# <R,U> 3-cycles



## blah (Jun 4, 2011)

All non-isomorphic cases. All HTM and QTM optimal.

R U R U R U' R' U' R' U' (10) - Good Snake
R U R U R2 U' R' U' R' U2 (10) - Goose Duck
R U R U R' U' R' U' R' U (10) - Normal Scissors
R U R U2 R' U' R' U' R2 U (10) - Good T
R U R U' R' U' R' U' R U (10) - Dog Dog
R U R2 U' R' U' R' U2 R U (10) - Good M
R U R U R U R' U' R' U' R2 (11) - Good Donut
R U R U R U2 R' U' R' U' R (11) - Duck Duck
R U' R U R U R U' R' U' R2 (11) - Normal U
R U' R' U' R U R U R U' R2 (11) - Weird Snake

Related to this thread on <M,U> 3-cycles. Names come from this thread on my classification of BH cases.

Awesomely enough, together with the <M,U> algs, 21 of the 27 cases are 2-gen.


----------



## uberCuber (Jun 4, 2011)

21/27 2-gen I like that


----------



## blah (Jun 4, 2011)

I'm thinking it's actually better than 21/27 = 77.8%. Lemme do a quick calculation.

Edit: WTF it's 384/440 cases that are 2-gen, that's *87.3%*  (In case you can't do the math, only 56/440 cases are not 2-gen-able.)


----------



## amostay2004 (Jun 4, 2011)

I sense blah is about to be super fast at BLD


----------

