The order is important because the triangles are created like this:
If face=[f0,f1,f2,f3,f4]
Triangles=(f0,f2,f1), (f0,f3,f2), (f0,f4,f3)
Now, if face=[f1,f2,f3,f4,f0]
Triangles=(f1,f3,f2), (f1,f4,f3), (f1,f0,f4) which are not the same triangles than above.