Date:  7 Jun 1982 15:34:28 EDT (Monday)
From: Roger Frye <frye at BBN-UNIX>
Subject: 4^3 breakage, notation, and solution
To: Cube-Lovers at MIT-MC
Cc: decvax!minow at BERKELEY, ISAACS at SRI-KL, frye at BBN-UNIX

About broken 4^3 center cubies:

The center cubies take all the stress of holding in the edges and corners.
The post which breaks is 4mm square compared to the 16mm square cubie.
When I called Games People Play about my broken cube, another cube had
just been returned with the same problem.  So I traded my broken cubie
for an unbroken one and picked up a spare.

About Minow notation for 4^3:

     Name the faces L, R, F, B, U, D.  This follows the 3x3 notation.  The inner
     edges are then l, r, f, b, u, d.  The front, upper, right quadrant
     consists of one corner cube, FUR, two edge cubes, FUr and FRu, and one
     center cube, fur.  [decvax!minow at Berkeley]

Isn't there still a mistake here?  I think of "fur" as being a spot buried
in the cube.  If you mean the four cubies in the upper right quadrant of
the front face, then the name of the center cubie would be "Fur".
If you mean the front, upper, right octant then the two other center
cubies are "Urf" and Rfu".

About 4^3 processes:

** SPOILER WARNING ** SPOILER WARNING ** SPOILER WARNING **

My process to exchange three edge cubies is a U face commutator:

(RDf URf UFl) =    R'd'R  U'  R'dR  U

I think of my other 4^3 process as exchanging two half centers:

(Rfu Flu Rbd)          \
(Rub Fur Rdf)           =   R2 u' R2 u
(RBd FRd BRu RFu FLu)  /

You can get lost trying to read the permutations.  Just think of it
as injecting the two upper cubies from the front face into the right
face in exchange for the two upper cubies from the right face.
This is a move ISAACS requested.

My solution strategy:

** SPOILER WARNING ** SPOILER WARNING ** SPOILER WARNING **

1) Solve the top center using random methods.
2) Solve the corners using 3^3 moves.  (See \\Jeff Conquers the Cube//.)
3) Solve all centers with my center process.
4) Solve all edges with my edge process.
5) If a 2-edge monoflip or exchange is left over:
5a) In 2^3 mode, turn top and rotate three corners back; i.e.
    Uu   (Rr)2 (Bb)2 Rr Ff R'r' (Bb)2 Rr F'f' Rr.
5b) In 3^3 mode, undo 5a; i.e.
    U'   L2 B2 L' F' L B2 L F L.
5c) Repeat steps 3 and 4.

 -Roger Frye