Secondary polytope of the cartesian product of two triangles.

For the case of the cartesian product of two triangles, 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.

The third image shows a Schlegel diagram of the product of two triangles.

Note that this secondary polytope is **not simple**: in the
second Schlegel diagram, you can see a vertex of degree 5. This
secondary polytope is also described in [1].

The file tri_x_tri.sec.poly contains all triangulations of the cartesian product of two triangles and its flip graph. This graph is also provided in gml format in the file tri_x_tri.sec.gml .

Model produced with: polymake 1.4, TOPCOM 0.9.0

Keywords
| secondary polytope; triangulation | |

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

Zentralblatt No.
| 01682986 |

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

- Master File: tri_x_tri.sec.poly
- Applet File: tri_x_tri.sec.facet5.jvx
- Applet File: tri_x_tri.sec.facet12.jvx
- Applet File: tri_x_tri.jvx
- Preview: tri_x_tri.sec.facet5.gif
- Preview: tri_x_tri.sec.facet12.gif
- Preview: tri_x_tri.gif
- Other: tri_x_tri.poly
- Other: tri_x_tri.sec.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