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A 3-cube with the property that each facet is perpendicular to its opposite.
Micha Sharir asked the question whether such a cube exists. This construction solves the problem in the affirmative.
It is fairly obvious that no such cube (quadrangle) exists in 2 dimensions. On the other the present example in dimension 3 can be used to lift the construction to higher dimensions: consider a prism over an n-dimensional Sharir-Cube and cut it suitably by a pair of halfspaces whose bounding hyperplanes are perpendicular in order to obtain an (n+1)-dimensional Sharir-Cube.
Model produced with: polymake 1.3.1
| Keywords | cube | |
| MSC-2000 Classification | 52B10 (52B12) | |
| Zentralblatt No. | 01682989 |
Submitted: Sun Sep 10 07:10:24 CET 2000.
Accepted: Mon Nov 20 17:06:57 CET 2000.
Technische Universität Berlin
Straße des 17. Juni 136
10623 Berlin
Germany
ziegler@math.tu-berlin.de
http://www.math.tu-berlin.de/~ziegler