Infinity cube

The principle of the infinity cube is simple and can be made by hand with simple paper cutting and pasting. First make 8 small cubes, then arrange the small cubes in a 2 by 2 by 2 way, and tape 8 edges together. When combined, there are 28 small squares exposed and 20 small squares hidden inside.

The infinity cube has far fewer permutations than the Rubik's Cube.

The Rubik's Cube group has ${\displaystyle 43{,}252{,}003{,}274{,}489{,}856{,}000\,\!={\frac {12!}{2}}\cdot 2^{12-1}\cdot 8!\cdot 3^{8-1}}$ permutations^[1][2] and is isomorphic to the following group, where ${\displaystyle A_{n}}$ are alternating groups and ${\displaystyle \mathbb {Z} _{n}}$ are cyclic groups:

${\displaystyle (\mathbb {Z} _{3}^{7}\times \mathbb {Z} _{2}^{11})\rtimes \,((A_{8}\times A_{12})\rtimes \mathbb {Z} _{2}).}$

The infinity cube only has 6 configurations.

• Yoshimoto Cube
• Paper model
• Fidget Cube
• 15 puzzle