Coxeter decompositions of hyperbolic polygons the sum of the angles of a hyperbolic triangle is less than 180 degrees. Coxeter decompositions are named after Harold Scott MacDonald Coxeter, an accomplished 20th century geometer. He introduced the Coxeter group, an abstract group generated by reflections. These groups have many uses, including producing the rotations of Platonic solids and tessellating the plane. Given a polygon "P", a group "G" can be generated by reflecting "P" around its sides. If the angles of "P" are /"k" for natural numbers "k", then "G" will be discrete. A Coxeter decomposition of a polygon is a decomposition into a finite number
Special right triangle Special right triangle A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. For example, a right triangle may have angles that form simple relationships, such as 45°–45°–90°. This is called an "angle-based" right triangle. A "side-based" right triangle is one in which the lengths of the sides form ratios of whole numbers, such as 3 : 4 : 5, or of other special numbers such as the golden ratio. Knowing the relationships of the angles or ratios of sides of these special right triangles