# Message #1425

From: Melinda Green <melinda@superliminal.com>

Subject: Re: [MC4D] Regular Polytopes in 4D

Date: Thu, 17 Feb 2011 13:07:06 -0800

Oops, I just realized that I was mixing up my dimensions and was talking

about regular 3D polytopes. In 4 dimensions there are regular star and

infinite polytopes but I don’t know how many there are.

I’ll just say one more thing about infinite polytopes: Although they

include an infinite number of repeated units when realized in a flat

infinite space, they are more naturally considered as /finite /polytopes

that live in finite, repeating spaces, exactly as Roice has shown with

his Magic Tile program. His images appear to have an infinite number of

polygons but they really have a finite number which is why you can solve

them. So what we call infinite might better be called "repeating", and

they deserve to be considered as first-class regular polytopes along

with the regular convex and star polytopes. I think that we tend to

disparage these varieties because they are harder to get our heads

around, but the math is just as elegant when spaces repeat or polygons

intersect with each other or with themselves.

-Melinda

On 2/17/2011 3:21 AM, Eduard Baumann wrote:

>

>

> Okay: 6 regular convexe finite polytopes.