The Schwarz triangles are Spherical Triangles which, by repeated reflection in their indices, lead to a set of congruent Spherical Triangles covering the Sphere a finite number of times.

Schwarz triangles are specified by triples of numbers . There are four ``families'' of Schwarz triangles, and the
largest triangles from each of these families are

The others can be derived from

where

and

**References**

Coxeter, H. S. M. *Regular Polytopes, 3rd ed.* New York: Dover, pp. 112-113 and 296, 1973.

Schwarz, H. A. ``Zur Theorie der hypergeometrischen Reihe.'' *J. reine angew. Math.*
**75**, 292-335, 1873.

© 1996-9

1999-05-26