Message #563

From: "thibaut.kirchner" <thibaut.kirchner@yahoo.fr>
Subject: Thibaut Kirchner
Date: Tue, 16 Sep 2008 23:17:02 -0000

Hello to all of you.
I’m Thibaut Kirchner, nearly 21 years old, and live near Paris, France.
I’m student in maths and computer science (fifth year after in
superior). Since a few days, I’m the 84th person having solved a 3^4
hypercube (actually, I’ve solved two of them).

I’m interested in solving puzzles which look like the traditional 3^3
cube since March, when a friend of mine taught me to solve the 3^3 and
the Pyraminx (at the French Open 2008).
Then I found how to solve the Megaminx, and then the 4^3 and 5^3 cubes
(parity errors were the more difficult).
I’ve been to some WCA competitions, but, if I like solving faster and
faster the same puzzles, what I really enjoy is to find methods and
algorithms to solve new puzzles. When I discovered Gelatinbrain
(http://users.skynet.be/gelatinbrain/Applets/Magic%20Polyhedra/) and
rediscovered the 3^4 hypercube (another friend of mine, Ilia Smilga,
solved it a few years ago, and I had heard of it), I decided to solve
as much puzzles from there as possible.

Now, I’m working at solving the 4^4 Hypercube and the Magic 120-Cell.
I believe I have a complete method to do them, the only thing I need
to complete the solution is some time, since it takes me a few minutes
to find some piece in this maelstrom of colors.
I expect to come with a full solution of the 4^4 in a few months, and
as for the Magic 120-Cell… It won’t be sooner than in a few years,
since it is really an enormous puzzle.

I’m looking forward to speaking about methods to solve the 3^4
hypercube, but before, I have some questions:

• I read that we don’t have a complete proof for the number of states
  of the Magic 120-Cell (would you mind if I call it Hyper-megaminx?
  Sounds better to me), because we don’t have enough formulas to orient
  all the pieces as we conjecture we can. Is it still true today? What
  cases remain to be treated? To solve the 3^4 hypercube, I found (or
  rather adapted from the 3^3 cube) and used a few formulas to orient
  different pieces, and I’m almost sure (and absolutely sure for the
  4-stickered and 3-stickered pieces) they can be adapted for the
  Hyper-megaminx.
  
• Can someone do a program to manipulate a Hyper-pyraminx (based on
  the 4D-simplex as the Pyraminx is based on the 3D-simplex), or
  Super-hypercubes (as hypercubes but center pieces are somehow oriented)?

Thibaut.

PS: Thank you for your invitation here.