Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

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Minimal triangulations and dissections of convex polytopes
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Jesus De Loera, University of California-Davis and ETH-Zurich**

In 1993 Klee and Gritzmann proposed two related natural questions:

1) QUESTION: Is it possible that by using auxiliary interior points one can triangulate a convex polytope P with fewer tetrahedra than when the set of vertices is just the vertex set of P?

2) A dissection of a convex d-polytope is collection of d-simplices with disjoint interiors whose union is the whole polytope. Unlike triangulations, simplices may intersect in sets other than common faces (i.e not a simplicial complex).

QUESTION: Is it possible that a minimal dissection is smaller than the minimal triangulation of the polytope?

In this talk we show a family of 3-dimensional convex polytopes with this property and its many interesting consequences. This is joint work with A. Below, U. Brehm, J. Richter-Gebert.

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