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

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.