Triangle sum to more than 180°. A hyperbolic triangle can be obtained by drawing on a negatively curved surface, such as a saddle surface, and a spherical triangle can be obtained by drawing on a positively curved surface such as a sphere. Thus, if one draws a giant triangle on the surface of the Earth, one will find that the sum of the measures of its angles is greater than 180°; in fact it will be between 180° and 540°. In particular it is possible to draw a triangle on a sphere such that the measure of each of its internal
Schwarz triangle of the reciprocals of these integers: This is simply a way of saying that in Euclidean space the interior angles of a triangle sum to , while on a sphere they sum to an angle greater than , and on hyperbolic space they sum to less. A Schwarz triangle is represented graphically by a triangular graph. Each node represents an edge (mirror) of the Schwarz triangle. Each edge is labeled by a rational value corresponding to the reflection order, being π/vertex angle. Order-2 edges represent perpendicular mirrors that can be ignored in this diagram. The Coxeter-Dynkin diagram represents this triangular