  We are interested in constructing zonotopes which are combinatorially
nonequivalent but have the same face vector. In this paper we introduce a
quadrilateral flip operation on graphs. We show that, if one graph is obtained
from another graph by a flip, then the face vectors of the graphical zonotopes
of these two graphs are the same. In this way, we can easily construct a class
of combinatorially nonequivalent graphical zonotopes which share the same face
vector. It is known that all triangulations of the n-gon are connected through
the flip operation. Thus their graphical zonotopes have the same face vector.
We will compute this vector and the total number of faces.
