Message #314

From: "ilia.smilga" <>
Subject: Hi everyone!
Date: Mon, 14 Aug 2006 13:57:18 -0000

Hello everyone!
My name is Ilia Smilga, I’m 17 and I live in Nantes, France (but I’m
soon moving to Paris), though I’m actually Russian. Please do not infer from my name that
I am a girl: you would not be the first person to make this mistake. This is my first
message on the list; I have been planning to post something for quite a
long time, but I didn’t have the time to write it.
In spring 2005, two things happened in my life: I bought a Rubik’s cube
and I started to take interest in multi-dimensionnal geometry. So at
some moment, the idea of a 4D analog to a Rubik’s cube came to my mind.
I was not at all sure whether there was an obvious and beautiful way to
do this. Then a year ago, I did a Google search and I found MC4D; it
made me very enthusiastic because I discovered that other people had
already done what I had thought about! I took up the challenge of trying
to solve the Rubik’s Hypercube without looking at the answer or taking
any hint. I was not at all sure that I would succeed: I told myself that
if I would, I’d have something to be proud of!
Unfortunately, I have a Mac and MC4D didn’t first work on my computer,
but I followed a link on the MC4D webpage and downloaded a Macintosh
Rubik’s Hypercube program. It is basically about the same object, but
the representation is quite different. The hypercube is shown as three
cubes side-to-side, each cube representing one hyperlayer. Each tessie
is represented by a single cubie. Those of its hyperstickers that are
facing in one of the three spatial dimensions are represented by 2D
stickers on the cubie, and the hypersticker facing the fourth dimension
is represented by the color of the cubie itself. You can rotate the
cubes in 3D to turn them around, but you cannot do actual 4D rotations;
instead, there is an operation called "reslicing", which is quite weird
because it seems to change the orientation of the whole thing. It is
maybe hard to explain, but easy to understand once you see it. This
representation has a big advantage and a big drawback when compared to
MC4D. The big advantage is that it is much easier to grasp and to
manipulate: the twists that do not involve the 4th dimension are
straightforward to understand; the others are a bit trickier, but still
easy to handle; the whole hypercube is spread out before you, and you
need very few view rotations. The big drawback is that it is much less
symmetrical: there is one dimension which is handled very differently
from the other three; hence, it is much less beautiful. This
representation influences your way to solve the puzzle, by making some
twists easier to see than others.
I started solving and in fact, it turned out to be much easier than I
thought it would be. The point is that although the structure of a
Rubik’s hypercube is more complex, in 4-space there are more degrees of
freedom, so it is easier to continue building the solution without
breaking what has already been done. For example, when you have done the
2 upper layers of a 3D Rubik’s Cube, if you don’t know any formulas you
are quite stuck: it’s very difficult to go any further. With the
tesseract, you can always turn a "side" cell (BTW : people often call
"faces" the elements of a 4D Rubik’s hypercube that you can twist: this
is incorrect, because a face is 2D. The proper name for a "3D face" is a
"cell"; a face, on a 4D Rubik’s hypercube, is a two-colored tessie),
then do some manipulations with the "bottom" and the "side" cells and
end up with the side cell in the same state as before, but some useful
work done on the bottom cell. So in a few weeks, I solved the Mac
Then I realized that at school, there were PC’s so I was able to run
MC4D from my school. I immediately downloaded MC4D and this time, it
took me only a week to finish. I already knew approximately what to do
and I knew I could do it. On the other hand, I had to adapt myself to
the different representation, so the second time the algorithm was not
quite exactly the same as the first time. My log file is currently in
the `Solutions’ folder.
Later, the Java version was developed, and we bought a new computer, so
now I am able to play MC4D from home. I hadn’t touched it for almost a
year, but when the summer holidays came, I returned to it and solved it
another couple of times. I don’t understand how you guys manage to solve
it in less than half an hour: it usually takes me a week or more to
solve! Once I have tried to solve it as fast as possible in one sitting.
I’ll never try it again: I spent almost three hours, staring into my
monitor and trying to imagine how it all worked in 4D; I do not know
whether my eyes or my brain were more screwed up at the end!
I haven’t yet tried the 4^4 or 5^4 puzzles, because I do not know yet
how to solve 4^3 and 5^3; however, when I move to Paris, I will be able
to borrow those cubes from some friends and hopefully solve them; then
I’ll be ready to move one dimension up. I have seen that 5D Rubik’s
hypercube have been built; it must be great, I really look forward to
trying it! Unfortunately, it is only for Windows… will there ever be a
Mac version?
I have got a proposal concerning MC4D. There is a problem: it is
difficult to grasp any single tessie in a single look, especially those
that have a lot of stickers (edges and corners), because the tessies
have their stickers spread far apart in the puzzle. The option to
highlight all the stickers belonging to any tessie is quite handy, but
not quite sufficient. What if on each hypersticker, each 2D face facing
another hypersticker had on it a mark (for example, a little square)
showing the color of the hypersticker it is facing? In this way, each
hypersticker would bear enough information to identify the whole tessie;
of course, it would be redundant, but still very useful. In this way,
you could solve the whole puzzle without making a single 4D rotation!
Yes, and I have another technical question: I don’t understand at all
how the macros work. I have tried to use them, but the reference
stickers system is rather obscure for me, and it seems to me that
something really weird is going on: I sometimes get the impression that
macros are executed with one move more or less than they sould have, or
that some more different cells get twisted that should. Can someone help

See you!