info prev up next book cdrom email home

Schläfli Function

The function giving the Volume of the spherical quadrectangular Tetrahedron:

\begin{displaymath}
V={\pi^2\over 8} f\left({{\pi \over p}, {\pi\over q}, {\pi\over r}}\right),
\end{displaymath}

where

${\textstyle{1\over 2}}\pi^2 f\left({{\pi\over 2}-x, y, {\pi\over 2}-z}\right)$
$ = \sum_{m=1}^\infty \left({D-\sin x\sin z\over D+\sin x\sin z}\right)^m {\cos(2mx)-\cos(2my)+\cos(2mz)-1\over m^2}-x^2-y^2-z^2,$
and

\begin{displaymath}
D\equiv \sqrt{\cos^2 x\cos^2 z-\cos^2 y}.
\end{displaymath}

See also Tetrahedron




© 1996-9 Eric W. Weisstein
1999-05-26