Secondary polytope of the 3-cube.

For the case of the 3-cube, all triangulations turn out to be regular, which means that all of them are vertices of the secondary polytope. This has dimension 4, and on the right you can see the Schlegel diagrams corresponding to two different facets.

Note that this secondary polytope is **not simple**: in the
second Schlegel diagram, you can see a vertex of degree 6.

The file 3-cube.sec.poly contains all triangulations of the 3-cube and its flip graph. This graph is also provided in gml format in the file 3-cube.sec.gml .

Model produced with: polymake 1.4, TOPCOM 0.9.0

Keywords
| secondary polytope; triangulation | |

MSC-2000 Classification
| 52B11 (52B55) | |

Zentralblatt No.
| 01682980 |

- I.M. Gelfand, M.M. Kapranov, A.V. Zelevinsky: Discriminants, Resultants, and Multidimensional Determinants, Birkhäuser (1994).

- Master File: 3-cube.sec.poly
- Applet File: 3-cube.sec.facet0.jvx
- Applet File: 3-cube.sec.facet7.jvx
- Preview: 3-cube.sec.facet0.gif
- Preview: 3-cube.sec.facet7.gif
- Other: 3-cube.poly
- Other: 3-cube.gml

Submitted: Sun Sep 10 07:10:24 CET 2000.

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

Technische Universität Berlin

Fachbereich Mathematik, MA 7-1

Straße des 17. Juni 136

10623 Berlin, Germany

pfeifle@math.tu-berlin.de

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