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Colunar Triangle

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

\begin{displaymath}
(p\ q'\ r'), (p'\ q\ r'), (p'\ q'\ r),
\end{displaymath}

where

\begin{displaymath}
{1\over p}+{1\over p'}=1
\end{displaymath}


\begin{displaymath}
{1\over q}+{1\over q'}=1
\end{displaymath}


\begin{displaymath}
{1\over r}+{1\over r'}=1.
\end{displaymath}

See also Schwarz Triangle, Spherical Triangle


References

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




© 1996-9 Eric W. Weisstein
1999-05-26