isSmooth checks for a Cone if the rays are a subset of a basis of the lattice. For a Fan it checks smoothness for every Cone.
i1 : C = posHull matrix {{1,2,3},{3,1,2},{2,3,1}}
o1 = {ambient dimension => 3 }
dimension of lineality space => 0
dimension of the cone => 3
number of facets => 3
number of rays => 3
o1 : Cone
i2 : isSmooth C
o2 = false
i3 : F = hirzebruch 3
o3 = {ambient dimension => 2 }
number of generating cones => 4
number of rays => 4
top dimension of the cones => 2
o3 : Fan