## Standard Tori

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

 (1) (2) (3)

The three different classes of standard tori arise from the three possible relative sizes of and . corresponds to the Ring Torus shown above, corresponds to a Horn Torus which touches itself at the point (0, 0, 0), and corresponds to a self-intersecting Spindle Torus (Pinkall 1986). If no specification is made, torus'' is taken to mean Ring Torus.

The standard tori and their inversions are Cyclides.

See also Apple, Cyclide, Horn Torus, Lemon, Ring Torus, Spindle Torus, Torus

References

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
1999-05-26