Hyperplane
A hyperplane is a space composed of 1 less dimension than the space that it occupies. Visually, a hyperplane in a two-dimensional space (a Cartesian plane) would be a line, which is one-dimensional. A hyperplane in a three-dimensional space would be a plane, or some surface, which is two-dimensional.
Hyperplane Media
Two intersecting planes in three-dimensional space. A plane is a hyperplane of dimension 2, when embedded in a space of dimension 3.