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 Polytopes (book) , and the third edition was reviewed telegraphically in . Regular Polytopes (book) Regular Polytopes is a mathematical geometry book written by Canadian mathematician Harold Scott MacDonald Coxeter. Originally published in 1947, the book was updated and republished in 1963 and 1973. The book is a comprehensive survey of the geometry of regular polytopes, the generalisation of regular polygons and regular polyhedra to higher dimensions. Originating with an essay entitled "Dimensional Analogy" written in 1923, the first edition of the book took Coxeter twenty-four years to complete. "Regular Polytopes" is a standard reference work on regular polygons, polyhedra and their