Alright I took a stab at this one. I modeled the group generated by all the ways to make a clockwise move followed by a counter-clockwise move on a skewb. There are 12 unique, non-trivial generators that each have an order of 30, which is extremely large by twisty standards. It is also a bit unusual because the cycles performed by a "generator" are not all the same size. Looking at the stickers we have a cycle of 5, two cycles of 3, and two cycles of 6 on every generator. This group is equivalent to the Alternating Skewb where configurations for which a counter-clockwise move must occur are not legal stopping positions, so this group has half the number of configurations as the Alternating Skewb (unless of course you wish to define it this way instead
After running some simple custom code that I've been developing for another project, I found that this group (puzzle) has 174,960 reachable elements (configurations). There are y configurations x moves away from solved as given in the following table:
8-79Just for fun, 64 of the 79 hardest positions have the centers solved exacltyTherefore the Alternating Skewb has 349,920 reachable configurations
, half that require a clockwise move next and half that require a counter-clockwise move next. These configurations are distributed from solved as:
17-? (possibly 0)
Oddly enough, I don't think it's trivial to fill in the question marks even though I have the exact value at all even depths. The first two are obviously 4 and 36 but I'm not sure about the others...
The normal Skewb has 3,149,280 configurations which means the Alternating Skewb has exactly 1/9th the state space of the normal Skewb.
I think that's enough for now. Someone else can contribute more
PS: Another point of interest that I just noticed: The Skewb can be solved in 11 moves at worst. It's kind of neat that the Alternating Skewb takes several extra moves for some states even though the set of states the Alternating Skewb can reach is strictly contained by the set of states the Skewb can reach