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 skew apeirohedron Regular skew apeirohedron In geometry, a regular skew apeirohedron is an infinite regular skew polyhedron, with either skew regular faces or skew regular vertex figures. According to Coxeter, in 1926 John Flinders Petrie generalized the concept of regular skew polygons (nonplanar polygons) to finite regular skew polyhedra in 4-dimensions, and infinite regular skew apeirohedra in 3-dimensions (described here). Coxeter identified 3 forms, with planar faces and skew vertex figures, two are complements of each other. They are all named with a modified Schläfli symbol {"l","m"|"n"}, where there are "l"-gonal faces, "m" faces around each vertex, with "holes" identified as "n"-gonal