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.

**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

1999-05-26