Flip-Connectivity of Triangulations of the Product of a Tetrahedron and Simplex

A flip is a minimal move between two triangulations of a polytope. The set of triangulations of a polytope was shown by Santos to not always be connected by flips, and it is an interesting problem to find large classes of polytopes for which it is. One such class which has received considerable attention is the product of two simplices. Santos proved that the set of triangulations of a product of two simplices is connected by flips when one of the simplices is a triangle. However, the author showed that it is not connected when one of the simplices is four-dimensional and the other has very large dimension. In this paper we show that it is connected when one of the simplices is a tetrahedron, thereby extending Santos’s result as far as possible.