12 Checkerboard Order 2 in 98 moves (scroll down for more)
10 Chevron pattern in 36 moves
5 spot pattern in 30 moves
12 checkerboard pattern in 87 moves
10 spot pattern in 48 moves
12 spot order 2 pattern
5 spot pattern new for 2020
New "cube in a cube" pattern for 2020
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.
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 order 3 in 56 moves (new method)
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