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Geometry: Gallery of Surfaces

Minimal Surfaces

Over 30 minimal surfaces (constant mean curvature of 0).

Non-Orientable surfaces

• 
  Moebius Strip
• 
  Klein Bottle

Surfaces showing the Projective Plane

• 
  Cross-Cap Surface,
• 
  Boy's Surface (Apery)
• 
  Boy's Surface (Bryant-Kusner)
• 
  Steiner Surface

Spherical Surfaces (K = 1)

• 
  Sphere
• 
  K=1 Surface of Revolution
• 
  Sievert-Enneper Surface
• 
  Spherical Helicoid

Pseudospherical surfaces (K = -1)

• 
  Pseudosphere
• 
  Conic K=-1 Surface of Revolution
• 
  Hyperbolic K=-1 Surface of Revolution
• 
  Kink Surface
• 
  Kuen Surface
• 
  Breather Surface
• 
  Breather (Parametric)
• 
  Dini Surface

CMC Surfaces (H = 1)

• 
  Unduloid

Conics Surfaces

• 
  Ellipsoid
• 
  Paraboloid
• 
  Hyperbolic Paraboloid
• 
  Hyperboloid of One Sheet
• 
  Hyperboloid of Two Sheet

Miscellaneous

• 
  Torus
• 
  Cyclide
• 
  Whitney Umbrella
• 
  Right Conoid
• 
  Monkey Saddle

Famous Algebraic Surfaces

• 
  Cayley Cubic
• 
  Clebsch Cubic
• 
  Kummer Quartic
• 
  Barth Sextic

Computer Graphics Toy Surfaces

The following surfaces have no mathematical significance. They are more for the looks.

• 
  Orthocircles
• 
  Deco-Cube Implicit Surface

Appendix

• Programs and supporting files used on this site.

• References and related websites

Acknowledgement

About 95% of images and surface data on this site are from Richard Palais's 3D-XplorMath software. I like to thank Richard for much of his personal help and encouragement over the years. I also like to thank Hermann Karcher for his help and some of his math expositions used on this website.

See also: A Visual Dictionary of Special Plane Curves