Date: Tue, 30 May 95 12:29:29 -0400
From: michael reid <mreid@ptc.com >
~~~ Subject: Re: AntiSlice Under M-conjugacy (and a problem with slice)

jerry writes

```[ ... ]
```
```Level       Positions     Strong      Weak        Total
Local Max   Local Max   Local Max
```
```6            184           1          35          36
```

>>beg the obvious question: what is that strong local maximum,
>>which is unique up to symmetry?

```[ ... ]
```
```Try instead, (L2R2)(U2D2)(F'B')(U2D2)(L2R2)(F'B').
```

This is a very pretty pattern which may well have a name, but I
don't know what the name is. Also, it is its own inverse.

```Is the length 12h in <Q,H>?  Is it a local maximum (strong or otherwise)
in <Q,H>?   Is the length 20q in <Q>?  Is it a local maximum in <Q>?
```

no, yes (otherwise), no, and yes, respectively.

we have seen this pattern several times recently. this is one of
those positions with 16 symmetries. i called it "four pluses" in my
message of may 11 (although i gave it in a different orientation)

```)     four pluses                 ( R2 F2 R2 U'D F2 R2 F2 UD' )
```

in fact, this maneuver is minimal in both the quarter turn and the
face turn metrics, so its length is 16q, 10f. it is a weak local
maximum in the face turn metric; one can check that no minimal
maneuver ends with the face turn R. however, using the 16 symmetries
which preserve the U-D axis, and inversion, we can give minimal
maneuvers which end with turns of any of the six faces. this shows
that it's a weak local maximum in the face turn metric. local
maximality in the quarter turn metric follows in a similar manner.

also, mark pointed out on april 16 that this position lies in the
center of the antislice group.

mike