Megaminx - Solutions

Solutions

Despite its daunting appearance and greater number of possible positions, the Megaminx is not much more difficult than the standard 3x3x3 Rubik's Cube. This is because it is not a deep-cut puzzle; it only has pentagonal face layers which are similar in structure to the square face layers of the cube. There are no pieces that do not have a counterpart on the cube. Many of the techniques employed in the solution of the Rubik's Cube can also be adapted for the Megaminx, except those that involve turning the center slice of the cube, since the Megaminx has no equivalent slice.

The 6-color Megaminx comes with an additional challenge which is not immediately obvious. Its edge pieces come in visually identical pairs, because of the duplicated colors of opposite faces. However, although visually indistinguishable, they are nevertheless mathematically bound in a parity relationship. In any legal position (reachable from the solved state without disassembling the puzzle), there is always an even number of swapped pairs of edges. However, since swaps may be between visually indistinct edges, one may find that having solved almost the entire puzzle, one is left with a pair of swapped (distinct) edges that seems to defy all attempts to exchange them. The solution is to swap a single pair of 'identical' edges to reverse the parity, and then restore the rest of the puzzle.

This property is absent in the 12-color Megaminx, because all its edges are visually distinct, and it would be immediately obvious that there is another pair of swapped edges besides the pair one is working with.

Besides solving a Megaminx the regular way, patterns can be made on it just like a Rubik's Cube. Examples of these include a star, checkerboard, and pentagon in a pentagon patterns.