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surface A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is ...
s, by Wikipedia page. ''See also List of algebraic surfaces, List of curves,
Riemann surface In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed ver ...
.''


Minimal surface In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below). The term "minimal surface" is used because these surfaces originally arose as surfaces tha ...
s

* Catalan's minimal surface * Costa's minimal surface *
Catenoid In geometry, a catenoid is a type of surface, arising by rotating a catenary curve about an axis (a surface of revolution). It is a minimal surface, meaning that it occupies the least area when bounded by a closed space. It was formally descri ...
* Enneper surface * Gyroid *
Helicoid The helicoid, also known as helical surface, after the plane and the catenoid, is the third minimal surface to be known. Description It was described by Euler in 1774 and by Jean Baptiste Meusnier in 1776. Its name derives from its similarity ...
* Lidinoid * Riemann's minimal surface * Saddle tower * Scherk surface * Schwarz minimal surface * Triply periodic minimal surface


Ruled surface In geometry, a surface is ruled (also called a scroll) if through every point of there is a straight line that lies on . Examples include the plane, the lateral surface of a cylinder or cone, a conical surface with elliptical directrix, t ...
s

*
Catalan surface In geometry, a Catalan surface, named after the Belgian mathematician Eugène Charles Catalan, is a ruled surface all of whose rulings are parallel to a fixed plane. Equations The vector equation of a Catalan surface is given by :''r'' = ''s'' ...
*
Right conoid In geometry, a right conoid is a ruled surface generated by a family of straight lines that all intersect perpendicularly to a fixed straight line, called the ''axis'' of the right conoid. Using a Cartesian coordinate system in three-dimensiona ...
* Conical surface *
helicoid The helicoid, also known as helical surface, after the plane and the catenoid, is the third minimal surface to be known. Description It was described by Euler in 1774 and by Jean Baptiste Meusnier in 1776. Its name derives from its similarity ...
*
Developable roller In geometry, a developable roller is a convex solid whose surface consists of a single continuous, developable face. While rolling on a plane, most developable rollers develop their entire surface so that all the points on the surface touch t ...
s ( sphericon,
oloid An oloid is a three-dimensional curved geometric object that was discovered by Paul Schatz in 1929. It is the convex hull of a skeletal frame made by placing two linked congruent circles in perpendicular planes, so that the center of each circl ...
) *
Hyperboloid of one sheet In geometry, a hyperboloid of revolution, sometimes called a circular hyperboloid, is the surface generated by rotating a hyperbola around one of its principal axes. A hyperboloid is the surface obtained from a hyperboloid of revolution by def ...
(doubly ruled) * Hyperbolic paraboloid (doubly ruled) * Rational normal scroll * Regulus


Non-orientable surfaces

* Klein bottle *
Real projective plane In mathematics, the real projective plane is an example of a compact non-orientable two-dimensional manifold; in other words, a one-sided surface. It cannot be embedded in standard three-dimensional space without intersecting itself. It has b ...
** Cross-cap **
Roman surface In mathematics, the Roman surface or Steiner surface is a self-intersecting mapping of the real projective plane into three-dimensional space, with an unusually high degree of symmetry. This mapping is not an immersion of the projective plan ...
** Boy's surface


Quadric In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas). It is a hypersurface (of dimension ''D'') in a -dimensional space, and it is de ...
s

*
Sphere A sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance from a given point in three-dimensional space.. That given point is th ...
* Spheroid ** Oblate spheroid * Cone (geometry) * Ellipsoid *
Hyperboloid of one sheet In geometry, a hyperboloid of revolution, sometimes called a circular hyperboloid, is the surface generated by rotating a hyperbola around one of its principal axes. A hyperboloid is the surface obtained from a hyperboloid of revolution by def ...
* Hyperboloid of two sheets * Hyperbolic paraboloid (a ruled surface) *
Paraboloid In geometry, a paraboloid is a quadric surface that has exactly one axis of symmetry and no center of symmetry. The term "paraboloid" is derived from parabola, which refers to a conic section that has a similar property of symmetry. Every plan ...


Pseudospherical surfaces

* Dini's surface *
Pseudosphere In geometry, a pseudosphere is a surface with constant negative Gaussian curvature. A pseudosphere of radius is a surface in \mathbb^3 having curvature in each point. Its name comes from the analogy with the sphere of radius , which is a surface ...


Algebraic surfaces

''See the list of algebraic surfaces.'' * Cayley cubic * Barth sextic * Clebsch cubic *
Monkey saddle In mathematics, the monkey saddle is the surface defined by the equation : z = x^3 - 3xy^2, \, or in cylindrical coordinates :z = \rho^3 \cos(3\varphi). It belongs to the class of saddle surfaces, and its name derives from the observation tha ...
(saddle-like surface for 3 legs.) * Torus *
Dupin cyclide In mathematics, a Dupin cyclide or cyclide of Dupin is any geometric inversion of a standard torus, cylinder or double cone. In particular, these latter are themselves examples of Dupin cyclides. They were discovered by (and named after) Charl ...
(inversion of a torus) * Whitney umbrella


Miscellaneous surfaces

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surfaces A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. Surface or surfaces may also refer to: Mathematics *Surface (mathematics), a generalization of a plane which needs not be flat * Sur ...