[next] [prev] [up] Date: Mon, 06 Dec 93 21:30:25 -0500 (EST)
[next] [prev] [up] From: Jerry Bryan <BRYAN%WVNVM.BITNET@mitvma.mit.edu >
[next] [prev] [up] Subject: Re: Unique antipode of edges only

On 12/06/93 at 10:45:00 mark.longridge@canrem.com said:
>-> I was somewhat startled to see the unique antipode of the 3x3x3 edges
>-> in the quarter-turn metric. Do you know what pattern that is?
>-> Dan

It's got to be all edges flipped in place.

I had to stare at my picture for a couple of minutes to be sure, but
yes it is. How did you know?

I would like to see the process generating the position!

This is doable, but it is a little harder said than done. My "data base"
is just a simple flat file with the states and the level associated with
each state. In the case of the 2x2x2, the file is about 625K, and
I have programs to search it readily. If you use the file in
"Solver mode", my "Solver program" just generates all successors of the
current node, finds each successor in the data base (it is a simple binary
search, the file is sorted), chooses one at level N-1 (there is always
at least one), and makes that the new current node. It stops when

I have a "Solver program" for the "corners plus centers of the
3x3x3" as well, but again the data base is small. It is actually
the original 625K file for the 2x2x2 case, plus three additional
625K files. This simple file structure was chosen to keep the file
small. There are no pointers, trees, or processes stored in the
data base.

The "edges of the 3x3x3 without centers" is a little tougher. Early
in the project, I generated a data base for the first few levels
(six or seven, I think), and I have a "Solver program" that will
work up to that level. However, the full "edges of the 3x3x3 without
centers" is a 4.2 gigabyte file on tape, so it is hard to process.
Also, the size of the equivalence classes is not in the data base,
only the level. I have to calculate the size of each equivalence
class, and it is an expensive calculation.

I made a pass at the
file and calculated the number of equivalence classes (took
125 hours on a mainframe), but I only saved a summary. I did not
save the number of equivalence classes for each state. I found
the antipodal by looking for level 15, since I knew there was
only one occurrence, and since the level was in the data base.

I did save the summaries by tape, so I should only have to look
on two tapes to find the other two equivalence classes which
have 24 elements.

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Robert G. Bryan (Jerry Bryan)              (304) 293-5192
Associate Director, WVNET                  (304) 293-5540 fax
837 Chestnut Ridge Road                     BRYAN@WVNVM
Morgantown, WV 26505                        BRYAN@WVNVM.WVNET.EDU

If you don't have time to do it right today, what makes you think you are
going to have time to do it over again tomorrow?

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