info prev up next book cdrom email home

Spindle Torus

\begin{figure}\BoxedEPSF{toruss3.epsf scaled 400}\end{figure}

One of the three Standard Tori given by the parametric equations

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

with $c<a$. The exterior surface is called an Apple and the interior surface a Lemon. The above left figure shows a spindle torus, the middle a cutaway, and the right figure shows a cross-section of the spindle torus through the $xz$-plane.

See also Apple, Cyclide, Horn Torus, Lemon, Parabolic Spindle Cyclide, Ring Torus, Spindle Cyclide, Standard Tori, Torus


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.

© 1996-9 Eric W. Weisstein