Similarity (geometry) similar polygons, corresponding sides taken in the same sequence (even if clockwise for one polygon and counterclockwise for the other) are proportional and corresponding angles taken in the same sequence are equal in measure. However, proportionality of corresponding sides is not by itself sufficient to prove similarity for polygons beyond triangles (otherwise, for example, all rhombi would be similar). Likewise, equality of all angles in sequence is not sufficient to guarantee similarity (otherwise all rectangles would be similar). A sufficient condition for similarity of polygons is that corresponding sides and diagonals are proportional. For given "n", all regular "n"-gons are
Regular polygon edges and faces in orthogonal projections "m"-cubes. In particular this is true for regular polygons with evenly many sides, in which case the parallelograms are all rhombi. The list gives the number of solutions for smaller polygons. The area "A" of a convex regular "n"-sided polygon having side "s", circumradius "R", apothem "a", and perimeter "p" is given by For regular polygons with side "s" = 1, circumradius "R" = 1, or apothem "a" = 1, this produces the following table: (Note that since formula_11 as formula_12, the area when formula_13 is tending to formula_14 as formula_15 grows large.) Of