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A Working 5D Rubik's Cube
Posted by
CmdrTaco
on Sun Jun 04, 2006 09:00 AM
from the i'm-still-confused-in-2d dept.
from the i'm-still-confused-in-2d dept.
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."
Related Stories
[+]
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."
[+]
4D Analogue of Megaminx Puzzle 80 comments
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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MY HEAD ASPLODE! (Score:5, Funny)
Re:MY HEAD ASPLODE! (Score:4, Funny)
Parent
Bet they cheated (Score:5, Funny)
Anyone know where you can buy one? (Score:5, Funny)
Also I will need a spare set of 4 dimensional stickers in case the original ones fall off.
Re:Anyone know where you can buy one? (Score:3, Funny)
To us, they look like white mice.
You see, they really were very clever hyper-intelligent, pan-dimensional beings.
Can you still... (Score:4, Funny)
Re:Can you still... (Score:5, Funny)
Parent
Don't look so surprised... (Score:3, Funny)
Damn... And I thought I was hopelessly nerdy.
I must look positively herculean next to these guys.
I remember spending the better part of an afternoon last summer trying to solve my girlfriend's father's 20 year old rubiks cube.
I was really close to solving it when it litterally fell apart in my hands. Turns out one of the (now grown up) kids had once tried to forcibly solve it with a screwdriver. Now, whenever you it get into a certain configuration (ie: a near-finished state) it loses all structural integrity.
I could have cried... I WAS SO CLOSE!!!
I was crazy to spend so long on a three diementional rubik's cube.
But, I don't know which is crazier... That someone made a four diementional version, or that people have already solved it.
4d Java Applet (Score:3, Interesting)
Really 4D/5D? (Score:4, Interesting)
"These are Rubik's cubes of the form 3d [gravitation3d.com], with the original popular puzzle being 33. We label the puzzles like this because they are a d-dimensional cube broken into 3d smaller pieces or "cubies" of the same dimension. For example, the 3D cube has 33 or 27 total 3-dimensional cubies."
Does adding cubies really mean adding a dimension, or does it mean simply making a more complicated 3D puzzle and giving it a fancy name? (Behold: the Fifth Dimension! Amaze Your Friends!)
I noticed in the 4D model [superliminal.com] that elements disappear and reappear with each move. What's up with that? What do the green cubes represent? Where are the pieces which disappear supposed to be going, and why can't we see the changes being made to this set of cubies? Is the invisible set a cheat on the part of the designers?
I have not played with the 5D version, and so have no questions about that one.
Re:Really 4D/5D? (Score:5, Informative)
The green cubes that appear and disappear as you make moves are from the 'hidden' face of the hypercube, which has 8 faces. Their projection is using a base unfolding, to understand what they've done consider the parallel from unfolding a 3d cube into 2d. Imagine you are staring precisely face on at a cube:
XXX
XXX
XXX
Now unfold all the sides connected to the X's so you can see them straight on:
OOO
OOO
OOO
AAAXXXBBB
AAAXXXBBB
AAAXXXBBB
MMM
MMM
MMM
If you started playing a game of rubik's cube on this, you'd soon see another letter show up whenever you made a move, let's call it G for green. Where do the G's come from? From the sixth face of the cube that wasn't visible due to the choice of unfolding. The face exactly opposite of the X's
Same thing in the 4d case. There are 8 faces, only 7 of which are visible due to their poor choice of unfolding technique.
Here's wolfram's hypercube page for more info:
http://mathworld.wolfram.com/Hypercube.html [wolfram.com]
Parent
Psh~ (Score:3, Funny)
Re:Psh~ (Score:5, Funny)
http://ptth.net/slashdot/2d_rubik's_cube.JPG [ptth.net]
Parent
Re:I see that... (Score:5, Funny)
You don't need to explain your reasons not to solve this puzzle.
Parent
Re:I see that... (Score:4, Insightful)
I see you've gotten spanked as a troll... Unfortunate. Personally, I don't suspect you of trolling, just stating a fact. However...
Whether you like it or not (and I say this as a
A pity, really, because
Regardless, you would do yourself a favor to get used to
Parent
Re:I see that... (Score:5, Funny)
Parent
Re:I see that... (Score:5, Funny)
Parent
Re:I see that... (Score:3, Funny)
Re:I see that... (Score:4, Funny)
Parent
No good deed... (Score:5, Funny)
Oh my god, you're right! It does look like he wrote this application in .NET solely for the purpose of being a huge burden on everyone! After thinking about it, I guess it really does have nothing to do with .NET probably being the language he's most familiar with. I'm sure that he probably did want to spend several months learning a new language for something that could best be described as an amusing diversion, but chose not to because he wanted to waste the few minutes it would take you to download and install .NET. Come to think of it, I'm sure the fact that most people already have .NET installed probably just makes him mad, because it mitigates the toll his application will take on society.
The fact that it's kind of cool is only a ruse in his more diabolical agenda of making your life miserable for five or so minutes. The fact that we are compelled to install it by means I don't quite understand yet only makes the situation worse. If only we had a choice whether or not we wanted to play with a 5-dimensional Rubik's Cube!
Personally, I think that if you're as outraged as I am, since you're obviously so much smarter then me, you should rewrite his application in a morally superior language. The kink in this fool's plan is that he seems to have forgotten to patent the application (but be careful, it could be another trick!), which leaves the door open for anyone to simply rewrite it!
Please start working on it right away, as this outrage must not go unanswered!
Parent
Re:I give up (Score:3, Informative)
You should read Diaspora [wikipedia.org] by Greg Egan.
Should be possible in a few minutes (Score:5, Informative)
Using a few simple, easy-to-learn algorithms, and with a few weeks practice it is possible for pretty much anyone to solve the 3D cube in just 2 or 3 minutes. Using a layer-by-layer method you can solve each piece one at a time in the first two layers, then learn 4 algorithms to fix the last layer (not necessarily in this order):
1) Rotate edges
2) Rotate corners
3) Permute corners
4) Permute edges
Sometimes you will have to use an algorithm twice. Each algorithm takes about 10 moves, and at a slow speed of one move per second and a bit of luck you can solve the last layer in under a minute. Here's a beginner's guide:
http://peter.stillhq.com/jasmine/rubikscubesoluti
If you want to get faster you need to learn more algorithms so that you can complete two steps at once.
A popular method which can be used to get very fast times is the Fridrich method, but it requires a lot of memorisation and lots and lots of practice:
http://www.ws.binghamton.edu/fridrich/cube.html [binghamton.edu]
Personally I managed to get times of under 1 minute by practising the cube every day in the bus to and from work.
Parent
4th dimension is not necessarily time (Score:3, Informative)
Re:4D ? 5D? (Score:4, Funny)
They were a 1970's group, they had a hit called "Aquarius".
Parent
Re:4D ? 5D? (Score:5, Informative)
Although time is said to be the 4th dimension is time, it is only an analogy. Time appears in several physical equations in a context similar to the 3 spatial dimensions, but it is always treated differently.
For example, the spacetime "distance" is calculated by:
sqrt(x^2+y^2+z^2-c^2*t^2)
Notice the negative sign and the additional speed-of-light factor.
If there were 4 spatial dimensions, the distance would be calculated by
sqrt(x^2+y^2+z^2 + v^2)
taking v as the displacement in the 4th dimension.
The Rubik's cube programs work by projecting 4 or 5 dimensions onto a 2 dimensional plane (your screen), basically in the same way that perspective is used to project 3D pictures onto 2D planes.
So the 4th and 5th dimension aren't mathematically or conceptually different to the familiar 3 dimensions. The only difference is that we cannot comprehend them.
Parent