Standard Tori


One of the three classes of tori illustrated above and given by the parametric equations


The three different classes of standard tori arise from the three possible relative sizes of a and c. c>a corresponds to the ring torus shown above, c=a corresponds to the horn torus which touches itself at the point (0, 0, 0), and c<a corresponds to a to a self-intersecting spindle torus (Pinkall 1986, pp. 30-31).

The unqualified term "torus" is generally taken to refer to a ring torus.

The standard tori and their inversions are cyclides.

See also

Apple Surface, Cyclide, Horn Torus, Lemon Surface, Ring Torus, Spindle Torus, Torus

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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.

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Standard Tori

Cite this as:

Weisstein, Eric W. "Standard Tori." From MathWorld--A Wolfram Web Resource.

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