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.

An Infinity cube made of dice being played with
An animation showing different moves and states of the Infinity cube (click to animate)

Construction

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The hinges are coloured, the glow denoting the next hinges to be employed. 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 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

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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 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

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References

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  1. ^ Schönert, Martin. "Analyzing Rubik's Cube with GAP". Archived from the original on 2013-01-20. Retrieved 2020-12-26.
  2. ^ 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.
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