Date: Sep 2, 1994 6:50 PM
Author: Daniel A. Asimov
Subject: Tesseract Projected Along a Main Diagonal

As is well-known, if a solid cube in 3-space is projected orthogonally
onto a plane that is perpendicular to one of the cube's main diagonals,
the result is a filled-in regular hexagon.

What happens if we go up one dimension? I.e., suppose we consider
the 4-cube ("tesseract") given by

T = { (x,y,z,w) in R^4 s.t. 0 <= x,y,z,w <= 1 }

and suppose we project it orthogonally onto a hyperplane (copy of R^3) in R^4
that is perpendicular to the (1,1,1,1) direction. What 3-dimensional solid
do we get? (I'll post my answer in about a week.)

(If you get an answer, please do not post it without a "Spoiler" warning
in the Subject line.)


Dan Asimov
Mail Stop T27A-1
NASA Ames Research Center
Moffett Field, CA 94035-1000

asimov@nas.nasa.gov
(415) 604-4799 w
(415) 604-3957 fax