Spindle Torus


One of the three standard tori given by the parametric equations


with c<a. The exterior surface is called an apple surface and the interior of a lemon surface. 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. The inversion of a spindle torus is a spindle cyclide (or parabolic spindle cyclide).

See also

Cyclide, Horn Cyclide, Horn Torus, Ring Torus, Standard Tori, Torus

Explore with Wolfram|Alpha


Gray, A.; Abbena, E.; and Salamon, S. Modern Differential Geometry of Curves and Surfaces with Mathematica, 3rd ed. Boca Raton, FL: CRC Press, pp. 305-306, 2006.Pinkall, U. "Cyclides of Dupin." Ch. 3, §3 in Mathematical Models from the Collections of Universities and Museums: Commentary. (Ed. G. Fischer). Braunschweig, Germany: Vieweg, pp. 28-30, 1986.Pinkall, U. "Dupinsche Zykliden." Ch. 3, §3 in Mathematische Modelle aus den Sammlungen von Universitäten und Museen: Kommentarband (Ed. G. Fischer). Braunschweig, Germany: Vieweg, pp. 30-33, 1986.

Referenced on Wolfram|Alpha

Spindle Torus

Cite this as:

Weisstein, Eric W. "Spindle Torus." From MathWorld--A Wolfram Web Resource.

Subject classifications