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Cyclide 是一对焦锥曲线，它们是两个单参数球面族的包络线，有时也称为 cyclid。Cyclide 是 四次曲面，且 cyclide 上的曲率线都是直线或圆弧 (Pinkall 1986)。标准环面及其在 反演球 反演球 
中的反演，
以点为中心，且半径为 
，由下式给出：
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都是 cyclide (Pinkall 1986)。上图展示了环形 cyclide、角形 cyclide 和纺锤形 cyclide。右图对应于 
位于环面本身的情况，分别称为抛物线环形 cyclide、抛物线角形 cyclide 和抛物线纺锤形 cyclide。
Bierschneider-Jakobs, A. "Cyclides." http://www.mi.uni-erlangen.de/~biersch/cyclides.htmlByerly, 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." Ch. 3, §3 in Mathematical Models from the Collections of Universities and Museums: Commentary. (Ed. G. Fischer). Braunschweig, Germany: Vieweg, pp. 28-30, 1986.Pinkall, U. "Dupinsche Zykliden." Ch. 3, §3 in Mathematische Modelle aus den Sammlungen von Universitäten und Museen: Kommentarband (Ed. G. Fischer). Braunschweig, Germany: Vieweg, pp. 30-33, 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.Weisstein, Eric W. "Cyclide。" 来自 MathWorld——Wolfram Web 资源。 https://mathworld.net.cn/Cyclide.html