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.

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.

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