Date: Sun, 18 Jun 95 08:25:49 -0400
From: Jerry Bryan <BRYAN@wvnvm.wvnet.edu >
Subject: Re: Crazy Corner Pattern
```On 06/17/95 at 05:38:00 mark.longridge@canrem.com said:
>On Mon, 17 Jan 1994 09:06:59 EST, Jerry wrote:
>>
>>     Counting M-conjugacy classes of the corners of Rubik's cube
>>     -----------------------------------------------------------
>>
>>                   M-Class     Number     Number
>>                     Size        of         of
>>                              Classes    Elements
>>
>>                         1        1  =        1     Start
>>                         2        1  =        2     +4 -4 Twist
>>                         3        3  =        9
>>                         4        1  =        4
>>                         6       34  =      204
>>                         8       33  =      264
>>                        12      301  =     3612
>>                        16      104  =     1664
>>                        24     9064  =   217536
>>                        48  1832428  = 87956544
>>
>>                     Total  1841970    88179840
```

I'm trying to find the 1 pattern with M-class size of 4 of the
corners group.
The only pattern that I can find is 4 alternate corners twisted
clockwise which is in the twist orbit.

It does not seem to be any pattern with just corners twisted in
place.

Jerry, if you could *please* identify this pattern before I go
nuts...... !

The position is called T-symmetric in Dan's taxonomy (actually,
there are four T subgroups of M, T1 through T4). The symmetry
is related to opposite corners, e.g., the UFL-DRB axis,
which is why there are four T subgroups.

Also, the position is Q-transitive, so you can check it out
in _Symmetry and Local Maxima_. I quote ".... each edge on the
girdle may be swapped with the diametrically opposite edge,
provided that the corners on the girdle are swapped with
their opposites as well." Here, you would fix the edges and
pay attention only to the swapping of the corners.

``` = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Robert G. Bryan (Jerry Bryan)                        (304) 293-5192
Associate Director, WVNET                            (304) 293-5540 fax