One of the three standard tori given by the parametric
equations
with 
.
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 
-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
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References
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. https://mathworld.wolfram.com/SpindleTorus.html
Subject classifications
