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 polytope providing a technique that allows the abstract regular polytope to be constructed from its symmetry group in a standard and straightforward manner. For examples of polygons in nature, see: Each of the Platonic solids occurs naturally in one form or another: Regular polytope In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry. All its elements or "j"-faces (for all 0 ≤ "j" ≤ "n", where "n" is the dimension of the polytope) — cells, faces and so on — are also transitive on the symmetries