3DXM Surface Gallery

Non-Orientable Surfaces

moebius strip twisting 001
Moebius Strip
kleinbottle left right 013
Klein Bottle
cross cap close disk 010
Cross-Cap Surface
boy surf apery grow 012
Boy's Surface (Apery)
boy bryant kusner equat 012
Boy's Surface (Bryant-Kusner)
steiner surface grow 021
Steiner Surface

Pseudospherical Surfaces (K = -1)

Pseudosphere
Pseudosphere
conic Keq 1 revol 007
Conic K=-1 Surface of Revolution
hyperb Keq 1 revol 011
Hyperbolic K=-1 Surface of Revolution
dini surface family 007
Dini Surface
breather morph 001
Breather Surface
kuen surface rot 003
Kuen Surface
2 soliton equal params 006
Two-Soliton Surface
Breather Soliton4-s269x232
Breather+Soliton
three-soliton different-s256x244
Three-Soliton
Sine-Gordon 4-Soliton Patch-s289x217
Four-Soliton

Spherical Surfaces (K = 1)

k1 surface of rev 001
K=1 Surface of Revolution
sievert enneper surface 005
Sievert-Enneper Surface
curvature1 helicoid mor 001
Spherical Helicoid

Constant Mean Curvature Surfaces (H = 1)

unduloid 005
Unduloid

Quadratic Surfaces

ellipsoid 4focus
Ellipsoid
paraboloid 0growrg 010
Paraboloid
hyperbolic paraboloid0b 009
Hyperbolic Paraboloid
hyperboloid1 4morph str 001
Hyperboloid of One Sheet
hyperboloid2 dimag1-s262x238
Hyperboloid of Two Sheet
polar grid rot stereogr 005
Sphere

Torus

torus
Torus
cyclides inverted tori 011
Cyclide
Bianchi Pinkall3
Bianchi-Pinkall Flat Tori
clifford cyclides morph 019
Clifford Torus
hopf fibered linked tor 001
Hopf Fibered Linked Tori

Miscellaneous

SnailShellOpen
Snailshell
constant width 1rot 012
Surfaces of Constant Width
whitney umbrella t 001
Whitney Umbrella
right conoid2helicoid 001
Right Conoid
eedirac belt icon y78b7-s264x237
Dirac Belt
monkey saddle
Monkey Saddle
norm 1 family 003
Norm One Family

Implicit Algebraic Surfaces

Non-Compact with Singularities

cayley cubic b 008
Cayley Cubic
clebsch cubic rotate 021
Clebsch Cubic
kummer quartic rotate 005
Kummer Quartic
barth sextic levels 003
Barth Sextic

Compact with larger Genus

pretzel morph 003
Pretzel surface
pilz morph53 009
Pilz surface
bretzel2
Bretzel2 implicit surface
bretzel5 morph 007
Bretzel5 implicit surface
orthocircles morph 008
Orthocircles
DecoCube 009
Deco-Cube Implicit Surface
deco tetahedron implici 004
Deco-Tetahedron
join two tori 004
Join of 2 Tori
“Mathematics at Your Fingertip” 3DXM software in action.

Differential Geometry on Curves and Surfaces

Lecture Note on Curves and Surfaces, 2005, Chuu-Lian Terng

A Modern Course on Curves and Surfaces, 2003, by Richard S Palais

3DXM Documentation on Surfaces

Surfaces.pdf

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We gratefully acknowledge support for the development of the 3D-XplorMath program and this website by The National Science Foundation through a CCLI Grant (DUE Award # 0514781).