Nonpolytopal nonsimplicial lattice spheres with nonnegative toric   g-vector
  We construct many nonpolytopal nonsimplicial Gorenstein* meet semi-lattices with nonnegative toric g-vector, supporting a conjecture of Stanley. These are formed as Bier spheres over the face posets of multiplexes, polytopes constructed by Bisztriczky as generalizations of simplices. 
Louis J. Billera and Eran Nevo
math.CO