Complete Search of Subgroup Defined by Edge Cubies

I recently completed a complete breadth-first search of the subgroup of the 3x3x3 cube defined only by the edge cubies. In other words, think of a cube where all the corner cubies are indistinguishable, and a state is defined only by the edge cubies. It took about 35 days on a dual-processor workstation, with three terabytes of disk storage. This was done without any use of symmetries. Here's the number of unique states at each depth:

0 1
1 18
2 243
3 3240
4 42807
5 555866
6 7070103
7 87801812
8 1050559626
9 11588911021
10 110409721989
11 552734197682
12 304786076626
13 330335518
14 248
Total 980995276800

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My Apologies

Right after my posting, I found that Tomas Rokicki had already done this calculation back in 2004. My apologies for not checking sooner, and sorry for taking up your time.
-rich korf


Actually, very useful confirmation; the numbers all match as they should. Glad to see you active in computer cubing again!

Full table for edges cubies...

This question is for both Rokicki and Korf.
Can you caracterize the 248 configurations at distance 14 ?
They might be useful in the search for a configuration at distance 21 in the whole cube...

The 248 configurations at depth 14

Unfortunately, I didn't save them. I'd have to rerun the computation from scratch.

At the very moment, I cannot.

At the very moment, I cannot. It would take some effort to locate the files, determine if I have that information or not, and if needed rerun the computation to dump the positions.

wow! no symmetry reduction used!

Good job!

Now both the QTM and FTM analyses of that group have been independently verified.