Colunar Triangle

Given a Schwarz Triangle $(p\ q\ r)$, replacing each Vertex with its antipodes gives the three colunar Spherical Triangles

$$(p\ q'\ r'), (p'\ q\ r'), (p'\ q'\ r),$$

where

$${1\over p}+{1\over p'}=1$$

$${1\over q}+{1\over q'}=1$$

$${1\over r}+{1\over r'}=1.$$

See also Schwarz Triangle, Spherical Triangle

References

Coxeter, H. S. M. Regular Polytopes, 3rd ed. New York: Dover, p. 112, 1973.