[User]
Suppose you have a 7-gon, with vertices numbered 1 through 7 in counterclockwise order. Draw the diagonal from vertex 2 to vertex 6, from vertex 5 to vertex 3, and  from vertex 7 to vertex 3. Then, rotate the entire setup, including the constructed diagonals, 3 vertices counterclockwise (so that vertex 1 ends up where vertex 4 was), and superimpose it on the original (so that the resulting diagram contains both the original diagonals and the rotated versions of the diagonals). The original 7-gon will be partitioned into a collection of smaller polygons. (Only count the "smallest" polygons, i.e, those that do not have any of the diagonals running through them; this is not a combinatorics problem.) How many such polygons will there be with 4 sides?

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