Triangulations pp 275-336 | Cite as

Some Interesting Configurations

  • Jesús A. De LoeraEmail author
  • Jörg Rambau
  • Francisco Santos
Part of the Algorithms and Computation in Mathematics book series (AACIM, volume 25)


We have seen in Section 3.4.1 that there is a friendly structure on the set of all triangulations of a planar point configuration: It is a connected graph with triangulations as nodes and flips between triangulations as edges. We also saw in Chapter 5 that, for arbitrary dimension, the regular triangulations are all connected by flips. In fact, we saw that all regular subdivisions correspond to faces of the secondary polytope. Nevertheless, as we will see in Chapter 7, for general triangulations in arbitrary point configurations of high dimension this needs not be true.


Bipartite Graph Maximal Chain Symmetry Class Characteristic Section Dual Complex 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jesús A. De Loera
    • 1
    Email author
  • Jörg Rambau
    • 2
  • Francisco Santos
    • 3
  1. 1.Department of MathematicsUniversity of California, DavisDavisUSA
  2. 2.Lehrstuhl für WirtschaftsmathematikUniversität BayreuthBayreuthGermany
  3. 3.Depto. Matemáticas Estadística y ComputaciónUniversidad de CantabriaSantanderSpain

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