A spindle torus is 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).
Meissner polyhedra have curved boundaries
that consist of pieces of spheres and spindle tori (Hynd 2023).
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.Hynd, R. "The Density
of Meissner Polyhedra." 8 Apr 2023. https://arxiv.org/abs/2304.04035.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
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