Some Interesting Configurations

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.