# Message #2697

From: Roice Nelson <roice3@gmail.com>

Subject: Re: [MC4D] About me

Date: Wed, 20 Mar 2013 11:33:13 -0500

On Tue, Mar 19, 2013 at 10:49 PM, Melinda Green wrote:

>

> 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.

>

>

Magic Puzzle Ultimate has some more complex twisting modes too (for

situations where single clicks aren’t enough to specify a twist). I was

going to search through the archives to find Andrey’s posts about this, but

then noticed he has instructions on his site:

http://astr73.narod.ru/MPUlt/instr.html

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.

>

>

I think you’d find the following interesting. If you vary the n-ball

radius, the dimension where the max volume occurs can be tuned to anything.

http://www.johndcook.com/blog/2012/10/23/dimension-5-isnt-so-special/

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

>

> *When n=4 we have a Schläfli symbol {p,q,r}, where both {p,q} and {q,r}

> must occur among the Platonic solids…. Since the only regular polytope in

> five dimensions are α5, β5, γ5, it follows by induction that in more than

> five dimensions the ony regular polytopes are αn, βn, γn.*

>

> I still don’t get it but I bet Roice will figure it out and explain it to

> us. :-)

>

Luckily Nan did while I slept :D His description definitely helped me

understand things more, so thanks Nan!

seeya,

Roice