Infinity Cube

Infinity cube[1] is a kind of mechanical puzzle toy with mathematical principles, the shape is similar to a Rubik's cube. It can be opened and put together from different directions, thus creating a visually interesting effect.

Infinity Cube

Construction
The dark colored line segments are the taped position, while the light black line segments are not taped. From the 6 cycle state of the Infinity cube, you can see that its group representation is isomorphic to .

The principle of the Infinity Cube is simple and can be made by hand with simple paper cutting and pasting. First make 8 small squares, then arrange the small squares in a 2 by 2 by 2 way, and tape 8 edges together. When combined, there are 24 small squares exposed and 24 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 have far fewer variations than the Rubik's Cube, so the representation is also much simpler.

Rubik's Cube group have elements[2][3]，and isomorphic to the below group，where 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

References
  1. "How To Make A Paper INFINITY CUBE!". Youtube.
  2. Schönert, Martin. "Analyzing Rubik's Cube with GAP".
  3. 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.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.