Date: Tue, 09 May 95 15:31:32 -0400
From: Jerry Bryan <BRYAN@wvnvm.wvnet.edu >
Subject: Re: more on the slice group
```On 04/14/95 at 16:03:31 mreid@ptc.com said:
```

i also calculated for the other slice metric. in this metric,
neighbors can have the same distance from start, so a "strong"
local maximum is a position all of whose neighbors are strictly
closer to start. a "weak" local maximum is a position none of
whose neighbors are further from start.

I might prefer an alternative set of definitions: 1) a local
maximum is a position none of whose neighbors are further from
Start, 2) a strong local maximum is a position all of whose
neighbors are strictly closer to Start, and 3) a weak local
maximum is a local maximum which is not a strong local maximum.
But in the table which follows, I adopt Mike's definition.

```90 or 180 degree     number of     number of strong    number of weak
slice turns        positions       local maxima       local maxima
```
```0                  1               0                   0
1                  9               0                   0
2                 51               0                   0
3                247               0                   7
4                428               0                 212
5                 32               8                  32
```

the strict local maxima are all equivalent under symmetries of
the cube. they are the composition of pons asinorum with any
of the eight positions called "six dots".

Under M-conjugacy, we have

```90 or 180 degree     number of     number of strong    number of weak
slice turns        positions       local maxima       local maxima
```
```0                  1               0                   0
1                  2               0                   0
2                  4               0                   0
3                 15               0                   2
4                 25               0                  16
5                  3               1                   3
```
``` = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Robert G. Bryan (Jerry Bryan)                        (304) 293-5192
Associate Director, WVNET                            (304) 293-5540 fax