Relation between the number of facets and of free faces

Question

First, give the definition.

1. A facet is any simplex in a complex that is not a face of any larger simplex. (aka maximal face)
2. A simplex $\tau$ is called a free face if it is the face of only one facet in a simplicial complex.

Here is an example. Suppose we have a simplicial complex {{1,2,3}, {3,4}}. {1,2,3} and {3,4} are all facets and {4}, {1,2}, {2,3}, {1,3} are free faces.

Here is my question: is there any research about the maximal number of free faces given an arbitrary simplicial complex which has n 0-simplex, which can be regarded vertices? Is there any relationship between the number of free faces and of the facets for an arbitrary simplicial complex?