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Surfaces that occur frequently in mathematics at all levels.
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.
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.
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.
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.