From @mitvma.mit.edu,@WVNVM.WVNET.EDU:BRYAN@WVNVM.WVNET.EDU Wed Jan 12 23:46:28 1994 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 AA20019; Wed, 12 Jan 94 23:46:28 EST Message-Id: <9401130446.AA20019@life.ai.mit.edu> Received: from MITVMA.MIT.EDU by mitvma.mit.edu (IBM VM SMTP V2R2) with BSMTP id 1427; Wed, 12 Jan 94 23:46:31 EST Received: from WVNVM.WVNET.EDU (NJE origin MAILER@WVNVM) by MITVMA.MIT.EDU (LMail V1.1d/1.7f) with BSMTP id 7322; Wed, 12 Jan 1994 23:46:31 -0500 Received: from WVNVM.WVNET.EDU (NJE origin BRYAN@WVNVM) by WVNVM.WVNET.EDU (LMail V1.1d/1.7f) with BSMTP id 4696; Wed, 12 Jan 1994 23:43:55 -0500 X-Acknowledge-To: Date: Wed, 12 Jan 1994 23:43:54 EST From: "Jerry Bryan" To: "Cube Lovers List" Subject: |G\M| - the Nineteen Cases We Know A - |BClass(X)| for X in GC\B (order of B-conjugate class for corners) B - |BClass(Y)| for Y in GE\B (order of B-conjugate class for edges) C - |GC[A]\B| (number of B-conjugate classes of size A for corners) D - |GE[B]\B| (number of B-conjugate classes of size B for edges) E - |BClass(X) * BClass(Y)| = |BClass(X)| * |BClass(Y)| / 2 F - |BClass(X) * BClass(Y)| * |GC[A]\B| * |GE[B]\B| / 48 (number of M-conjugates of |GC[A]\B * GE[B]\B) A B C D E F 1152 24 75,392 4 13,824 86,851,584 1152 48 75,392 2 27,648 86,851,584 1152 72 75,392 12 41,472 781,664,256 1152 96 75,392 16 55,296 1,389,625,344 1152 144 75,392 110 82,944 14,330,511,360 1152 192 75,392 70 110,592 12,159,221,760 1152 288 75,392 1,544 165,888 402,296,537,088 1152 384 75,392 1,252 221,184 434,952,732,672 1152 576 75,392 128,858 331,776 67,149,128,466,432 1152 1152 75,392 851,493,140 663,552 887,442,335,689,605,120 24 1152 1 851,493,140 13,824 245,230,024,320 48 1152 1 851,493,140 27,648 490,460,048,640 72 1152 3 851,493,140 41,472 2,207,070,218,880 96 1152 1 851,493,140 55,296 980,920,097,280 144 1152 14 851,493,140 82,944 20,599,322,042,880 192 1152 15 851,493,140 110,592 29,427,602,918,400 288 1152 135 851,493,140 165,888 397,272,639,398,400 384 1152 32 851,493,140 221,184 125,557,772,451,840 576 1152 2,208 851,493,140 331,776 12,995,229,448,765,440 Total 901,082,361,368,033,280 Note that we have covered over 99.99 percent of edge positions (which are combined with all corner positions), and over 96.9 percent of the remaining corner positions (which are combined with all edge positions). Hence, we have covered about 99.99969 percent of all positions. However, that last fraction of a percent is going to be devilishly difficult. = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 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?