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Mail-from: From reid@math.brown.edu Tue Aug 5 14:31:16 1997
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Date: Tue, 5 Aug 1997 14:33:36 -0400
From: michael reid
To: cube-lovers@ai.mit.edu
Subject: 20f maneuvers for superfliptwist
because of the historical interest in the pattern superfliptwist, i
decided to find all 20f maneuvers for it. this took about 114 hours
of searching, using the symmetry reductions i described in an earlier
message.
by "all" maneuvers, i mean that any 20 face turn sequence for
superfliptwist can be transformed in to one on my list by conjugating
by one of the 24 symmetries that fix superfliptwist, or by inverting
the sequence and conjugating by the cube rotation C_U , and perhaps
again by one of the 24 symmetries. some extra processing by hand
was required to eliminate inverse pairs. hopefully i haven't made
any errors here. the list of maneuvers is
U R F' B U' D' F U' D F L F' L' U R D F U R L (20f, 20q)
U F D L U R' F' R F U' D F U' D' F' B L U R L (20f, 20q)
U R' F' U' F' R' B' D2 R' D R L' B R F B2 R' U' B D' (20f, 22q)
U F L D L F R U2 F U' F' B R' F' R2 L' F D R' D' (20f, 22q)
U R' U' D F' U' F2 B' U L F' R L' U B L B U F R2 (20f, 22q)
U R' U' D F' U' B' R' F' R U F2 R U B L B U F R2 (20f, 22q)
U F L D L F R U2 F U' F' B R' F' L' U' R' U F R2 (20f, 22q)
U F R' F' L' U' R' U' D F' U F2 R U L B L U F R2 (20f, 22q)
U F D L D F R L' U' L F U2 D' F' U' F' B R' F R2 (20f, 22q)
U F D L D F R U2 F R U' R' D' F' U' F' B R' F R2 (20f, 22q)
U R B D2 L B R' D' R' B L' D2 L B' D2 R' F B2 D' R (20f, 24q)
U R' B L2 U' L2 U' B U' L2 D R B D F U2 R' L' B' R' (20f, 24q)
U F B' R' U2 L U' R2 B' L' F2 U' R' D' L2 U D B D' B (20f, 24q)
U R L2 F U F U F L D2 L' D' L U' D F2 B L' F R2 (20f, 24q)
U R L' B' R' F R' F' B' D2 F U B L2 D R U2 B D' B2 (20f, 24q)
U R' U2 D F B' R F' R' F2 R U B U B U R2 L B L2 (20f, 24q)
U R' B R U' L' U2 B' R2 L' D B2 L U' B R F U B L2 (20f, 24q)
U R' D2 B' U' F2 R' D' L' U2 R L B L' B R F B' D' R2 (20f, 24q)
U F D L U F' R U2 B R' L2 U' F2 R' F' L U L' F R2 (20f, 24q)
U F2 R' U' F' R' L2 U B U L' F B' U2 D L U' D' B R2 (20f, 24q)
U F' B' L F B2 U' D L' B U B R' L2 D' B' R' D2 B R2 (20f, 24q)
U R2 B L' U2 B' R' L F2 D F L2 D R' F2 D' R L' U2 B (20f, 26q)
U F R' L D B R2 U2 L2 D' R' D' R L2 U' F L D2 B R2 (20f, 26q)
U F2 L D B' R L2 F' R' F' L2 B2 R2 U F R' L D B R2 (20f, 26q)
U F2 R' L' U F' U' D2 B2 U' B D R' L2 D2 L2 D2 F U2 B' (20f, 28q)
the maneuver that herbert kociemba found is equivalent to the 28q
maneuver.
the two maneuvers that are 20q long can be obtained from one another
by inverting the first, then cyclically shifting the antislice to the
end of the maneuver, and then reorienting.
the first of the 26q maneuvers is quite interesting. it can also be
written as
(U R2 B L' U2 B' R' L F2 D C_UF)^2
where C_UF is a cube rotation about the UF - DB edge axis (as in
bandelow's book).
mike