[next] [prev] [up] Date: Mon, 25 Sep 95 00:44:40 +0100
[next] [prev] [up] From: Michiel Boland <boland@sci.kun.nl >
[next] [prev] [up] Subject: Re: Order problems

Jerry wrote:
>I would be curious to hear how you are doing your search. It is
>trivial to see how to calculate the order of a particular
>position. However, it is not obvious to me how to find a
>position of a particular order. I hope it is not the case that
>it is in the archives and I just haven't seen it.

I use a simple brute-force method, that is, I compute the order
of each transform and the number of quarter turns. If there is
already a transform with that order & number of qt, I forget all
about it and go to the next transform.

I have the C source available for anyone who wants to peek at it.

Note that (almost) all transforms start with UxRx, since you
have to twist two adjacent faces in order to get something with
order other than 1, 2 or 4. That saves a bit of time.

On my PC, i finished all transforms of length 6 (quarter- and
half turns), and did some of length 7. Fortunately, as I
mentioned earlier, I managed to get it to work on a somewhat
faster machine, and am now waiting for the results of that. I am
searching all transforms of 10 quarter turns or less.

A process with order 110 must have an even number of quarter
turns, since the permutation on the edges has to be even (the
only possibility is to have an 11-cycle on the edges, which is
an even permutation).
Therefore, since there are no processes with order 110 with 6 or
less quarter turns, this proves that the one of length 8 is
indeed the shortest possible.


Michiel Boland <boland@sci.kun.nl>
University of Nijmegen
The Netherlands

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