Message #2697

From: Roice Nelson <>
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:

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.

> 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!