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.
Schwarz triangle (p q r) on sphere |
Schwarz triangle graph |
Order 2 edges represents perpendicular mirrors which can be ignored in this diagram. The Coxeter-Dynkin diagram represents this triangular graph with order-2 edges hidden.
A Coxeter group can be used for a simpler notation, as (p q r) for cyclic graphs, and (p q 2) = for (right triangles), and (p 2 2) = ×.