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  2. Rubik's Cube group - Wikipedia

    en.wikipedia.org/wiki/Rubik's_Cube_group

    The Rubik's Cube is constructed by labeling each of the 48 non-center facets with the integers 1 to 48. Each configuration of the cube can be represented as a permutation of the labels 1 to 48, depending on the position of each facet. Using this representation, the solved cube is the identity permutation which leaves the cube unchanged, while ...

  3. Centered polyhedral number - Wikipedia

    en.wikipedia.org/wiki/Centered_polyhedral_number

    In mathematics, the centered polyhedral numbers are a class of figurate numbers, each formed by a central dot, surrounded by polyhedral layers with a constant number of edges. The length of the edges increases by one in each additional layer.

  4. Optimal solutions for the Rubik's Cube - Wikipedia

    en.wikipedia.org/wiki/Optimal_solutions_for_the...

    [1] The maximal number of face turns needed to solve any instance of the Rubik's Cube is 20, [2] and the maximal number of quarter turns is 26. [3] These numbers are also the diameters of the corresponding Cayley graphs of the Rubik's Cube group. In STM (slice turn metric), the minimal number of turns is unknown.

  5. Rubik's family cubes of varying sizes - Wikipedia

    en.wikipedia.org/wiki/Rubik's_family_cubes_of...

    The big advantage of numbers is that they reduce the complexity of solving the last cube face when markings are in use (e.g. if the set-of-four sequence is 1-3-4-2 (even parity, needs two swaps to become the required 1-2-3-4) then the algorithm requirement is clear.

  6. Rubik's Revenge - Wikipedia

    en.wikipedia.org/wiki/Rubik's_Revenge

    A solved Rubik's Revenge cube. The Rubik's Revenge (also known as the 4×4×4 Rubik's Cube) is a 4×4×4 version of the Rubik's Cube.It was released in 1981. Invented by Péter Sebestény, the cube was nearly called the Sebestény Cube until a somewhat last-minute decision changed the puzzle's name to attract fans of the original Rubik's Cube. [1]

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