Secondary polytope of the 3-cube EG-Models Home

image 3-cube.sec.facet0.gif
image 3-cube.sec.facet7.gif
Electronic Geometry Model No. 2000.09.031


Julian Pfeifle


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


  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