# megaminx: megaminx In permutations: The Symmetric Group: Permutations of a Finite Set

## Description

A set of generators for the megaminx group

## 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[,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.

## Author(s)

Robin K. S. Hankin

`megaminx_plotter`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38``` ```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) ```