r1ckp puzzle

description.md

r1ckp puzzle

This is a gist to understand @r1ckp puzzle as shown by the following tweet:

I built a puzzle cube I can't solve pic.twitter.com/wcMCK6to5k

— Rick (@r1ckp) July 2, 2016

<script async src="//platform.twitter.com/widgets.js" charset="utf-8"></script>

Cutout

        +---+---+
        | a | b |
        +---+---+
        | c | d |
+---+---+---+---+---+---+
| m | n | e | f | i | j |
+---+---+---+---+---+---+
| o | p | g | h | k | l |
+---+---+---+---+---+---+
        | q | r |
        +---+---+
        | s | t |
        +---+---+
        | u | v |
        +---+---+
        | w | x |
        +---+---+

Given the face with efgh is top:

One 90° move of the cube around the x-axis forward sends the color at

• a to c, c to e, e to g, g to q, q to s, s to u, u to w and w to a
• b to d, d to f, f to h, h to r, r to t, t to v, v to x and x to b

a -90° move around the x-axis backwards does the opposite of the above.

Again, given the face with efgh is top:

One 90° move of the cube around the y-axis to the left sends the color at

• m to n, n to e, e to f, f to i, i to j, j to x, x to w and w to m
• o to p, p to g, g to h, h to k, k to l, l to v, v to u and u to o

a -90° move around the y-axis to the right does the opposite of the above.

A move around the z-axis does nothing.

Group

A short analysis of the of the puzzle points out that not every possible coloring of the facelets is solvable. In fact the chance of getting a solvable puzzle when you pick the colors randomly is fairly slim, i.e. 1 in 632468286450.

group.gap

# a b c d e f g h i j  k  l  m  n  o  p  q  r  s  t  u  v  w  x
# 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

sym24 := SymmetricGroup(24);

r1ckp := Group([
  ( 1,  3,  5,  7, 17, 19, 21, 23)( 2,  4,  6,  8, 18, 20, 22, 24),
  (13, 14,  5,  6,  9, 10, 24, 23)(15, 16,  7,  8, 11, 12, 22, 21)
]);

Print(IsSymmetricGroup(r1ckp), " ", Index(sym24, r1ckp), " ", Order(r1ckp));