[next] [prev] [up] Date: Mon, 14 Nov 94 11:59:00 -0500
[next] [prev] [up] From: Mark Longridge <mark.longridge@canrem.com >
[next] ~~~ [up] Subject: <U, R> Antipode!

With Jerry's help I have found a process for one of the <U, R>
antipodes! Note the number of turns required in the h turn metric.
I applied the turn R1 to the position so the program only needed to
search 24 q turns deep.

First Antipodal Process    (25 q, 20 q)
UR13 = U2 R1 U3 R2 U3 R2 U3 R1 U2 R3 U1 R3 U3 R1 U1 R2 U1 R3 U1 R3

Also....      UR13 ^ 2 = I

Using current techniques, this required a run of about 11 hours.

It remains to be seen how the Kociemba algorithm resolves this
position, and I will try this next.

Although somewhat unrelated, I found a square's group process
for 6 X order 2 (the pons asinorum) by hand, which does
not move the centres:

U2 B2 L2 U2 D2 L2 F2 T2
F2 U2 L2 F2 B2 L2 D2 F2   (16 h, 32 q)

-> Mark <-
email: mark.longridge@canrem.com

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