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 tothe 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 takento 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.
- Ker
- Keratoid Cusp
- Kernel (Integral)
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- Kernel Polynomial
- Kervaire's Characterization Theorem
- Ket
- k-Form
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- Khinchin Constant
- Khintchine-Lévy Constant
- Khintchine's Constant
- Khovanski's Theorem
- Kiepert's Conics
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- Kieroid
- Killing's Equation
- Killing Vectors
- Kimberling Sequence
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