shadowslice e
Member
Are there any algorithms that cycle in a prime number greater than 12 that do not have rotations or wide moves in them? (eg R,y would be R B L F etc).
Well I didn't go into that really. My logic was that you could have a 2 swap of c/e, 3 swap of c/e... 8swap c/e,9 swap e... up to 12 and you could flip but that you only take 2 and you could have a 3 for twist but (but as said before 3<12) so the largest prime would be 11 and all else would be combinations of the cycles.It's not possible. The order of the cube group is 2^27 × 3^14 × 5^3 × 7^2 × 11, so the largest prime order of any element is 11. (It doesn't matter whether you allow rotations or not.)
On big cubes you can get order-23 elements but not any larger, for the same reason. (Larger as in larger primes; 29, 31, 37, 43, etc. are all illegal on big cubes, but you can get order 24, 26, 28, 30, 33, 34, etc.)
Well, for a start they can only affect either only corners or only edges or the same number of both (so only 7 out of the algs you've listed would have both corners and edges at the same time).Now I'm all curious... what are the known cases for prime cycles so far? Can we get example algs of lower primes?
# of Cycles - Alg
2 - T Perm
3 - U perm
5 - (R U R' U)
7 - ???
11 - ???
13 - ???
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