megaminx
A set of generators for the megaminx group
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[,12] |
Gy | Gray |
Vector megaminx_colours shows what colour each facet has at
start. Object superflip is a megaminx operation that
flips each of the 30 edges.
Robin K. S. Hankin
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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.