A cubical 4-polytope with the graph of the 5-dimensional cube.

In [4] we showed that for arbitrary n>d there is a cubical d-polytope, which arises as a projection of a combinatorial n-cube, and whose [d/2-1]-skeleton is isomorphic to the [d/2-1]-skeleton of the n-dimensional cube. This solves a problem of Babson, Billera, and Chan [1].

The polytope whose Schlegel diagram is shown here is a member of this 2-parameter family where d=4 and n=5. Examples with d=2 and arbitrary n>2 have been constructed before by Goldfarb [3].

Model produced with: polymake 1.3.1

Keywords
| cubical polytopes; graphs of polytopes | |

MSC-2000 Classification
| 52B12 (52B11, 52B05) | |

Zentralblatt No.
| 01682988 |

- Eric K. Babson, Louis J. Billera, and Clara S. Chan:
*Neighborly cubical spheres and a cubical lower bound conjecture*, Israel J. Math.**102**(1997), 297-315. - Ewgenij Gawrilow and Michael Joswig:
*polymake*, http://www.math.tu-berlin.de/diskregeom/polymake. - Donald Goldfarb:
*On the complexity of the simplex algorithm*, in Advances in optimization and numerical analysis, Proc. 6th Workshop on Optimization and Numerical Analysis, Oaxaca, Mexico, January 1992, Kluwer (1994), 25-38. - Michael Joswig and Günter M. Ziegler:
*Neighborly cubical polytopes*, Discrete Comput. Geometry, to appear.

- Master File: C45_Master.poly
- Applet File: C45_Applet.jvx
- Preview: C45_Preview.gif

Submitted: Mon May 1 09:32:05 CET 2000.

Accepted: Mon Nov 20 17:06:57 CET 2000.

TU BerlinGünter M. Ziegler

Sekr. MA 7-1

Straße des 17. Juni 136

10623 Berlin

Germany

joswig@math.tu-berlin.de

http://www.math.tu-berlin.de/~joswig

TU Berlin

Sekr. MA 7-1

Straße des 17. Juni 136

10623 Berlin

Germany

ziegler@math.tu-berlin.de

http://www.math.tu-berlin.de/~ziegler