Differential Geometry and Geometric Structures
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Students' Work: Dupin Cyclides


The cyclides of Dupin arise from cones of revolution, cylinders of revolution, and tori under the inversion with respect to a sphere. Any cyclide is a channel surface (envelope of a one-parameter family of spheres) in two different ways. All their curvature lines are circles (or lines). The image depicts a cyclide that is homeomorphic to a torus together with its curvature lines.
(Courtesy of Boris Odehnal.)

Created by Matthias Budil (2007) using POV-Ray - The Persistance of Vision Raytracer.

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Archimedean Solids
Confocal Quadrics
Dupin Cyclides
Elliptic Linear Congruence
Geodesics on a Cone
Helices on a Helicoid
Hyperosculating Spheres
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Klein Bottle
Menger Sponge
Möbius Tetrahedra
Pascal's Pyramid
Pipe Surfaces
Planar Sections of a Torus
Platonic Solids
Prince Rupert's Cube
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Schwarz Lanterns
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Stationary Points
Striction Curves

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Last modified on February 18th, 2016.