[next] [prev] [up] Date: Wed, 07 Feb 96 02:47:00 -0500
[next] [prev] [up] From: Mark Longridge <mark.longridge@canrem.com >
[next] ~~~ [up] Subject: < U, F, R > group

> there was never any response to this, but i'll give my solution

I am working on an engine to search optimal paths for < U, F, R > but
it's not done yet. It's certainly within the bounds of computibility:

Size (u_f_r) = 170,659,735,142,400 (hmmm, 170 trillion maybe not!)
let  X  =  U2 F R' F2 R F2 R F2 R' F U2 .

then X produces two two-cycles of corner-edge pairs. the commutator
[ X , C_UFR ] produces "cube in a cube" in 22 face / 32 quarter turns
and only turns the faces U, F and R.

the notation C_UFR refers to a rotation of the whole cube, and
[ a, b ] denotes the commutator a b a^-1 b^-1 .



Although harder to remember, X + ( X * C_UFR) will do.

U2 F1 R3 F2 R1 F2 R1 F2 R3 F1 U2
F2 R1 U3 R2 U1 R2 U1 R2 U3 R1 F2        (22 f, 32 q)
-> Mark <-

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