Horn Torus

$\begin{figure}\BoxedEPSF{torush3.epsf scaled 500}\end{figure}$

One of the three Standard Tori given by the parametric equations

$\displaystyle x$	$\textstyle =$	$\displaystyle (c+a\cos v)\cos u$	(1)
$\displaystyle y$	$\textstyle =$	$\displaystyle (c+a\cos v)\sin u$	(2)
$\displaystyle z$	$\textstyle =$	$\displaystyle a\sin v$	(3)

with

. The inversion of a horn torus is a Horn Cyclide (or Parabolic Horn Cyclide). The above left figure shows a horn torus, the middle a cutaway, and the right figure shows a Cross-Section of the horn torus through the

-plane.

References

Gray, A. ``Tori.'' §11.4 in Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 218-220, 1993.

Pinkall, U. ``Cyclides of Dupin.'' §3.3 in Mathematical Models from the Collections of Universities and Museums (Ed. G. Fischer). Braunschweig, Germany: Vieweg, pp. 28-30, 1986.