# The Square's Group Antipodes

Use the following sequences to generate the described pattern from a
solved state, and it's inverse to get back from the pattern to a
solved state.

Note from Cubeman:
I first posted to Cube-lovers about the Square's group antipodes on Sun Aug 8, 1993. As far as I know, I was the first person to discover them. There are 16 distinct antipodes up to M-conjugacy. In this case, the antipodes are the positions farthest from start in the square's group of the 3x3x3 cube.

Shortly afterward on Aug 13, 1993 Dan Hoey organized the antipodes by symmetry group.

p66x, p80, p99, and p100 have symmetry group P=<(td)(frbl),(fb),(lr)>
p67x and p130 have symmetry group.................Q=<(td),(frbl)>
p135x and p137 have symmetry group..............S=<(td),(fb)(lr),(fr)(bl)>
p108, p128x, p129x, p131x, p132, and p136x have symmetry group HP=<(fb),(lr)>
p133x and p134x have symmetry group............HS=<(td),(fb)(lr)>

p66...Double 4 corner sw...L2 B2 R2 F2 L2 F2 T2 R2 (T2 D2 F2 T2) F2 L2 D2...(15 f)
C Conjugates = 6....M Conjugates = 6

p67...Antipode 2...R2 B2 D2 F2 D2 F2 T2 L2 (T2 D2 F2 T2) L2 T2 B2...(15f)
C Conjugates = 6....M Conjugates = 6

p80...2 DOT, Invert T's...R2 B2 D2 R2 B2 L2 B2 L2 (T2 D2 F2 T2) F2 L2 T2...(15 f)

p99...2 DOT, 4 ARM...R2 B2 D2 L2 B2 L2 F2 L2 (T2 D2 F2 T2) F2 L2 T2...(15 f)

p100...2 Cross, 4 ARCH 1...R2 B2 T2 R2 F2 L2 F2 L2 (T2 D2 F2 T2) F2 L2 T2...(15 f)

p130...2 Cross, 4 ARCH 2...L2 B2 D2 B2 L2 D2 F2 L2 (T2 D2 F2 L2) F2 L2 T2...(15 f)

p135...2 X, 4 T...L2 B2 D2 F2 T2 F2 T2 L2 (T2 D2 F2 T2) L2 D2 F2...(15 f)

p137...2 X, 4 ARM...L2 F2 T2 B2 T2 F2 T2 L2 (T2 D2 F2 T2) L2 D2 F2...(15 f)

p108...2 DOT, 2 T, 2 ARM...L2 F2 T2 R2 B2 L2 F2 L2 (T2 D2 F2 T2) F2 L2 T2...(15 f)

p128...2 H, 2 T, 2 CRN...L2 B2 R2 F2 L2 F2 T2 R2 (T2 D2 F2 T2) F2 L2 T2...(15 f)

p129...2 H, 2 T, 2 ARCH...R2 F2 L2 F2 L2 F2 T2 R2 (T2 D2 F2 T2) F2 L2 T2...(15 f)

p131...2 H, 2 ARM, 2 ARCH...L2 F2 R2 D2 B2 L2 D2 L2 (T2 D2 F2 T2) F2 L2 F2...(15 f)

p132...2 Cross, 2 ARCH, 2 CRN...L2 F2 D2 R2 F2 L2 B2 L2 (T2 D2 F2 T2) F2 L2 D2...(15 f)

p133...2 Cross, 2 T, 2 ARM...L2 F2 D2 F2 D2 F2 T2 L2 (T2 D2 F2 T2) L2 T2 B2...(15 f)

p134...2 CRN, 2 X, 2 ARCH...L2 F2 D2 B2 T2 F2 T2 L2 (T2 D2 F2 T2) L2 T2 B2...(15 f)

p136...2 H, 2 ARM, 2 CRN...R2 F2 L2 T2 B2 L2 T2 L2 (T2 D2 F2 T2) F2 L2 B2...(15 f)

Back to Main