---
tag: R2TA1PAPJ7
kind: concept
name: Rubik's Cube group
aliases: [rubik-group, rubiks-cube-as-a-mathematical-group]
sources:
  - wikipedia: en:2467690@r1373989405
    locator: Rubik's Cube group
    note: adopted
    mention: wikipedia://en/2467690
    sections: [Summary]
same_as:
  wikidata: Q3123152
  wikipedia: Rubik's Cube group
inventory: [RF1Y9DXZAK]
---

## Summary

The **Rubik's Cube** group $(G, \cdot )$ represents the mathematical structure of the Rubik's Cube mechanical puzzle. Each element of the [[set|0BSJ7RQ9BW]] $G$ corresponds to a cube move, which is the effect of any sequence of rotations of the cube's faces. With this representation, not only can any cube move be represented, but any position of the cube as well, by detailing the cube moves required to rotate the solved cube into that position. Indeed, with the solved position as a starting point, there is a [[one-to-one correspondence|0GG9TVW90M]] between each of the legal positions of the Rubik's Cube and the elements of $G$. The group [[operation|0580ZJSA3Q]] $\cdot$ is the [[composition|0THBK9V825]] of cube moves, corresponding to the result of performing one cube move after another.