Magic Cube 4D
MagicCube4D is a fully functional fourdimensional analog of Rubik's cube plus
dozens of beautiful new 4D puzzles besides just the hypercube
. The image above shows the
3^{4 }
puzzle in its solved state. Click on it for a simple
resizable applet version that you can interact with to get a feeling
for how it works. Then download the fullfeatured application below and
try to solve it.
or right click here and select "Save Link as"
The program is packaged in an executable jar
file which should run on any system with a Java virtual machine
installed. Save it to your desktop or anywhere you like, so long as you
can find it later. Simply double click it to launch.
Please read the
FAQ for a more complete description of the puzzle. The
Java applet or application
should run on any machine, but if either one fails to start you probably just need to install a current Java virtual machine.
Click here for the latest version.
Don Hatch and
Melinda Green have developed this puzzle on and off starting in 1988.
Jay Berkenbilt and
Roice Nelson
later joined and made major contributions. Don and Jay were the first to have solved the puzzle making extensive use of
macros. Roice was the first person to solve the puzzle without using macros. For his solution he extended Philip Marshall's 3D
"Ultimate Solution to Rubik's Cube" into 4D. You can
learn Roice's solution if you don't feel like trying to solve it yourself first.
Project Pages
Want to learn more or get involved? The following quick links will tap you straight in.
Nerd Notes
The mathematically inclined may be interested to know that the number of possible states for the 4D cube is exactly
(24!x32!)/2 x 16!/2 x 2^23 x (3!)^31 x 3 x(4!/2)^15 x 4
which can also be expressed as
32! 24! 16! 2^22 6^32 12^15
or in decimal as
1  756  772  880  709  135  843  168  526 
 079  081  025  059  614  484  630  149 
 557  651  477  156  021  733  236  798 
 970  168  550  600  274  887  650  082 
 354  207  129  600  000  000  000  000 
For comparison, the normal 3D Rubik's Cube has only43 252 003 274 489 856 000
unique positions which is still huge. On the other hand, the 4D cube
has more potential positions than the total number of atoms in the
universe! Far more. Talk about a needle in a cosmic haystack! Click the
following link to learn how to
calculate 4D cube permutations.
Surprisingly, even though the number of 4D cube positions is
frighteningly large this doesn't mean this puzzle is that many times
harder to solve. If you can already solve the 3D cube, then you're more
than half way to solving this one. All the techniques you already know
will apply here as well.
Related Puzzles

MagicCube5D  Roice wrote an amazing 5D version of this puzzle that he and some others have even solved.
After you get into the 4D halloffame you may want to try for the
5D HallOfInsanity.
Here is a video showing the world record
shortest 5D solution by Andras Ecseki. And if
the
3^{5}
with its 810 stickers frightens you, just know that Matthew Sheerin solved
the
7^{5}
with 24010 stickers!

Magic120Cell  Roice's standalone 4D analog of the
Megaminx twisty puzzle.
This monster is composed of 120 hyperfaces each of
which is a dodecahedron looking exactly like a Megaminx. It has a total
of 7,560 hyperstickers and a truly astounding 2.3 x 10^{8126}possible
positions, only one of which is the solved state. Before going any
further, we should really stop and meditate on just how big a number
that is because you really don't see numbers like that every day.
Remember above how there are more
3^{4}
positions than particles in the universe? Well
imagine that every particle in the universe is really a tiny universe
with as many particles as ours. That's a lot more, right? Now imagine
that all of those particles in all of those universes is also a whole
universe like ours. Much more, right? well imagine repeating that
exercise 100 levels deep, and you're getting close to the number of
positions in this puzzle. MagicCube4D now also supports this puzzle but
Roice's version is better if you intend to make a serious attempt at
solving it. Noel Chalmers became the first person to solve this
behemoth. Be sure to watch the timelapse video of
Noel's solution on YouTube. Congratulations, Noel!

Andrey Astrelin recently joined our
community and immediately broke several of our most cherished records.
Not satisfied he then wrote and released his own
seven
dimensional version!
MagicCube7D solves
the problem of visualizing such a highdimensional object by starting
with our familiar 4D projection and then partially unrolling the last
three dimensions using a clever fractallike design. Not just one
puzzle, this amazing piece of code supports all 12 cubes from
3^{4}
through
5^{7}. Oh, and then he went and solved the
3^{7}. Nice going Andrey!

Magic Cube 3D
 David Vanderschel wrote a 3D Rubik's cube
simulator using the 3D equivalent of the 4D projection and user
interface to the 4D puzzle. It may seem odd to create a 3D analog of a
4D analog of a 3D puzzle but there is a logic to it as it helps to make
clear the meaning of the working and user interface of the higher
dimensional puzzles.

MagicCube2D 
Just for fun, and to see what the equivalent 2D puzzle would look like.

A
4D building blocks game by Henryk Trappmann gives us yet another interesting activity to do in 4dimensions.

Magic Cube 4D for Android. Visit
this link from the web or
this link from your Android smartphone to get the mobile version.

MagicTile from Roice lets you roll your own 2D hyperbolic twisty puzzles including the amazing
Klein's Quartic as well as Euclidean, elliptical, IRP, and even 4D skew polyhedra! MagicTile is a thing of beauty.
 Magic Hyperbolic Tile {6,3,3}
from Andrey is the 3D version of Roice's MagicTile because it lives in
a hyperbolic 3space. This puzzle turns out to be devilishly hard but
also gloriously beautiful to behold.

Magic Puzzle Ultimate
also from Andrey is his version of MagicCube4D. The
user interface is quite different and some experienced users prefer it.
It includes some brand new puzzles including the much desired and very
difficult 24cell, the 48cell and the 600cell along with deepcut, truncated, runcinated, rectified and snub versions of many of these, plus some 5D and 6D puzzles.

2D implementations of
3D and
4D twisty cubes by
Alex.
 New! RefleCube  Nan Ma gives us a 3D Rubik's cube with the ability to allow only reflection moves and other combinations of that basic idea.
License
We hope you enjoy our puzzles and would love
your feedback. We only require that if you want to use it for some
commercial purpose such as adding it to a game pack, or using it as a
demo to help sell your product, that you get our written approval first.
Programmers are free to use and modify the
code for noncommercial purposes as long as obvious credit for the
source of the code and the designs it embodies are clearly made, and
ports and derived versions of 4D Magic Cube programs are not distributed
without the express written permission of the authors.
Other 4D Cube Puzzle Implementations
Web Pages Linking to this one
(found using
Google link lookup)
Back to the Superliminal home page.