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
Euclidean tilings by convex regular polygons figures, which are also called "m"-Archimedean tilings. For edge-to-edge Euclidean tilings, the internal angles of the polygons meeting at a vertex must add to 360 degrees. A regular -gon has internal angle formula_1 degrees. There are seventeen combinations of regular polygons whose internal angles add up to 360 degrees, each being referred to as a "species" of vertex; in four cases there are two distinct cyclic orders of the polygons, yielding twenty-one "types" of vertex. Only eleven of these can occur in a uniform tiling of regular polygons, given in previous sections. In particular, if three polygons meet at a