Infinity cube

An infinity cube is a kind of mechanical puzzle toy with mathematical principles. Its shape is similar to a 2×2×2 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.

Mathematics

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 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.

See also

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

References

External links

Wikimedia Commons has media related to Infinity Cube.

• Magic Folding Cube – Mathematische-Basteleien