The Group C_4v

Up to M-symmetry there are 448 cubes which exactly have the symmetries of this subgroup. All cubes are generated in 19 moves or less. A few nicer examples are listed below.

The table gives the number of cubes up to M-symmetry which exactly have C_4v-symmetry, the average maneuver length is 14.88:

Distance	Number	Distance	Number
0f	0	11f	10
1f	1	12f	37
2f	0	13f	70
3f	0	14f	67
4f	0	15f	49
5f	2	16f	61
6f	0	17f	83
7f	1	18f	53
8f	3	19f	4
9f	1	20f	0
10f	6

If you are interested in a list of all optimal maneuvers for this subgroup, the are included in the file C4v.zip.

Name	shortest maneuver with exactly this symmetry
Generator	D2 (1f*)

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

Name
Generator	R2 L2 U' B' F' R' L' U' D' B' F' R' L' D' R2 L2 (16f*)

Name
Generator	B2 L2 R2 F2 D' L2 B2 F2 R2 U' (10f*)

Name
Generator	L' R B' L2 D2 L2 F' U2 L2 U2 F' L R' U' (14f*)

Name
Generator	R2 B' F U2 R2 U2 B F' R2 (9f*)

Name
Generator	L2 F2 L2 R2 F2 R2 U2 (7f*)

Name
Generator	L2 B2 F2 R2 D U2 L2 B2 F2 R2 U' (11f*)

Name
Generator	D2 F R U R' F' L2 R D' B' D L2 R' (13f*)

Name
Generator	B2 L R' D2 B F2 R2 D2 L R' F2 R2 U' (13f*)

Name
Generator	U' L2 F2 L2 U2 R' L F' L2 U2 L2 F2 R L' (14f*)

Name
Generator	L2 B2 F2 R2 D' U2 L2 B2 F2 R2 U' (11f*)

Name
Generator	D B2 L2 R2 F2 U' L2 B2 F2 R2 (10f*)

Name
Generator	U R' L B' U2 L2 U2 B' L2 D2 L2 F' R L' (14f*)

Name
Generator	L2 F2 L2 F R' D2 F2 L D L2 R2 D' B' R2 U2 F R' (17f*)

Cube display with AnimCubeJS

The Group C4v

The Group C_4v