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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