Message #1425

From: Melinda Green <>
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.


On 2/17/2011 3:21 AM, Eduard Baumann wrote:
> Okay: 6 regular convexe finite polytopes.