The Megaminx Pattern Archive

# The Megaminx Pattern Archive

The megaminx is a rubikized platonic dodecahedron

#### 10 star pattern

U Face = Red, L Face = Orange, F Face = Blue, R Face = Yellow

M1 10 spot...(L+ R- C_U-)^36
The 10 spot is Order 5 because it rotates the centres about a face
Here L and R refer to opposite sides of the dodecahedron.

In this case L and R are not separated by a face, as are the sequences below.
Note the centre pieces are rotating in a counter-clockwise direction.

#### 10 spot in 50 moves (old method used 72 moves)

M2 3 Cycle...(uf, lf, rf) R+ F+ U+ F- U- R- L- U- F- U+ F+ L+...(12f, 12u)
M3a 2 flip...(ul, uf) R- F- U+ L- U- L+ F+ R+ L+ F+ U- R+ U+ R- F- L-...(16f, 16u)
M4 12 spot type a...(L+ R- C_U-)^36 C_F- (L+ R- C_U-)^36
The 12 spot type a is Order 3 since it rotates the centres about a corner
Like M1, here L and R refer to opposite sides.
The operator C_F- means "rotate the dodecahedron counter-clockwise about face F".
This face ends up with being blue with the red centre.

#### 12 spot in 116 moves (old method needed 144 moves)

m5 12 spot type b...(L+ R- C_U-)^36 C_F- (L+ R- C_U-)^36 C_F+ (L+ R- C_U-)^36
The 12 spot type b is Order 2 since it rotates the centres about an edge

In summary, there are twenty-four 10 spots, thirty-five 12 spots and one 0 spot
24 + 35 + 1 = 60 which account for all 60 orientations in space of the megaminx
The thirty-five 12 spots come in 2 types, twenty of order 3 and fifteen of order 2

Credits: The pictures above were created using the Maple package mega.mpl created by Professor David Joyner and the operators of Mark Longridge
Many thanks to Tom Rokicki and Lucas Garron for twizzle and twsearch

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