List of surfaces

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

A Scherk surface

• 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

A right conoid

• 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

A Klein bottle

• Klein bottle
• Real projective plane
  • Cross-cap
  • Roman surface
  • Boy's surface

Quadrics

A hyperboloid of two sheets

• Sphere
• Spheroid
  • Oblate spheroid
  • Prolate spheroid
• Ellipsoid
• Cone (geometry)
• Hyperboloid of one sheet
• Hyperboloid of two sheets
• Hyperbolic paraboloid (a ruled surface)
• Paraboloid

Pseudospherical surfaces

• Dini's surface
• Pseudosphere

Algebraic surfaces

Main article: List of algebraic surfaces

The Barth sextic

• 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

• Boy's surface
• Cantor tree surface
• Homoeoid
• Jacob's ladder surface
• Loch Ness monster surface
• Morin surface
• Seashell surface
• Superegg
• Supertoroid
• Wallis's conical edge
• Whitney umbrella

See also

• List of curves
• Riemann surface