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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 maxima0 1 0 0 1 9 0 0 2 51 0 0 3 247 0 7 4 428 0 212 5 32 8 32the 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 maxima0 1 0 0 1 2 0 0 2 4 0 0 3 15 0 2 4 25 0 16 5 3 1 3

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