Coinage of the terms 2c2c and 2c2c' for 3BLD exec

[abunickabhi]

We are already familiar with 2e2e and 2e2e' which emerge in edges. We execute them to avoid cycle breaks and save an alg.

1. 2e2e is a direct two 2-swap between 4 edges, for example the Z perm
2. 2e2e' is a two 2-swap with a 2 flip between one edge of the 2-swap and one edge of another 2-swap

I want to have the same coinage for corners (I have not seen it being discussed in my 14 years of BLD career), the way to solve these cases is just 2 RUD gen UFR (or other floating buffer) commutator

1. 2c2c is a direct two 2-swap between 4 corners, for example the E perm
2. 2c2c' is a two 2-swap with a 2 twist between one corner twisted clockwise in a 2-swap and one corner twisted anti-clockwise in another 2-swap or vice-verse (direction of twist being cw or ccw for first 2-swap or second 2-swap)
3. 2c2c3cw is a two 2-swap with a "3 twist clockwise" between one corner of the 2-swap and two corners of another 2-swap
4. 2c2c3ccw is a two 2-swap with a "3 twist anti-clockwise" between one corner of the 2-swap and two corners of another 2-swap

If I am missing a case type for any 2c2c*, do let me know in the replies. I am not an advanced BLDer so please pardon my ignorance, relevance and mistakes.

 

[abunickabhi]

Okay I think I missed a type, will describe the case better when I wake up tmw.

2c'2c' is a two 2-swap with a 2 twist between one corner twisted clockwise in a 2-swap and one corner twisted anti-clockwise in another 2-swap and the same 2 twist between the remaining 2 corners.

 

[abunickabhi]

The classification is much simpler than I imagined, there is just 2c2c,2c2c' and 2c2c''.

2c2c3cw and 2c2c3ccw are just one twist away from a 2c2c or a 2c2c'