Slashdot Mirror
4D Analogue of Megaminx Puzzle
roice writes "The crazy hypercubists who created the
4D and
5D Rubik's cubes (here are previous
Slashdot posts on
the 4-D one and
the 5-D one)
have now developed a free
working 4-dimensional software analogue of the
Megaminx puzzle. Composed of
120 dodecahedral cells, the
underlying structure is arguably the most beautiful of 4D geometrical shapes,
with amazing symmetries and no analogue in dimensions higher than 4.
Though some have already begun working on solutions for this 'Hyperminx,' it has
yet to be solved by anyone. Also, when it comes to
number of positions, it dwarfs the previous puzzles by many thousands of
orders of magnitude!"
In MY days, we were more than happy to have 2D and 3D!
Damn kids these days!
For a true 4-dimensional Rubiks Cube, one that incorporates Time. Of course solving it will be incredibly disappointing, since after you do solve one, it turns out that it was solved all along.
which this margin is too narrow to contain. Strangely the solution implies that if you have 4 integers x,y,z>0 and n>2 then x^n+y^n!=z^n, but I don't know why the heck that would be important.
Visualize our three dimensions as a bounded volume in 3-space. Then you can kind-of imagine the 4th and 5th spatial dimensions discreetly as 1- and 2-d arrays of such volumes.
...have I seen this Megaminx puzzle before.... Oh yes, that's right, the US tax system. Seriously, this is wonderful. Once a problem is solved, then further work is merely optimization and refactoring. There's nothing new. Puzzles that have an algorithmic solution, but where the solution is unknown at this time, are interesting because they require discovery that is potentially within reach of anyone. Puzzles for which only a herustic definitely exists are also interesting for much the same reason. Problems with no solution, or where it is not yet possible to prove it is possible to find any solution, are interesting more because the work required might well involve whole new branches of mathematics being developed, real frontier work rather than simply filling in the gaps. Puzzles of this kind also draw people who might otherwise consider maths or science "boring" into those fields. Science outside of "profitable" fields like computer programming tend to rely on sparking the imagination of the next generation. There's no other reason to go into such a subject than the pursuit of knowledge, once you eliminate all status and monetary value.
It's a small world and it smells funny; I'd buy another if it wasn't for the money; Take back what I paid (SoM)
Ever played the latest Prince of Persia (Sands of Time) series? They were 3D games where you had to use another dimension (time travel) to navigate puzzles because things were [un]available in different times. Heck, go back to Zelda series for a 2D game where travel to a dream-world allows more freedom of movement.