
MagicCube4D is a fully functional four-dimensional analog of Rubik's cube. The image above shows the 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. Download the full-featured application below and try to solve it. Please read the FAQ for a more complete description of the puzzle. If the Java applet or application fail to start you may need to install a Java virtual machine. Click here for a current one.
Don Hatch and Melinda Green have developed it on and off over many years. Jay Berkenbilt later joined to help with Linux support and source control. Don and Jay were the first to have solved the puzzle making extensive use of macros. Roice Nelson 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. Using Philip's techniques Roice and others have continued to find ever shorter solutions so that the record currently recovered by Roice required only 334 twists! You can find documentation of these and other milestones in the MagicCube4D Hall Of Fame. If you solve it with or without reading the solution, send us your log file and we'll list you in the MagicCube4D hall of fame too!
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
| 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 only 43 252 003 274 489 856 000 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. 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. We maintain a 4D cube mailing list for discussing these and other related topics. Please feel free to read the archives and post your own thoughts and questions.
Believe it or not, Roice wrote a 5D version of this
puzzle that he and some others have even solved! After you get into
the 4D hall-of-fame you may want to try for the 5D
Hall-Of-Insanity.
New! Levi Wegner recently solved the 65 puzzle! This monster has 12,960 stickers, and it took him 24 days, averaging roughly six hours per day. It is a good thing that the program supports macros otherwise this 1.9 million twist solution would have been essentially impossible.
Roice also created Magic120Cell.
Just like there can be Rubik-style puzzles based on 3D shapes other
than cubes, it is possible to do the same with different 4D shapes. The
Magic120Cell is the 4D analog of the Megaminx twisty puzzle in the
shape of the dodecahedron. This monster is composed of 120 hyperfaces
each of which is a dodecahedron looking exactly like a Magaminx. It has
a total of 7,560 hyper-stickers and a truly astounding 2.3 x 108126
possible positions, only one of which is the solved state. Noel
Chalmers just became the first person to solve this puzzle. Be sure to
watch the time-lapse video of Noel's
solution on YouTube. Congratulations, Noel!
Also
of interest: David Vanderschel wrote a 3D Rubik's cube
simulator using the 3D equivalent of the 4D projection and user
interface to the 4D puzzle which he naturally calls Magic Cube 3D.
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 4D puzzle.
Just for fun, to see what the
equivalent 2D puzzle would look like, click the following link to see MagicCube2D!
We don't much care what you do with MagicCube4D. We simply hope you enjoy it and would love your feedback. Give it to your friends, post it on the net, whatever you like. 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. Feel free to link to this page to always have access to the current versions.Log File Utilities
Programmers are free to use and modify the code for non-commercial 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
- A small Perl program by Jay Berkenbilt that counts the twists in a log file ignoring marks, scramble twists, and rotation moves.
- A large Perl program by Don Hatch which implements a complete solution algorithm. Feed it either a complete log file or just the first part which describes a scrambled cube state and it outputs a complete log file containing a set of twists that will return a scrambled state to the solved state.
Web Pages Linking to this one (found using google link lookup)
- Java applet - corners only
- Dan Velleman's Rubik's Tesseract for the Mac
- Rubik's Hypercube by Nate Berglund.
- Slashdot Article Be sure to scroll to the bottom to see discussion threads.
- Meffert's Puzzle Links page. Buy your puzzles from him!
- cube links page of Matt Young
- Puzzles section of Xah Lee's Great Math Programs page
- Philip Marshall's ULTIMATE SOLUTION TO RUBIK'S CUBE
- Le Rubik's cube page for French speaking cube lovers. also on their software page
- Aaron Burnham's Collection of Hyper-Dimensional Links in Australia
- From Don and my resumes, plus Jay's home page. Hell, a little self-promotion never hurts!
- Jaap's Puzzle Page Links
- < temple of the > screaming-penguin </ temple of the > Ohhhhhhh Kay
- Many-dimensional Geometry page of The Geometry Junkyard. A Great math site.
- Drexel University's Math Forum library Magic Cube 4D listing.
- Random mention in the on-line diary of David Chess. Whatever.
- Rubik's Cube page of Georges Helm
- In the Resources section of Joshua Bell's Magic Polyhedra* Patents page.
- HyperDimension page of Ishihama Yoshiaki.
- Joshua Bell's Magic Polyhedra Patents page.
- Tetraspace: Garrett Jones's Links to sites about the fourth dimension.
- Linux Links Puzzles page.
- FreshPorts is maintaining a build of MC4D? Who are they???
- Andy likes the 4D cube. Thanks Andy!
- In the "Nerdy" section of CoMedia's Fun page.
- In the links section of Conceptis Puzzles.
- Roll your own 3D puzzles with the Ultimate Magic Cube.