   Date: Mon, 03 Jul 95 14:59:00 -0400   From: Mark Longridge <mark.longridge@canrem.com >
~~~ ~~~ Subject: Crazy Corner Pattern Revisited

Jerry writes:

In their position, the UFL and RBD corners are
in place, and the other three pairs are swapped. The "girdle"
includes the three pairs that are swapped. Hence, there
is an axis of symmetry along the UFL-RBD axis. The odd number of
swaps is compensated by an odd number in the edges. The compensation
is not required for corners only.

```R D D
U U D
U U B
```
```D L L  F F D  L L F  L F F
R L L  F F B  L R R  B B F
R R B  R B B  U R R  B B U
```
```U U L
U D D
F D D
```

Much is explained! (And this is all the way back in file "cube01" in
the archives, Date: 14 December 1980 1916-EST).

```What does the 1916- mean in front of EST???
```

If we put the edges in place in Jerry's (and Dan's) position
then we have a position M-conjugate to the one I posted.
(re-posted below).

```        F U U
U U U
D U L
R L B   R F B   D R R   B B D
L L L   F F F   R R R   B B B
U L L   F F U   L R F   L B F
D D B
D D D
R D U
```

Jerry Continues:

...there is an axis of symmetry along the UFL-RBD axis. The odd
number of swaps is compensated by an odd number in the edges.
The compensation is not required for corners only.

Great! We both concur that this pattern is in the swap orbit.
There is another position with M-class 4 in the twist orbit,
but that one is *utterly* impossible unless one corner twists
on it's own (perhaps due to desperate cube turning?)

There are 2 other types of position with M-class 4, and that is
pinwheels and pinwheels + pons asinorum.

```-> Mark <-
```

(I must be cubing too much, 1916-EST has to be 7:16 pm Eastern
Standard Time).     