From: jbuddenh@artsci.wustl.edu (Jim Buddenhagen)
Newsgroups: rec.arts.sf.written,sci.math
Subject: Re: Tesseracts and visualizing in 4D
Date: 12 Apr 1997 16:18:22 GMT

Pertti Lounesto (lounesto@dopey.hut.fi) wrote:
: nancyl@universe.digex.net (Nancy Lebovitz) writes:
: :>> I may have met someone who could visualize a fourth dimension, but
: :>> it's a damned hard thing to check. I asked her how many corners
: :>> a hypercube (same thing as a tesseract) has--this is easy to figure
[...]
: If you want the test to include enumeration of parties of regular 
: polytopes in 4D, then there is a good test (for a non-mathematician):
: All the five regular polyhedrons in 3D have analogs in 4D, but there
: is a sixth regular polytope in 4D, which has no analog in 3D. This
: polytope has 24 vertices, it has 24 octahedrons as 3D-faces, it has
: 96 1D-edges.  You could, for instance, tell her that there is a
: regular polytope formed by 24 octahedrons, and ask how many vertices
: it has.  Even better test would be a qualitative question: describe
: the vertex figure of that polytope (it is 3D-cube).  
[...]
: -- 
: Pertti Lounesto            http://www.math.hut.fi/~lounesto

You can free-view a stereo pair of the regular 24 vertex polytope at
Tony Smith's home:  http://galaxy.cau.edu/tsmith/1TSmath.html
--
 Jim Buddenhagen   jbuddenh@artsci.wustl.edu