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.
- Harmonic Brick
- Harmonic Conjugate Function
- Harmonic Conjugate Points
- Harmonic Coordinates
- Harmonic Decomposition
- Harmonic Divisor Number
- Harmonic Equation
- Harmonic Function
- Harmonic-Geometric Mean
- Harmonic Homology
- Harmonic Logarithm
- Harmonic Map
- Harmonic Mean
- Harmonic Mean Index
- Harmonic Number
- Harmonic Progression
- Harmonic Range
- Harmonic Ratio
- Harmonic Segment
- Harmonic Series
- Harmonic System of Points
- Harmonious Graph
- Harnack's Inequality
- Harnack's Theorems
- Harshad Number