acute triangulations of polyhedra and the euclidean space
We study the problem of acute triangulations of convex polyhedra and the space ? n . Here an acute triangulation is a triangulation into simplices whose dihedral angles are acute. We prove that acute triangulations of the n -cube do not exist for n ? 4. Further, we prove that acute triangulations of the space ? n do not exist for n ? 5. In the opposite direction, in ? 3 we construct nontrivial acute triangulations of all Platonic solids. We also prove nonexistence of an acute triangulation of ? 4 if all dihedral angles are bounded away from ?/2.
triangulations polyhedra