Date: Fri, 06 Jan 95 23:53:00 -0500
From: Mark Longridge <mark.longridge@canrem.com >
~~~ ~~~ Subject: More cube terms
```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.