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Colunar Triangle

Given a Schwarz triangle (p q r), replacing each polygon vertex with its antipodes gives the three colunar spherical triangles

(p q^' r^'),(p^' q r^'),(p^' q^' r),
(1)

where

1/p+1/(p^')=1
(2)
1/q+1/(q^')=1
(3)
1/r+1/(r^')=1.
(4)

See also

Schwarz Triangle, Spherical Triangle

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References

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

Referenced on Wolfram|Alpha

Colunar Triangle

Cite this as:

Weisstein, Eric W. "Colunar Triangle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ColunarTriangle.html

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