again tomorrow?