From:

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Notes on Notation and Terminology for Rubik's Cube --------------------------------------------------In the "Handbook of Cubik Math":

cubicles are in lower case, cubies are in UPPER CASE.

If we use the 6 letters to describe the 6 faces and the various

pieces and positions, e.g. UR, UF, UL, UB are the 4 edge pieces

of the U face and URF, UFL, ULB, UBR are the 4 corner pieces.

We agree to list the facelets at a corner in clockwise order.

This gives the following edge & corner cubicles:

uf, ul, ub, ur, rf, fl, lb, br, df, dl, db, dr

urf, ufl, ulb, ubr, dfr, dlf, dbl, drb

and the following edge & corner cubies:

UF, UL, UB, UR, RF, FL, LB, BR, DF, DL, DB, DR

URF, UFL, ULB, UBR, DFR, DLF, DBL, DRB

By adhering to these conventions we can establish a standard

notation for cube positions.

The sequence R2 U3 F1 B3 R2 F3 B1 U3 R2 (9 q+h, 12 q) generates a 3-cycle of edges. The cycle representation of this sequence would be ( UF, UR, UB ) in ( ur, ub, uf).

Thus cubie UF resides in cubicle ur

cubie UR resides in cubicle ub

cubie UB resides in cubicle uf

If we assume that the unreferenced cubies are in proper position

and orientation we have enough information to completely

describe a cube in a way which provides more information on it's

cycle structure.

If an edge pair is flipped we refer to ( FU, LU ) in ( uf, ul) If a corner triple is twisted clockwise we refer to ( RFU, FLU, LBU ) in ( urf, ufl, ulb )Here are a couple more examples:

The super-flip has a cycle representation of

( FU, LU, BU, RU, FR, LF, BL, RB, FD, LD, BD, RD )

( uf, ul, ub, ur, rf, fl, lb, br, df, dl, db, dr )The 6 X order 3 has a cycle representation of

(( FR, FU, UR ) ( BR, FD, LU ) (BU, RD, FL ) ( BD, DL, BL)) (( uf, ur, rf ) ( df, ul, br ) (dr, fl, ub ) ( dl, lb, db))

-> Mark <-

Email: mark.longridge@canrem.com

P.S. I'm not certain if the previously mentioned Rubik Algebra

uses something like this, but I am going to add it to my

cube program.