This is a list of surfaces in mathematics. They are divided into minimal surfaces, ruled surfaces, non-orientable surfaces, quadrics, pseudospherical surfaces, algebraic surfaces, and other types of surfaces.
Minimal surfaces
- Catalan's minimal surface
- Costa's minimal surface
- Catenoid
- Enneper surface
- Gyroid
- Helicoid
- Lidinoid
- Riemann's minimal surface
- Saddle tower
- Scherk surface
- Schwarz minimal surface
- Triply periodic minimal surface
Ruled surfaces
- Catalan surface
- Right conoid
- Conical surface
- Helicoid
- Developable rollers (sphericon, oloid)
- Hyperboloid of one sheet (doubly ruled)
- Hyperbolic paraboloid (doubly ruled)
- Rational normal scroll
- Regulus
Non-orientable surfaces
Quadrics
- Sphere
- Spheroid
- Ellipsoid
- Cone (geometry)
- Hyperboloid of one sheet
- Hyperboloid of two sheets
- Hyperbolic paraboloid (a ruled surface)
- Paraboloid
Pseudospherical surfaces
Algebraic surfaces
- Cayley cubic
- Barth sextic
- Clebsch cubic
- Monkey saddle (saddle-like surface for 3 legs.)
- Torus
- Dupin cyclide (inversion of a torus)
- Whitney umbrella
Miscellaneous surfaces
- Boy's surface
- Cantor tree surface
- Homoeoid
- Jacob's ladder surface
- Klein bottle
- Loch Ness monster surface
- Morin surface
- Seashell surface
- Superegg
- Supertoroid
- Wallis's conical edge
- Whitney umbrella