Solutions
Despite its appearance, the puzzle is in fact equivalent to a shape modification of the original 3x3x3 Rubik's Cube. Its 4 corner pieces and 4 face centers together are equivalent to the 8 corner pieces of the Rubik's Cube, its 6 edge pieces are equivalent to the face centers of the Rubik's Cube, and its non-center face pieces are equivalent to the edge pieces of the Rubik's Cube. Thus, the same methods used to solve the Rubik's Cube may be used to solve the Master Pyramorphix, with a few minor differences: the edge pieces are sensitive to orientation, unlike the usual coloring scheme used for the Rubik's Cube, and the face centers are not sensitive to orientation. In effect, it behaves as a Rubik's Cube with a non-standard coloring scheme where face-center orientation matters, and the orientation of 4 of the 8 corner pieces do not matter.
Unlike the Square One, another shape-changing puzzle, the most straightforward solutions of the Master Pyramorphix do not involve first restoring the tetrahedral shape of the puzzle and then restoring the colors; most of the algorithms carried over from the 3x3x3 Rubik's Cube translate to shape-changing permutations of the Master Pyramorphix. Some methods, such as the equivalent of Phillip Marshal's Ultimate Solution, show a gradual progression in shape as the solution progresses; first the non-center face pieces are put into place, resulting in a partial restoration of the tetrahedral shape except at the face centers and corners, and then the complete restoration of tetrahedral shape as the face centers and corners are solved.
Read more about this topic: Pyramorphix, Master Pyramorphix
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