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A cyclide is a pair of focal conics which are the envelopes of two one-parameter families of spheres, sometimes also called a cyclid. The cyclide is a quartic surface, and the lines of curvature on a cyclide are
all straight lines or circular arcs (Pinkall 1986). The standard tori and their inversions
in an inversion sphere  centered at a point  and of radius  , given by
are both cyclides (Pinkall 1986). Illustrated above are ring cyclides, horn
cyclides, and spindle cyclides.
The figures on the right correspond to  lying on the
torus itself, and are called the parabolic
ring cyclide, parabolic
horn cyclide, and parabolic
spindle cyclide, respectively.
 Bierschneider-Jakobs,
A. "Cyclides." http://www.mi.uni-erlangen.de/~biersch/cyclides.html
Byerly, W. E. An Elementary Treatise on Fourier's Series, and Spherical, Cylindrical,
and Ellipsoidal Harmonics, with Applications to Problems in Mathematical Physics.
New York: Dover, p. 273, 1959.
Eisenhart, L. P. "Cyclides of Dupin." §133 in A Treatise on the Differential Geometry of Curves and Surfaces.
New York: Dover, pp. 312-314, 1960.
Fischer, G. (Ed.). Plates 71-77 in Mathematische Modelle aus den Sammlungen von Universitäten
und Museen, Bildband. Braunschweig, Germany: Vieweg, pp. 66-72, 1986.
JavaView. "Classic Surfaces from Differential Geometry: Dupin Cycloid." http://www-sfb288.math.tu-berlin.de/vgp/javaview/demo/surface/common/PaSurface_DupinCycloid.html.
Marsan, A. "Cyclides." http://www.engin.umich.edu/dept/meam/deslab/cadcam/Cyclides/cyclide.html.
Nordstrand, T. "Dupin Cyclide." http://jalape.no/math/dupintxt.
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.
Salmon, G. Analytic Geometry of Three Dimensions. New York: Chelsea,
p. 527, 1979.
Trott, M. Graphica 1: The World of Mathematica Graphics. The Imaginary
Made Real: The Images of Michael Trott. Champaign, IL: Wolfram Media, pp. 16
and 84, 1999.
Wells, D. The Penguin Dictionary of Curious and Interesting Geometry.
London: Penguin, p. 62, 1991.
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