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