The DoDot M12 is a twisty puzzle that mechanically demonstrates Mathieu group M12. It’s a modification of my original vertex-turning dodecahedron where sets of three turning axes are geared together internally. This gearing was chosen to greatly reduce the number of possible permutations of the ‘dot’ pieces, which behave according to the rules of the 12-element M12 permutation group. The edge pieces of the puzzle behave as 6 disjoint orbits of 5 pieces, which makes them easy to solve. I greyed out the petals to avoid making the puzzle too complicated.