Message #2687

From: Melinda Green <>
Subject: Re: [MC4D] About me
Date: Tue, 19 Mar 2013 20:49:33 -0700

On 3/19/2013 6:18 PM, Philip Strimpel wrote:
> Hello Melinda,
> Many thanks for the kind welcome! :) What version of the 24 cell would you like me to solve? There are quite a few!

Well first up should definitely be the FT model since that is clearly
the main one. Maybe you can produce the shortest solution. That will get
Nan and Andrey’s attention!

You are right that there quite a few variations and I don’t understand
most of them. One ls labeled "deep cut" which is always a bit
intimidating. Snub polyhedra are always interesting and pretty, so you
might try the Snub24Cell too.

> Also, I don’t know if it is because my computer is two slow or not, but I can’t seem to understand how to twist anything besides 3^4 and 120 cell.

Most stickers in most of those puzzles are not controls. We call them
"grips" in the code. Just poke at different shaped stickers to see which
will twist and how they work.

> I would really enjoy attempting some of the 5 and 6d puzzles. My computer is waaay too slow to even try the 600 cell though. :( Now THAT would be awesome to solve! Maybe even a 120 cell pentultimate would be an idea for a future 4d puzzle! :• I am curious though…

The full version of the 600-cell is the only remaining 4D platonic
puzzle that has not yet been solved, and seeing how unafraid you are,
you might take a look. It sounds impossible, but then that was what I
said about its 120-cell duel and I was not just wrong, I was very wrong!

For someone as bright as you, I’m sure that you can become a well paid
programmer if you put your mind to it. Programming is often all about
solving puzzles. Dirty, ugly, nasty puzzles sometimes but often very
satisfying to solve. You definitely deserve a proper computer and the
funds to build and patent puzzles if that is your passion.

> How come there can’t be a 5d dodecahedron? I know it would probably have hundreds or thousands of cells to it, but does nobody know of it because it would be too big to comprehend, or is it really virtually and physically impossible? Has anybody else thought of this? Just something to bring to the table…

Roice beat me to it, but yes, there is no equivalent dimensions 5 and
above. It seems pretty barren out there, much like the outer planets of
our solar system. Sort of like just ice, gas and rock instead of
tetrahedra, cube, and octahedra.

4D is definitely the only one in the rich habitable zone and is where
all the action is. 4D is also one of the few spaces where spheres pack
perfectly, along with 2D where 6 pennies can exactly surround a 7th. I
wonder if this has anything to do with the fact that the volume of the
unit spheres is greatest between dimensions 4 and 5. I’ve attached some
code I wrote to calculate that maximum. It’s interesting because that
maximum is not on a integer dimension though it is closer to 5 than to 4.

3D is the real oddball where things just never seem to fit quite right.
I suspect that might be the reason that it is where we live, because
high complexity is what evolution loves best.

Roice asks why 4D has the most regular polytopes, and I think that is a
really good question with probably an equally good answer. I found this
one cryptic attempt from a deaf community of all places:

/4d space is said to be the richest one because there's so many<br>
forms with 64 convex uniform ones outside of infinite series, as<br>
opposed to the 18 we have besides prisms in 3d. Including nonconvex<br>
uniform ones brings us to 75 (plus one special one) in 3d and well<br>
over 1000 in 4d. Then for some reason, spaces of five and higher<br>
dimensions have only 3 convex regular polytopes each, rather than 5<br>
and 6 for 3d and 4d space./

It doesn’t help me much, and uses the phrase "for some reason".

Cracking my bible (Regular Polytopes) to chapter and verse 7-8 gives

/When n=4 we have a Schläfli symbol &#123;p,q,r&#125;, where both &#123;p,q&#125; and<br>
&#123;q,r&#125; must occur among the Platonic solids.... Since the only<br>
regular polytope in five dimensions are α5, β5, γ5, it follows by<br>
induction that in more than five dimensions the ony regular<br>
polytopes are αn, βn, γn./

I still don’t get it but I bet Roice will figure it out and explain it
to us. :-)