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BACKGROUND

On the 3^3, many people use variants of a 3-cycle of edges,

more-or-less as follows:

let Rs = Right slice = R'L + roll cube so front is up

T (for tri-cycle?) = Rs U2 Rs' U2 = (UF,DF,UB) to cycle 3 edges on a slice

Some people use it in the form R2 D' - T - D R2 = (UF,UR,UB) to get 3 on a face, without

flips, and some use

Rs' U - T - U' Rs = Rs' U Rs U2 Rs' U Rs = (UF,LU,RU)

for 3 on a face, with flips, since it saves a move due to

U2 U' = U. END BACKGROUND

Now, this move, when transferred to the 4^3, seems to be the basis

of both Richard Pavelle's "S" move of 16-May, and Bernie Cosell's "M"

move of 17-May (Bernie using a left slice version of the third form).

The move Roger Frye describes on 7-June is also the same as this

(re-oriented to a different face), and so is the "quite long" tool I

use. To move only edges requires S3, and to move only centers

requires S5!!! I still would like a "nice" (preferably short) center

pair move.

SPOILER SPOILER SPOILER

We have now several 3-cycles:

(UBl,UFr,LDf) = U2 f' D f - U2 f' D' f (from Minh Thai's book) (UFl,BUl,RUb) = l' - R U R' U' - l - U R U' R' (Minow, 6-June) (RDf,URf,UFl) = R' d R - U' - R' d R - U (Frye, 7-June)

Note that all of these have corresponding 3-cycles of centers, by

simply substituting a slice for its' corresponding edge in each of the

moves. For instance, in Thai, substitute d for D; in Minow, r for R,

etc. There is also a version which cycles an edge an center together,

by rotating the appropriate face and slice together.

In fact, it looks as though any simple move on the 4^3 will have a

left and right version, a forward and back version, and a slice and

edge version or two, along with combinations of these. Is there any

way to put these into a canonical form so we can recognize related

moves? What about canonical form on the 3^3?

One more spoiler: to switch opposite centers (all 4 cubies):

(F,B) = (r2 U2 l2 U2)3.

END SPOILER END SPOILER END SPOILER

Can the notation be usefully extended so as to talk about UB as

the pair of upper back edges, F as the front 4 center cubies, and Fu

as the upper two of F, etc. It might make notating the permutations

easier. Is there any notation to make various repeats easier; for

instance, some expansion of "squared" to indicate "primed"

(commutator) type repeat, or a repeat with all quarter twists in the

opposite direction. Maybe ( )2 means repeat; ( )i2 means repeat

with sub-parts "primed", and ( )-2 repeats with qtws opposite. The

purpose is to try to make it more obvious what each move is really

doing, and to be able to compare moves easier.

Has anybody given any thought to notation the 5^3?

By the way, if Bill Mann is listening, would you describe your

transform (mentioned by Edmond on 23-May)?

--- Stan

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