The kernel of a polygon is defined by the set of points from which the entire polygon's boundary is visible. We define a polar polygon as a polygon for which the origin is strictly contained inside its kernel.
For example, only the first of the following is a polar polygon (the kernels of the second, third, and fourth do not strictly contain the origin, and the fifth does not have a kernel at all):
Note that polygons should be counted as different if they have different set of edges, even if they enclose the same area. For example, the polygon with vertices \[(0,0),(0,3),(1,1),(3,0)] is distinct from the polygon with vertices \[(0,0),(0,3),(1,1),(3,0),(1,0)].