What of triangulations are we interested in?

Given a point configuration, there are several triangulations of the convex hull of the points, using only the given points. For example, the point configuration made by the vertices of a pentagon has five triangulations indicated in the figure.
Triangulations are not merely existing, but they have some structure. In the example of the pentagon, pairs of triangulations which can change to each other by changing one edge (such operations are called flips) are connected by dotted lines. So, with respect to this local transformation, the five triangulations are forming a structure of a pentagonal graph.
The aim of our research is to study the structure of triangulations in general dimension.

Our results (Publications)

Applications of triangulations

Polytopes often become easier to handle when divided into smaller parts. There are many areas requiring techniques to handle three dimensional point configurations, and triangulations become important there. Examples of such areas are computer graphics, simulations for engineering, and handling 3D structures of DNA or proteins in biology.
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Last modified: Wed Jan 5 20:31:32 2005