megaminx

0th

Percentile

megaminx

A set of generators for the megaminx group

Keywords
datasets
Details

Each element of megaminx corresponds to a clockwise turn of 72 degrees. See the vignette for more details.

megaminx[, 1] W White megaminx[, 2]
Pu Purple megaminx[, 3] DY
Dark Yellow megaminx[, 4] DB Dark Blue
megaminx[, 5] R Red megaminx[, 6]
DG Dark Green megaminx[, 7] LG
Light Green megaminx[, 8] O Orange
megaminx[, 9] LB Light Blue megaminx[,10]
LY Light Yellow megaminx[,11] Pi
Pink megaminx[, 1] W White

Vector megaminx_colours shows what colour each facet has at start. Object superflip is a megaminx operation that flips each of the 30 edges.

Aliases
  • megaminx
  • megaminx_colours
  • superflip
  • W
  • Pu
  • DY
  • DB
  • R
  • DG
  • LG
  • O
  • LB
  • LY
  • Pi
  • Gy
Examples
# NOT RUN {
data(megaminx)
megaminx
megaminx^5  # should be the identity
inverse(megaminx)  # turn each face anticlockwise


megaminx_colours[permprod(megaminx)]  # risky but elegant...

W    # turn the White face one click clockwise (colour names as per the
     # table above)


megaminx_colours[as.word(W,129)]      # it is safer to ensure a size-129 word;
megaminx_colours[as.word(W)]          # but the shorter version will work


# Now some superflip stuff:

X <- W * Pu^(-1) * W * Pu^2 * DY^(-2) 
Y <- LG^(-1) * DB^(-1) * LB * DG      
Z <- Gy^(-2) * LB * LG^(-1) * Pi^(-1) * LY^(-1)


sjc3 <- (X^6)^Y * Z^9  # superflip (Jeremy Clark)


p1 <- (DG^2 * W^4 * DB^3 * W^3 * DB^2 * W^2 * DB^2 * R * W * R)^3
m1 <- p1^(Pi^3)

p2 <- (O^2 * LG^4 * DB^3 * LG^3 * DB^2 * LG^2 * DB^2 * DY * LG * DY)^3
m2 <- p2^(DB^2)

p3 <- (LB^2 * LY^4 * Gy * Pi^3 * LY * Gy^4)^3
m3 <- p3^LB

# m1,m2 are 32 moves, p3 is 20, total = 84

stopifnot(m1+m2+m3==sjc3)




# }
Documentation reproduced from package permutations, version 1.0-5, License: GPL-2

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