[Unofficial] 3 layer pentahedron. 8.02 single, 13.94 ao5

[infrabread]

 

[abunickabhi]

Nice solves.

How many possibilities does this puzzle have?

 

[White KB]

Nice solves.

How many possibilities does this puzzle have?

I think it's this formula (correct me if I'm wrong):

(6! * 6! * 3! * 2^3)/2= 12,441,600 combinations. My reasoning is that there are 6 corners that can be swapped and 6 U/D edges that can be swapped, and also 3 E slice edges that can be swapped, making for 3,110,400 possible permutations of the puzzle. Parity states relating to permutation are possible on this cube even without affecting the middle layer edges.

Then there is the added factor that on this puzzle, middle layer edges can become misoriented: By simply performing R2 B2 L2 you can take the front edge from its place and return it back to its place while also making it misoriented. This is not a parity issue, however, since once you return the other 2 edges to their place using B2, you will find that there are 2 edges that are misoriented. It is for this reason that we multiply by 2^3 to account for every possible edge orientation from taking the puzzle apart and putting it back together, then divide by 2 because single edge orientation parity is not possible, no matter which moves are performed.