Explanation of Notation for Higher Order Cubes
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The notation used here was originally developed by Dr. David Singmaster
in his book "Notes on Rubik's Magic Cube".
As an extension of the standard UDFBRL notation, where a capital letter
representing the rotation of a face is suffixed by a number indicating
the number of clockwise turns to be made. It has been the practise of
the Cube-Lovers mailing list and my own research to use the suffix of
3 rather than ' because it looks more uniform and in the case of the
magic dodecahedron or magic hexagon we have a richer notation.
In the case of Rubik's Revenge, it was Dr. Singmaster's idea to use
lower case letter to mean: turn the adjacent slice. I have perhaps
misused his notation in the case of p1 to have Rr3 to equal R3 r3.
In the case of the 5x5x5 cube I used the suffix m to mean the middle
slice, so we have fm3 to mean: turn the middlemost slice adjacent to
the front face.
To measure the length of a process we defer to the count of slice
moves where a slice is NxNx1.
4x4x4 processes (measured in slice moves)
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p1 Flip LD edge pair (r3 D3) ^3 + (r1 D1) ^4 + Rr3 D3 R1 D1 r1 D3 R3 (25)
D1 R1 D3
p2 Flip UB edge pair r2 D2 l3 D1 R3 U1 R3 U3 l3 U1 R1 U3 l1 R1 D1 r2 (16)
p3 Flip UF edge pair r2 (D2 l1)^2 D1 l3 r3 d2 l1 r1 D3 l3 r3 d2 B2 r1 (23)
(doesn't move centres) B2 l3 B2 l1 B2 r2
p3a Flip LB edge pair L2 d1 R2 d1 R2 d3 L2 u3 B2 u2 B2 u3 B2 R2 B1 r3 (21)
(improvement) B3 R2 B1 r1 B1
p3b Flip UF edge pair R2 r2 B2 L1 U2 l1 U2 r3 U2 r1 U2 F2 r1 F2 L3 l3 (19)
(even better) B2 R2 r2
p4 Adj (Ffl, Frd) Swap R1 U3 (l3 U2)^4 l3 U1 R3 U1 l1 U3 R1 U1 l1 U3 R3 (24)
of edges U1 l2 U3
p5 Opp (Ufr, Dfl) Swap F1 R1 F3 U3 (l3 U2)^4 l3 U1 R3 U1 l1 U3 R1 U1 l1 (30)
of edges U3 R3 U1 l2 U3 R1 F1 R3 F3
5x5x5 processes (measured in slice moves)
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Flip 2 middlemost edges at FD and BD with:
p1 (fm1 D1) ^3 + fm1 D2 + (fm1 D1) ^3 + fm1 (disturbs some centres) (25)
followed by:
D1 + (fm2 u2) ^2 + (fm2 l2) ^2 + D3 (corrects the centres)
Flip 2 middlemost edges at UF and DF with:
p1a rm3 F3 D1 R3 F1 D3 rm1 D1 F3 R1 D3 F1 (12)
Flip 4 middlemost edges at UF, UB, BD, RD (40)
p2 (lm D1) ^20