Using Standard Rotation To Write A Solution
1) Using the first letter of the code, find the standard position (see below) of the letter-piece and rotate the cube so that the first letter-piece is in that position. If the piece has two ways to rotate to the standard position then both ways must be considered. Only the letters K, L, M, N, and O have this ambiguity. However, they are infrequently the first letter of a code since they are towards the end of the alphabet and the codes are always arranged in alphabetical order.
2) Using either a pencil and a piece of paper or a text editor, the cube solution(s) are written into a right-handed coordinate system with the origin at the lower left and the bottom layer of the cube at the left. For instance:
t t t r f t u f f
r r c r m c u u f
c c c m m m u m f
3) Write the 27 letters of the diagram into a twitter string using the order top row, middle row and bottom row. This is especially useful for tweeting solutions to codes you have solved!
solution=tttrftuffrrcrmcuufcccmmmumf
4) If the first letter code has the rotational ambiguity, look at the two twitter strings and take the first string in alphabetical order.
Canonical Positioning Of The “A” Piece
Here is the canonical position of the “A” piece given the 3x3x3 case. Staying in this position, it can be shifted to four locations:
Its original location with no shift:
. . . . . . . . .
. a . . . . . . . shift (0,0,0)
a a a . . a . . .
A 1 unit shift in the z-direction:
. . . . . . . . .
. . . . a . . . . shift (0,0,1)
. . . a a a . . a
A 1 unit shift in the y-direction:
. a . . . . . . .
a a a . . a . . . shift (0,1,0)
. . . . . . . . .
And a 1 unit shift in both the y-direction and z-direction:
. . . . a . . . .
. . . a a a . . a shift (0,1,1)
. . . . . . . . .
More Examples Of Canonical Positioning
Below are the rest of the canonical positions for the fifteen five-polycubes given the 3x3x3 case. This covers all of the different pieces that can possibly start a code (and thus need to be in their canonical position):
the letter b shift (0,0,0):
. . . . . . . . .
. . b . b b . . .
. . . b b . . . .
the letter c shift (0,0,0):
. . . . . . . . .
. . c . . c . . .
c c c . . . . . .
the letter d shift (0,0,0):
. . . . . . . . .
. . d . . . . . .
d d d . . d . . .
the letter e shift (0,0,0):
. . . . . . . . .
. e . . e . . . .
e e e . . . . . .
the letter f shift (0,0,0):
. . . . . . . . .
f f f . . . . . .
. . f . . f . . .
the letter g shift (0,0,0):
. . . . . . . . .
. g . . . . . . .
g g . . g g . . .
the letter h shift (0,0,0):
. . . . . . . . .
. h . . . . . . .
h h h h . . . . .
the letter i shift (0,0,0):
. . . . . . . . .
. i i . i . . . .
i i . . . . . . .
the letter j shift (0,0,0):
. . . . . . . . .
. j j . . j . . .
j j . . . . . . .
the letter k shift (0,0,0):
. . . . . . . . .
. k . . k k . . .
k k . . . . . . .
the letter l shift (0,0,0):
. . . . . . . . .
l l . . . . . . .
. l . . l l . . .
the letter m shift (0,0,0):
. . . . . . . . .
. m . . . . . . .
m m m . m . . . .
the letter n shift (0,0,0):
. . . . . . . . .
. . . . . n . . .
n . . n n n . . .
the letter o shift (0,0,0):
. . . . . . . . .
. . o . . . . . .
o o o o . . . . .