Secondary polytope of the cartesian product of two triangles

Author

Description

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

References

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

Files

• 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
• Other: tri_x_tri.poly
• Other: tri_x_tri.sec.gml

Author's Address

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