Projected Products of Polytopes
  We construct a 2-parameter family of 4-dimensional polytopes with extreme combinatorial structure: In this family, the ``fatness'' of the f-vector gets arbitrarily close to 9, the ``complexity'' (given by the flag vector) gets arbitrarily close to 16.   The polytopes are obtained from suitable deformed products of even polygons by a projection to four-space. 
G\"unter M. Ziegler