It is well known that a (smooth complete) fan $\Delta$ corresponds to a (smooth proper) toric variety $X= X_\Delta$.

My question is whether there is a relationship between the number of maximal cones in $\Delta$ and a geometric invariant of $X$. (as the number of 1-dimensional cones is the number of torus invariant prime divisor)

Here, we call a cone in $\Delta$ maximal if it is not contained in any other cone in $\Delta$.