E-symmetric positions

These are the positions that are invariant under all rotations of the cube producing an even permutation of the six faces. There are 72 such positions; 24 have more symmetry, namely H-symmetry, and 4 of these have M-symmetry. The other 48 positions fall into 12 patterns, as shown below. I have also calculated all minimal maneuvers, using my optimal cube solver.

[E-symmetric pattern #1]
F' B' U R' U' D R L' U R' D' L U' D R L' D' L F' B' (20q*, 20f)
F R L F U' D' F R2 L2 U2 D2 B R' L' B U D B (18f*, 22q)
[E-symmetric pattern #2]
F' R2 U D R' L' U' F B R2 F' U' D' F' B U' D' B' (20q*, 18f*)
[E-symmetric pattern #3]
F' B' R' L' F B U D R' L' U' D' (12q*, 12f*)
[E-symmetric pattern #4]
F U2 R F B R' U2 B R L B U' D' R' L U' L2 (20q*, 17f*)
[E-symmetric pattern #5]
F R' F L U D' L' U R U' D F' D' B U D' B' R' F R' (20q*, 20f)
F2 U D2 L2 F U D F' L2 U F B U R' L' F' B R (18f*, 22q)
[E-symmetric pattern #6]
F B R' L' F B U' D' R L U' D' (12q*, 12f*)
[E-symmetric pattern #7]
F R U2 F L B U D' F L D F' B D R B D (18q*, 17f*)
[E-symmetric pattern #8]
F U2 F' B D B' L B L D' B2 R' D F D F' R D2 F' (22q*, 19f)
F' R2 D2 F U' D F2 R B2 L F2 R D2 F B' U' F' B' (18f*, 24q)
[E-symmetric pattern #9]
F' R F U R2 U F' L' D F U2 R' F' B2 R' D' R' B' U' (22q*, 19f*)
[E-symmetric pattern #10]
F R2 B' L' U' L' F' B D B R B R F U' R U2 D2 F' (22q*, 19f*)
[E-symmetric pattern #11]
F B R2 U' F L F U' F B' R F' U' B' R L' B' R L (20q*, 19f)
F R2 U D' F2 L' U D L2 B U D' F B' U' D2 F B (18f*, 22q)
[E-symmetric pattern #12]
F R' D B U D F' L B D R' F R' L B' U' F' B' L F' D L (22q*, 22f)
F B U F L2 D2 F2 B R F B R F' L2 D2 R2 U2 B U (19f*, 26q)

Symmetric positions | Cube page | Home page | E-mail

Updated May 24, 2005.