An Infinity cube is a kind of mechanical puzzle toy with mathematical principles. Its shape is similar to a 2×2 Rubik's cube. It can be opened and put back together from different directions, thus creating a visually interesting effect.
Construction[edit]
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[edit]
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 permutations than the Rubik's Cube.
Rubik's Cube group have permutations[1][2] and isomorphic to the below groupware are alternating groups and are cyclic groups：
The largest group representation for Infinity Cube only contains 6 elements, and can be represented as:
See also[edit]
References[edit]
- ^ Schönert, Martin. "Analyzing Rubik's Cube with GAP".
- ^ Tom Davis, "Rubik's Cube. Part II", p.23 in, Zvezdelina Stankova, Tom Rike (eds), A Decade of the Berkeley Math Circle, American Mathematical Society, 2015 ISBN 9780821849125.