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Topic: Tesseract Projected along a Main Diagonal
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Daniel A. Asimov

Posts: 35
Registered: 12/6/04
Tesseract Projected along a Main Diagonal
Posted: Sep 2, 1994 9:07 PM
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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 include a "Spoiler" warning in the Subject line.)

Dan Asimov
Mail Stop T27A-1
NASA Ames Research Center
Moffett Field, CA 94035-1000
(415) 604-4799 w
(415) 604-3957 fax

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