Main > Curves and Surfaces > Surfaces > Common Surfaces
Surfaces that occur frequently in mathematics at all levels.
Hyper-Planes Subspaces of Rn that have dimension n-1.
Quadratic Surfaces Surfaces that satisfy a certain type of implicit equation.
Spheres Cylinders and Cones A few common geometric objects.
Cubes and Prisms More well-known geometric objects.
Polyhedra Many-faced surfaces in R3.
Famous Surfaces Well-known and interesting surfaces.


A hyper-plane is a subspace of Rn with dimension n-1. A plane passing through the origin is a hyperplane in R3, for example.

Quadratic Surfaces

Surfaces of the form Ax2 + Bxy + Cxz + Dy2 + Eyz + Fz2 + Gx + Hy + Iz + J = 0 are known as quadratic surfaces. Examples include the ellipsoid, paraboloid, hyperboloid, sphere, and hyperbolic paraboloid.

Spheres Cylinders and Cones

The sphere, cylinder, and cone are well-known surfaces with simple parameterizations.

Cubics and Prisms

Cubics and prisms are well-known geometric objects with multiple four-sided faces.


Polyhedra are formed by "gluing" together a bunch of polygons so that their edges touch and the resulting object encloses a region of space.

Famous Surfaces

These surfaces have been studied by famous mathematicians for their interesting properties and appearances. Many are named for the mathematicians that studied them. See the complete index for examples.