# Message #2272

From: schuma <mananself@gmail.com>

Subject: Re: Regular abstract polytopes based on {5,3,4} and {4,3,5}

Date: Thu, 14 Jun 2012 00:26:51 -0000

The {3,5,3} has been added last night.

I was also thinking of adding "navigating inside 3-sphere" to the 3-hyperbolic space, where we can see, for example, the spherical hypercube when we are inside the 3-sphere. Then I found this playlist on youtube, showing the 120-cell, 600-cell and 24-cell in this way.

http://www.youtube.com/watch?v=_RCAlhVlsWY&feature=bf_prev&list=PL09DF17B94CA3C6FD

An interesting phenomenon is the retracting red edges. They just come when you assume light travels along the great circles of the hypersphere. Ideally, if there’s no limit of sight, you can see your back no matter which direction you are looking at, because light can travel a circle to your eyes. I really wonder what it means by saying "I can see myself in each direction". Does anyone have an idea?

Given that these videos exist, should I include the regular spherical polytopes in my applet?

Nan

— In 4D_Cubing@yahoogroups.com, "schuma" <mananself@…> wrote:

>

> Thanks. I’ve added Z-ordering to correctly draw the edges. I just copied some code from the 5-tetrahedral compound.

>

> For some reason I forgot about {3,5,3}. Maybe it’s because I’ve made an 11-cell. I’ll try to include it into this applet to make it "complete", in the sense that it includes all the regular honeycombs of H3 with finite cells and vertex figures.

>

> At some point I’ll write down the coordinates of these things to document them.

>

> Nan

>

> — In 4D_Cubing@yahoogroups.com, Roice Nelson <roice3@> wrote:

> >

> > Really nice Nan. It’s instructive to be able to switch between these three

> > honeycombs. It’s a great applet, which I’ll definitely share with

> > others as I have the chance!

> >

> > Of these three, I think I’d most like to see a puzzle based on the {4,3,5}

> > - perhaps with topological rather than purely geometric slicing, done in a

> > way to make it feel MC4D-like.

> >

> > There’s only one suggestion I have. Some of the thick lines can be covered

> > by thin lines behind them, so it seems there is a z-ordering problem. In

> > OpenGL, the depth buffer does all the work for you, but I don’t imagine the

> > drawing framework you are working with has something like this. It can be

> > a difficult problem, and you may decide it’s not worth the effort to

> > address, but I thought I’d mention it.

> >

> > Best,

> > Roice

> >

> > On Tue, Jun 12, 2012 at 1:04 PM, schuma <mananself@> wrote:

> >

> > > Hi,

> > >

> > > {4,3,5} and {5,3,5} are online now, at the same address:

> > >

> > > http://people.bu.edu/nanma/InsideH3/H3.html

> > >

> > > These two honeycombs with the icosahedral vertex figure seems less

> > > intuitive than {5,3,4}.

> > >

> > > Nan

> > >

> > >

> >

>