AT-symmetric positions

There are 4 different AT symmetry groups; each preserves one of the corners of the cube (and therefore also the opposite corner). Here we fix the UFR (and thus also the DLB) corner. There are 48 positions that are invariant under all such symmetries; 16 of them have more symmetry, namely T-symmetry, and 4 of these even have M-symmetry. The other 32 positions pair up into 16 patterns, as shown. I have even calculated all minimal maneuvers, using my optimal cube solver.

[AT-symmetric pattern #1]
F U D R2 B D2 L' U2 F L2 U D F' (17q*, 13f*)
[AT-symmetric pattern #2]
F R2 U F U' F' R B' R B U' L' U L F' (16q*, 15f)
F B U2 L U' F2 B2 D F2 B2 L' U2 F' B' (14f*, 20q)
[AT-symmetric pattern #3]
F R F R' F B U' L D' B' L B D F' L' U F B' (18q*, 18f)
F2 R U' B' U2 R F B' D' R2 F D F2 B2 R' F2 (16f*, 22q)
[AT-symmetric pattern #4]
F U' L F2 B2 R2 D' B' R2 F R L' D' R' D' (19q*, 15f*)
[AT-symmetric pattern #5]
B D' L2 F' U2 L' F2 D' R2 F' D2 L' B (18q*, 13f*)
[AT-symmetric pattern #6]
B R B2 U' R2 U' L2 B2 L2 D R' L' F2 U' F' (21q*, 15f*)
[AT-symmetric pattern #7]
B D B' R' U' L' U' R' L' F B U' D F U D B U2 (19q*, 18f)
F B2 U' F D' F' R' F R' U' D B R2 D2 R2 L2 (16f*, 21q)
[AT-symmetric pattern #8]
F L U' L' F B' U B' R L2 D' R' F D R U2 D2 (20q*, 17f*)
[AT-symmetric pattern #9]
F L' U2 B R2 D2 L2 U' D R' F' B U D2 B R B D' (23q*, 18f*)
[AT-symmetric pattern #10]
B R D R' L U D F2 B2 D B2 D2 B L' B' U' F U' (22q*, 18f*)
[AT-symmetric pattern #11]
F R' L' F' B U F' B L' U R' F U' R D' B2 U' F D' F R' (22q*, 21f)
B R2 U2 B2 D B' D R U' D' L U F' U F2 D2 L2 F (18f*, 24q)
[AT-symmetric pattern #12]
F D2 R U' F R' B' D' L2 F' U' D' L2 B L F2 U2 D' (23q*, 18f*)
[AT-symmetric pattern #13]
F U B U F' B2 U' B' R' B' U D' R' L F U B R' B' L2 (22q*, 20f)
F D' F U2 D F2 B2 U R L' D' F L B' R L' U' D2 F2 (19f*, 24q)
[AT-symmetric pattern #14]
F R U F2 U' D' F R' B D R U2 R B' D B' D R L' (21q*, 19f*)
[AT-symmetric pattern #15]
F L B D L' F' L B U L' F' U2 D2 B R L F (19q*, 17f*)
[AT-symmetric pattern #16]
B L' F B U' R' F' U' B' U' R' L D' B' D' F' R' D' L B' (20q*, 20f)
F D R2 F R L2 F2 B2 U2 D2 R F' R2 D' F' (15f*, 22q)

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Updated May 24, 2005.