The Nine Morse Generic Tetrahedra
Dirk Siersma, Martijn van Manen · SIAM Journal on Discrete Mathematics · 2008
There are two types of shapes for a generic triangle—acute and obtuse. These shapes are also distinguished by the (topological) Morse theory of the minimal distance function to the vertices. We can use the same method for a tetrahedron, and we show in this paper that there exist nine generic shapes. These can be described by a Morse poset or by a Gabriel graph. We also report on some computer experiments and compare our classification to another criterion used in computational geometry.