The Group D3

Up to M-symmetry there are 208 cubes which exactly have the symmetries of this subgroup. All cubes but 4 up to M-symmetry are generated in 19 moves or less. 4 cubes needs 20 moves, they also have antisymmetry. They are depicted below, together with a few nicer examples of this class.

The table gives the number of cubes up to M-symmetry which exactly have D3-symmetry, the average maneuver length is 17.81:

Distance
Number
Distance
Number
0f
0
11f
1
1f
0
12f
2
2f
0
13f
0
3f
0
14f
6
4f
0
15f
5
5f
0
16f
14
6f
0
17f
26
7f
0
18f
85
8f
0
19f
65
9f
0
20f
4
10f
0


If you are interested in a list of all optimal maneuvers, download the file D3.zip. The four 20f*-maneuvers also are included in the file 20moves.zip.

Name
shortest maneuver with exactly this symmetry
Generator
D B D U2 B2 F2 L2 R2 U' F U (11f*)
Name
Generator
L U L2 R2 U' L U L R' B' U' L' B L R' U' (16f*)
Name
Generator
U R2 D F' L D2 U2 R' D2 U2 F D' R2 U' (14f*)
Name
Generator
L2 U L' U B' L B' U F' D' B U2 B L2 D F U' (17f*)
Name
Generator
F U L2 B' R2 D2 B D F' R' F D2 B2 D L2 R' U' (17f*)
Name
Generator
U' F U' L2 B2 L2 D R D2 F D L2 B2 L2 U' R U' (17f*)
Name
 
Generator
D' L R2 B F2 D F2 L2 U2 L2 F L R D2 U2 F' R D' R' U' (20f*)
Name
Generator
F' D R2 F' L' D' F U R U L2 F L' U' B U2 F2 U2 R2 U' (20f*)
Name
Generator
R F' D F' R' D L2 U' L2 D B' F2 R D' L F2 U' L2 R' U' (20f*)
Name
Generator
R U2 B F' U2 L F U F' D' R B D2 B U L2 R F2 R' U' (20f*)

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© 2017  Herbert Kociemba