Congruence (geometry) size. (Most definitions consider congruence to be a form of similarity, although a minority require that the objects have different sizes in order to qualify as similar.) For two polygons to be congruent, they must have an equal number of sides (and hence an equal number—the same number—of vertices). Two polygons with "n" sides are congruent if and only if they each have numerically identical sequences (even if clockwise for one polygon and counterclockwise for the other) side-angle-side-angle-... for "n" sides and "n" angles. Congruence of polygons can be established graphically as follows: If at any time the step cannot
Regular Polytopes (book) 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 higher dimensional analogues. It is unusual in the breadth of