Infinity cube

An infinity cube is a kind of mechanical puzzle toy with mathematical principles. Its shape is similar to a 2×2x2 Rubik's Cube, but with a different mechanism. It can be opened and put back together from different directions, thus creating a visually interesting effect.

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 43,252,003,274,489,856,000 = 12 ! 2 ⋅ 2 12 − 1 ⋅ 8 ! ⋅ 3 8 − 1 {\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 A n {\displaystyle A_{n}} are alternating groups and Z n {\displaystyle \mathbb {Z} _{n}} are cyclic groups:

( Z 3 7 × Z 2 11 ) ⋊ ( ( A 8 × A 12 ) ⋊ Z 2 ) . {\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

Wikimedia Commons has media related to Infinity Cube.

• Magic Folding Cube - Mathematische-Basteleien