Acute triangulations of polytopes

Igor Pak
University of California, Los Angeles (UCLA)

A simplex in Rd is called acute if all its dihedral angles are < ¼=2. An acute tri-
angulation of a polytope is a triangulation (as a CW-complex) into acute simplices.
The problem of ¯ning acute triangulations is of interest in discrete geometry, the
¯nite element method, and other applications.
In this talk I will survey a number of known and recent results on acute tri-
angulations. In particular, we describe a complete solution for certain classes of
polytopes. We conclude with some open problems.
Part of the talk is based on the recent paper joint with Eryk Kopczy¶nski and
Piotr Przytycki.

Presentation (PDF File)

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