The Group D_2h(edge)

Up to M-symmetry there are 960 cubes which exactly have the symmetries of this subgroup, all of them are selfinverse. There are 5 cubes up to M-symmetry which need 20 moves .All other cubes can be solved within 19 moves or less. Some examples are listed below.

The table gives the number of cubes up to M-symmetry which exactly have D_2h(edge)-symmetry, the average maneuver length is 16.26:

Distance	Number	Distance	Number
0f	0	11f	28
1f	0	12f	42
2f	0	13f	57
3f	0	14f	54
4f	0	15f	71
5f	0	16f	106
6f	0	17f	254
7f	2	18f	218
8f	4	19f	107
9f	1	20f	5
10f	11

If you are interested in a list of all optimal maneuvers, they are included in the file D2he.zip. The five 20f*-maneuvers also are included in the file 20moves.zip.

Name	shortest maneuver with exactly this symmetry
Generator	U R2 L2 D2 F2 B2 U (7f*)

Name
Generator	D2 L F' D L' F D2 U2 B' R D' B R' U2 (14f*)

Name
Generator	B2 F2 L2 R2 U' B2 F2 D2 L2 R2 U' (11f*)

Name
Generator	R2 F2 R' F D2 B' D F2 D' B D2 F' R' (13f*)

Name
Generator	B F' L D' U' B L2 D2 B2 F R L' U R2 U' L2 U' (17f*)

Name
Generator	F2 L2 B2 L2 R' U R2 U' B L2 B' U R2 U' R' (15f*)

Name
Generator	D R2 B2 L2 D2 B2 R2 F2 R2 D' U' R2 U' (13f*)

Name
Generator	B' U' B' U L D' U B' L R2 B D L B' R2 U' (16f*)

Name
Generator	L F' D L' F D2 U2 B' R D' B R' (12f*)

Name
Generator	D R' B F' U F2 U' B' F R' D U' B2 R2 U' (15f*)

Name
Generator	F2 L2 F2 R U R2 U' B L2 B' U R2 U' R' (14f*)

Name
Generator	L2 B2 D2 U2 R2 U R B U L2 R2 D' F' R' U' (15f*)

Name
Generator	F2 U R2 D B F' R' D U F' U2 R2 B L R' U' (16f*)

Name
Generator	F2 L2 D' R2 D F2 L' R2 B D' B2 D B' L F2 U R2 U' (18f*)

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The Group D2h (edge)

The Group D_2h(edge)