Name or algorithm for procedure to find the kth intersection of convex polygons.

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I am trying to determine the general name of something in Geometry/Computational Geometry.

If there are N convex polygons in R^2. Is there a name for the polygon(s) that result from the intersection of at least k < N of those polygons? Or if there is no name, is there a name for such an action or algorithm?

For example I have N=5 convex polygons on a plane and I want to find where say k=3 or more of them overlap, is there a name for that? I have attached a graphical example so you can see what I mean.

I have been calling it the k-intersection, but that does not seem to be standard.

Any help is appreciated.

intersection of polygons