A zonotope and a product of two simplices with disconnected flip graphs

Abstract

We give an example of a three-dimensional zonotope whose set of tight zonotopal tilings is not connected by flips. Using this, we show that the set of triangulations of ${\Delta }^4\times {\Delta }^n$ is not connected by flips for large $n$. Our proof makes use of a non-explicit probabilistic construction.

28 pages