# Working with fans - Part 2

Now we construct a new fan to show some other functions.
 i1 : C1 = coneFromVData matrix {{1,1,-1,-1},{1,-1,1,-1},{1,1,1,1}}; i2 : C2 = coneFromVData matrix {{1,1,1},{0,1,-1},{-1,1,1}}; i3 : C3 = coneFromVData matrix {{-1,-1,-1},{0,1,-1},{-1,1,1}}; i4 : C4 = coneFromVData matrix {{1,-1},{0,0},{-1,-1}}; i5 : F = fan {C1,C2,C3,C4} o5 = F o5 : Fan

This is not a ''very nice'' fan, as it is neither complete nor of pure dimension:

 i6 : isComplete F o6 = false i7 : isPure F o7 = false

If we add two more cones the fan becomes complete.

 i8 : C5 = coneFromVData matrix {{1,-1,1,-1},{-1,-1,0,0},{1,1,-1,-1}}; i9 : C6 = coneFromVData matrix {{1,-1,1,-1},{1,1,0,0},{1,1,-1,-1}}; i10 : F = addCone({C5,C6},F) o10 = F o10 : Fan i11 : isComplete F o11 = true

For a complete fan we can check if it is projective:

 i12 : isPolytopal F o12 = true

If the fan is projective, the function returns a polyhedron such that the fan is its normal fan, otherwise it returns the empty polyhedron. This means our fan is projective.