N-dimensional Sequential Move Puzzle - Magic 120-cell

Magic 120-cell

Geometric shape: 120-cell or hecatonicosachoron

The 120-cell is a 4-D geometric figure (4-polytope) composed of 120 dodecahedrons, which in turn is a 3-D figure composed of 12 pentagons. The 120-cell is the 4-D analogue of the dodecahedron in the same way that the tesseract (4-cube) is the 4-D analogue of the cube. The 4-D 120-cell software sequential move puzzle from Gravitation3d is therefore the 4-D analogue of the Megaminx dodecahedral 3-D puzzle.

The puzzle is rendered in only one size, that is three cubies on a side, but in six colouring schemes of varying difficulty. The full puzzle requires a different colour for each cell, that is 120 colours. This large number of colours adds to the difficulty of the puzzle in that some shades are quite difficult to tell apart. The easiest form is two interlocking tori, each torus forming a ring of cubies in different dimensions. The full list of colouring schemes is as follows;

• 2-colour tori.
• 9-colour 4-cube cells. That is, the same colouring scheme as the 4-cube.
• 9-colour layers.
• 12-colour rings.
• 60-colour antipodal. Each pair of diametrically opposed dodecahedron cells is the same colour.
• 120-colour full puzzle.

The controls are very similar to the 4-D Magic Cube with controls for 4-D perspective, cell size, sticker size and distance and the usual zoom and rotation. Additionally, there is the ability to completely turn off groups of cells based on selection of tori, 4-cube cells, layers or rings.

Gravitation3d has created a "Hall of Fame" for solvers, who must provide a log file for their solution. As of November 2011, the puzzle has been solved six times.

Achievable combinations:

This calculation of achievable combinations has not been mathematically proven and can only be considered an upper bound. Its derivation assumes the existence of the set of algorithms needed to make all the "minimal change" combinations. There is no reason to suppose that these algorithms will not be found since puzzle solvers have succeeded in finding them on all similar puzzles that have so far been solved.