Equiangular polygon Equiangular polygon In Euclidean geometry, an equiangular polygon is a polygon whose vertex angles are equal. If the lengths of the sides are also equal (that is, if it is also equilateral) then it is a regular polygon. Isogonal polygons are equiangular polygons which alternate two edge lengths. The only equiangular triangle is the equilateral triangle. Rectangles, including the square, are the only equiangular quadrilaterals (four-sided figures). For a convex equiangular "n"-gon each internal angle is 180(1-2/n)°; this is the "equiangular polygon theorem". Viviani's theorem holds for equiangular polygons: A rectangle (equiangular quadrilateral) with integer side lengths may be tiled
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