The rule applies to POLYHEDRA (3D shapes) not Polygons, which are 2D Faces + Vertices - Edges = 2
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the first rule of a polygon is that it must have straight lines to devolope its sides. the second rule of a polygon is that it must be enclosed with no openings. the last rule of a polygon is that it has to have at least three sides.
Number of lines of symmetry = Number of sides of the regular polygon
it seems to me that the only polygon of your description is a square
A type of polygon is a rhombusial polygon, trysectalnict polygon, and a equilateral polygon.