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
Möbius strip Klein bottle Real projective plane Cross-cap Roman surface Boy's surface
Quadrics
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
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 Breather surface Cantor tree surface Channel surface Clebsch surface Gaussian curvature Gaussian surface Generalized helicoid Homoeoid Jacob's ladder surface Kuen surface Klein surface Loch Ness monster surface Morin surface Seashell surface Superegg Supertoroid Wallis's conical edge Whitney umbrella Zoll surface
See also List of curves Riemann surface