# Message #565

From: David Smith <djs314djs314@yahoo.com>

Subject: Re: [MC4D] Thibaut Kirchner

Date: Tue, 16 Sep 2008 20:32:40 -0700

Hi Thibaut,

Welcome to the 4D_Cubing group! Congratulations on solving the 3^4 cube!

I also do speedcubing, but my times are probably not close to yours - I average

around a minute.

Regarding Magic120Cell and the number of positions, finding algorithms is not

my area of expertise. I used to be more interested in verifying that the upper

bound is exact, but now I am content with just finding the upper bound, being

confident that it is almost certainly the exact number (because the mathematics

indicates that it is, and there has never been a permutation puzzle in which

the mathematically justified upper bound was not exact). Roice Nelson, who

also posts on this group, told me that he has found the permutation algorithms

required, but I am not sure if anyone has discovered any orientation ones.

Also, thank you very much for your insights on the problem I may attempt to

work on. I may not work on it for some time though, because I am working on

a number of other problems leading up to the upper bound for the number of

positions of an n^d Rubik’s Cube, and its super and super-super variants, which

I am planning to write a short book about.

I am glad that you have decided to join this group, and although I am a relatively

new member, wanted to welcome you here. Once again congrats for solving

the 3^4 cube (this is something I still have to try), and good luck with your

aspirations for solving the larger cubes and Magic120Cell.

All the Best,

David

— On Tue, 9/16/08, thibaut.kirchner <thibaut.kirchner@yahoo.fr> wrote:

From: thibaut.kirchner <thibaut.kirchner@yahoo.fr>

Subject: [MC4D] Thibaut Kirchner

To: 4D_Cubing@yahoogroups.com

Date: Tuesday, September 16, 2008, 7:17 PM

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.