One might think that all about Rubik’s cube has been said after its invention in the second half of the 20th century: detailed instructions to follow and solve it, variants of the original \(3\times 3 \times 3\) version, computer-vision aided systems to read in a cube state and solve it physically by making use of robotics and so on. We want to understand how it works by describing precisely what happens when certain operation is applied to it and how operations affect its state in general. In the end, we seek an explicit closed formula or algorithm for solving it that should be a consequence of these properties.

The implicit geometrical symmetries of the cube seen as an object in the space, the cyclic nature of operations and the fact that cube state transitions are permutations of its forming sub-cubes motivate us to express its properties in the language of group theory. This will also allow us to have a mathematical perspective of the puzzle and apply any classical result from the theory when it’s appropriate. We haven’t been exposed to any similar approach to it, so we intend that our development of the solution here is authentic and hopefully also useful to any further study on it.

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