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4D Analogue of Megaminx Puzzle

Posted by timothy on Tue May 13, 2008 10:23 AM
from the pretty-puzzling dept.
Math Software Entertainment Games
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!"
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[+] Four-Dimensional Rubik's Cube Craziness 296 comments
roice writes "Rubik's junkies and puzzlers will be interested in this software rendered four-dimensional analog of Rubik's Cube. With over 1.75E120 possible combinations, it's a mind bender. Free versions are available for both Windows and Linux, and they even publish their source code for download. Solving it will get your name listed in their Hall Of Fame, and there is also a running competition for the most efficient solution. To help get you started, you can check out a solution algorithm based on techniques used to solve the popular three-dimensional version."
[+] A Working 5D Rubik's Cube 171 comments
Melinda Green writes "Readers who enjoyed the previous Slashdot postings regarding the 4-dimensional Rubik's cube called MagicCube4D will be interested to know that a couple of brilliant developers have recently created a working 5-dimensional Rubik's cube. Operating a 5 dimensional puzzle projected all the way down to a 2D computer screen may seem a hopeless task but the full 5D puzzle has already been solved by 3 people. Also noteworthy is the fact that the 4D puzzle has now been ported to Java and is available as both a full-featured desktop application and as an Applet."
Submission: 4D analogue of Megaminx Puzzle by roice (679660)
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  • Get off my lawn! (Score:3, Funny)

    by Anonymous Coward on Tuesday May 13 2008, @10:33AM (#23391572)
    In MY days, we were more than happy to have 2D and 3D!

    Damn kids these days!
  • Crazy bastards actually went and did it.

  • I'm holding out (Score:4, Interesting)

    by jayhawk88 (160512) <rockchalk88@yahoo.com> on Tuesday May 13 2008, @10:39AM (#23391636) Homepage
    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.
    • For a true 4-dimensional Rubiks Cube, one that incorporates Time.

      Or it could incorporate a thyme dimension. "It looks solved, but it just doesn't snmell solved..."

    • Re: (Score:3, Informative)

      by omeomi (675045)
      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.

      Here you go, it's already been invented: http://gizmodo.com/gadgets/rubik.s-cube/the-idiots-cube-256889.php [gizmodo.com]
    • A real puzzle should involve:

      - 4 dimensions.
      - non-linear Time.
      - curvature of space.
      - non-linear mutation of laws of physics.
      - inconstant truthness of mathematical axioms.

      • - non-linear mutation of laws of physics.
        That's easy to deal with. You just remodulate the shield harmonics and then reverse the polarity of the neutron flow.
      • You mean like politics..?
      • Oh wow, that's a lot like the real universe. Kudos for cracking that joke.

        The only thing I think I need to point out is that mathematical axioms are variant because they're a product of our mind.

    • Re: (Score:2, Interesting)

      by Tabernaque86 (1046808)
      I imagine solving a puzzle involving Time as a variable would be much like l'espirit d'escalier: By the time you figure out a solution, it's too late to implement it unless you can travel back in time 10 minutes. If you try to use your solution now, you're just going to end up making a fool of yourself.
  • Is it readily apparent to everyone else that this thing really is an analog of a 4-D MagicCell puzzle? It's very possible that it is and going right over my head. But from looking at this, it appears to me this is more analogous to people in a 2-D world taking a Sliding Puzzle game (like this <http://en.wikipedia.org/wiki/Sliding_puzzle>) and adding 3 more to form a square, with each Sliding Puzzle being a piece within the "meta-Sliding Puzzle", and calling that analogous to a 3-D puzzle... ?

    I'm not s
    • I'm not sure, but the 4D software cubes I've played with before seem to be actually 4D. In your sliding puzzle analog, sliding a square on one side would have an effect in the orientation of the squares on the other sides. So in the 4D Rubik's cube model, turning a side on one of the cubes would also rotate something else on one of the other cubes. I can solve the 3x3 Rubik's original, and almost solve the 4x4 variant, but the 4D cubes are next to impossible in my mind.
    • Well, until someone invents a 4-D monitor (and the necissary brain structure to comprehend it) a projection into 3-D space is the best we can do.

      To use your analogy of a 3-D sliding puzzle in a 2-D world; a 3-D sliding puzzle would be a cube (with six sides) and only one square missing. Projected down to a 2-D surface we would see three of the sides (distorted from their square shape). When rotated, the sides would change shape and size, and dissapear and reapear. We can never see more than three sides a

        • Re:is the analogy self-evident? (Score:4, Informative)

          by Culture20 (968837) on Tuesday May 13 2008, @12:12PM (#23392670)
          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.
        • You mean something like this? [kongregate.com] It's a 2D game, but you need to maneuver through time as well.
  • since the sides of the normal Rubik's cube are colored, it was already 4D.

  • I have a marvelous solution to the 4D Megaminx (Score:5, Funny)

    by Anonymous Coward on Tuesday May 13 2008, @10:55AM (#23391778)
    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.

  • I just don't understand this four-dimensional gobbledygook. I mean, I can imagine how you'd need another axis to graph something along, but how the heck you visualize four dimensions, or how a thing could BE four-dimensional, just doesn't make sense to me.

    It's like imaginary numbers - I see that it works on paper, but what the heck?

    • 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.
      • right, but don't forget that if you had imagined an array of 2D sheets of paper, you wouldn't really capture the idea that in 3D you can rotate, bend, and fold the paper in ways that go beyond just shuffling the sheets of paper around in the array.
    • Years ago I wrote a bunch of code that was sort-of a 4-D CAD system. You could draw elements composed of line segments and assemble them into wireframe objects. You could also feed it faces and have it shade them.

      It supported all of the various 4-D visualization projections and you could rotate, zoom and even do perspective in 4D. You really can visualize 4D if you work with it long enough.

      The code was written for an SGI workstation, but used relatively generic window ops. All of the transformations wer

      • Re: (Score:2, Informative)

        by quickgold192 (1014925)
        actually, what we see on the screen is a two-dimensional representation of the three dimensional representation of the four-dimensional object :-/

  • Now where... (Score:5, Insightful)

    by jd (1658) <imipak@yahCOFFEEoo.com minus caffeine> on Tuesday May 13 2008, @11:59AM (#23392500) Homepage Journal
    ...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.

    • Re: (Score:2, Insightful)

      by Anonymous Coward
      *sees wall of text*
      *looks at user id*
      *mods insightful*
    • It's thousands of orders of magnitude more of a babe magnet than the original cube. Which means if you can solve it then you have a snowball's chance in hell of attracting a babe.

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