
Tesseract Projected Along a Main Diagonal
Posted:
Sep 2, 1994 6:50 PM


As is wellknown, if a solid cube in 3space is projected orthogonally onto a plane that is perpendicular to one of the cube's main diagonals, the result is a filledin regular hexagon.
What happens if we go up one dimension? I.e., suppose we consider the 4cube ("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 3dimensional 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 T27A1 NASA Ames Research Center Moffett Field, CA 940351000
asimov@nas.nasa.gov (415) 6044799 w (415) 6043957 fax

