Geometry: Gallery of Surfaces

2018-04-10 Note: updated version is at http://virtualmathmuseum.org/

Minimal Surfaces

Geometry: Gallery of Minimal Surfaces (H=0)

Non-Orientable surfaces

moebius strip R2ByG-s250
Moebius Strip
klein bottle 50997-s250
Klein Bottle

Surfaces showing the Projective Plane

cross-cap t5hFb-s250
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 X4wKq-s250
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 34mDg-s250
Ellipsoid
paraboloid xMhhC-s250
Paraboloid
hyperbolic paraboloid 4fCHP-s250
Hyperbolic Paraboloid
hyperboloid 1 C2xyn-s250
Hyperboloid of One Sheet
hyperboloid2 DrC4B-s250
Hyperboloid of Two Sheet

Miscellaneous

torus 76N94-s250
Torus
cyclide
Cyclide
whitney umbrella pHfBR-s250
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 77100-s250
Orthocircles
decocube M6Dgs-s250
Deco-Cube

References on Mathematical Surface

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.

Check out my friends professor Richard Palais and Robert Palais's book. Many free chapters in PDF. Differential Equations, Mechanics, and Computation

Differential Equations  Mechanics  Computation Richard Palais-s
http://ode-math.com/

See also: A Visual Dictionary of Special Plane Curves