Simplicial 2-spheres obtained from non-singular complete fans
  We prove that a simplicial 2-sphere satisfying a certain condition is the underlying simplicial complex of a 3-dimensional non-singular complete fan. In particular, this implies that any simplicial 2-sphere with $\leq 18$ vertices is the underlying simplicial complex of such a fan. 
Yusuke Suyama
math.CO math.AG math.AT