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 withAn animation showing different moves and states of the Infinity cube (click to animate)
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.
MathematicsEdit
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.
^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 ISBN9780821849125.
External linksEdit
Wikimedia Commons has media related to Infinity Cube.
infinity, cube, kind, mechanical, puzzle, with, mathematical, principles, shape, similar, rubik, cube, opened, back, together, from, different, directions, thus, creating, visually, interesting, effect, made, dice, being, played, withan, animation, showing, di. 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 withAn animation showing different moves and states of the Infinity cube click to animate Contents 1 Construction 2 Mathematics 3 See also 4 References 5 External linksConstruction Edit 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 Z 6 displaystyle mathbb Z 6 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 EditLike 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 43 252 003 274 489 856 000 12 2 2 12 1 8 3 8 1 displaystyle 43 252 003 274 489 856 000 frac 12 2 cdot 2 12 1 cdot 8 cdot 3 8 1 permutations 1 2 and isomorphic to the below groupware A n displaystyle A n are alternating groups and Z n displaystyle mathbb Z n are cyclic groups Z 3 7 Z 2 11 A 8 A 12 Z 2 displaystyle mathbb Z 3 7 times mathbb Z 2 11 rtimes A 8 times A 12 rtimes mathbb Z 2 The largest group representation for Infinity Cube only contains 6 elements and can be represented as Z 6 displaystyle mathbb Z 6 See also EditPaper model Fidget Cube 15 puzzleReferences Edit Schonert 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 External links Edit Wikimedia Commons has media related to Infinity Cube Magic Folding Cube Mathematische Basteleien How To Make A Paper INFINITY CUBE on YouTube Retrieved from https en wikipedia org w index php title Infinity cube amp oldid 1155033012, wikipedia, wiki, book, books, library,
