Sharir's Cube EG-Models Home

image SharirCube.gif
Electronic Geometry Model No. 2000.09.028


Günter M. Ziegler


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



Submission information

Submitted: Sun Sep 10 07:10:24 CET 2000.
Accepted: Mon Nov 20 17:06:57 CET 2000.

Author's Address

Günter M. Ziegler
Technische Universität Berlin
Straße des 17. Juni 136
10623 Berlin