A normal hyperplane is a common term used in mathematics and geometry, but there are many synonyms for this term that can be used interchangeably. Some of the common synonyms for a normal hyperplane include perpendicular hyperplane, orthogonal hyperplane, and normal vector. These terms are all related to the idea of a hyperplane that is perpendicular or orthogonal to a given vector or set of vectors. Other synonyms for a normal hyperplane may include orthogonal subspace, normal line, normal bundle, and normal curvature. These terms all relate to the concept of a plane or space that is perpendicular or orthogonal to a certain direction or vector.