Secondary polytope of the "mother of all examples" EG-Models Home

image mother.sec.gif
image mother.gif
Electronic Geometry Model No. 2000.09.033


Julian Pfeifle


Secondary polytope of the "mother of all examples".

This point configuration was dubbed by Jesús de Loera as the "mother of all examples" for a point configuration admitting non-regular triangulations. A very similar example producing a non-projective toric variety already appeared in 1973 in [1].

There are exactly two non-regular triangulations of this configuration, the one shown and its mirror image. These two triangulations coincide in the GKZ embedding of the flip-graph, in the red vertex of the hexagonal face shown on the right.

The file mother.sec.poly contains all triangulations of this point configuration and its flip graph. This graph is also provided in gml format in the file mother.sec.gml .

Model produced with: polymake 1.4, TOPCOM 0.9.0

Keywords secondary polytope; triangulation
MSC-2000 Classification 52B11 (52B55)
Zentralblatt No. 01682982


  1. G. Kempf, F. Knudsen, D. Mumford, B. Saint-Donat: Toroidal embeddings. I., Springer LNM 339 (1973).


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