Secondary polytope of the cartesian product of two triangles EG-Models Home

image tri_x_tri.sec.facet5.gif
image tri_x_tri.sec.facet12.gif
image tri_x_tri.gif
Electronic Geometry Model No. 2000.09.037


Julian Pfeifle


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


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


Submission information

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

Author's Address

Julian Pfeifle
Technische Universität Berlin
Fachbereich Mathematik, MA 7-1
Straße des 17. Juni 136
10623 Berlin, Germany