Archives

Breadth First Enumeration
2014-09-27 19:58:23.094 VoidCubeClient[508:5903]  0             1             1
2014-09-27 19:58:23.095 VoidCubeClient[508:5903]  1             1            12
2014-09-27 19:58:23.099 VoidCubeClient[508:5903]  2             5           114
2014-09-27 19:58:23.101 VoidCubeClient[508:5903]  3            17         1,068
2014-09-27 19:58:23.105 VoidCubeClient[508:5903]  4           130         9,951
2014-09-27 19:58:23.133 VoidCubeClient[508:5903]  5         1,018        92,592
2014-09-27 19:58:23.333 VoidCubeClient[508:5903]  6         9,204       860,852
2014-09-27 19:58:25.033 VoidCubeClient[508:5903]  7        83,789     7,991,856
2014-09-27 19:58:40.300 VoidCubeClient[508:5903]  8       774,323    74,114,319
2014-09-27 20:01:03.984 VoidCubeClient[508:5903]  9     7,159,250   686,774,712
2014-09-27 20:25:47.908 VoidCubeClient[508:5903] 10    66,273,224 6,360,091,030


Coset Enumeration

Void Cube Model 1.0
	Group: R, U, F, TR, TU, TF
	Coset Base Subgroup: Subgroup with solved corner cubies and the
	   UF and UR cubies in the solved position regardless of orientation.
	484,989,120 cosets of size 7,431,782,400
	Coset Symmetry Reduction: Oh+

Cosets solved since launch: 3,429,943
Average time per coset: 0:00:00.068

Server Status:
Void Cube Enumerator Server

Enumeration to depth: 13

Snapshot: Friday, October 3, 2014 at 6:56:34 PM Central Daylight Time

 Depth             Reduced             Elements
   0                     1                    1 
   1                     2                   12 
   2                    18                  114 
   3                    50                1,068 
   4                   447                9,951 
   5                 2,008               92,592 
   6                19,000              860,852 
   7               124,184            7,991,856 
   8             1,136,806           74,114,319 
   9             9,028,936          686,774,712 
  10            82,411,850        6,360,091,030 
  11           711,657,402       58,868,124,048 
  12         6,507,640,604      544,562,369,684 
  13        58,275,341,089    5,033,855,951,932 
  
 Sum        65,587,362,397    5,644,416,382,171 

484,989,120 of 484,989,120 cosets solved

Elapsed Time: 0:12:14:50

This work was performed using the <R, U, F, TR, TU, TF> group model. This model was discussed in a previous thread. It must be pointed out here that the <R, U, F, TR, TU, TF> metric is exactly the same as the <R, U, F, L, D, B> metric since TR = L , TU = D and TF = B on the void cube. It makes no difference if the left face is rotated holding the rest of the cube rigid or if the left face is held rigid and the rest of the cube is rotated in the opposite direction, the rearrangement of the cubies is the same. If a distinct state of the void cube is at say depth 13 in the <R, U, F, TR, TU, TF> metric it will be at depth 13 in the <R, U, F, L, D, B> metric.