Geometry: Gallery of Surfaces

Differential Equations, Mechanics, and Computation

Minimal Surfaces

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

Non-Orientable surfaces

moebius strip
Moebius Strip
klein bottle
Klein Bottle

Surfaces showing the Projective Plane

cross-cap
Cross-Cap Surface
boys apery
Boy's Surface (Apery)
boys bryant-kusner
Boy's Surface (Bryant-Kusner)
steiner
Steiner Surface

Spherical Surfaces (K = 1)

sphere
Sphere
k1-sor
K=1 Surface of Revolution
sievert-enneper
Sievert-Enneper Surface
spherical helicoid
Spherical Helicoid

Pseudospherical surfaces (K = -1)

pseudosphere
Pseudosphere
conic k-1 sor
Conic K=-1 Surface of Revolution
hyperbolic k1 sor
Hyperbolic K=-1 Surface of Revolution
kink
Kink Surface
kuen
Kuen Surface
breather
Breather Surface
breather p
Breather Surface
dini
Dini Surface

CMC Surfaces (H = 1)

unduloid
Unduloid

Conics Surfaces

ellipsoid
Ellipsoid
paraboloid
Paraboloid
hyperbolic-paraboloid
Hyperbolic Paraboloid
hyperboloid1
Hyperboloid of One Sheet
hyperboloid2
Hyperboloid of Two Sheet

Miscellaneous

torus
Torus
cyclide
Cyclide
whitney umbrella
Whitney Umbrella
right conoid
Right Conoid
monkey saddle
Monkey Saddle

Famous Algebraic Surfaces

cayley cubic
Cayley Cubic
clebsch cubic2
Clebsch Cubic
kummer
Kummer Quartic
barth sextic
Barth Sextic

Computer Graphics Toy Surfaces

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

orthocircles
Orthocircles
decocube
Deco-Cube Implicit Surface

Appendix

Programs and supporting files used on this site.

References and related websites

Acknowledgement

Almost all the 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

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