Infinity Cube
Infinity cube is a kind of mechanical puzzle toy with mathematical principles, the shape is similar to a formula_1 Rubik's cube. It can be opened and put together from different directions, thus creating a visually interesting effect. Construction. 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. Mathematics. Like  the Rubik's Cube, the various states of the Infinity cube can be represented as a group, but the Infinity cube has far fewer variations than the Rubik's Cube, so the representation is also much simpler. Rubik's Cube group have formula_2 elements，and isomorphic to the below group，where formula_3 are alternating groups and formula_4 are cyclic groups： The largest group representation for Infinity cube only contains 6 elements, and can be represented as: