We don't have synonyms for hyperplanes yet — it may be a rare, specialized, newly coined, or misspelled word. The closest thesaurus entries we have are hyperplane.
(n) :
(geometry) An n-dimensional generalization of a plane; an affine subspace of dimension n − 1 that splits an n-dimensional space. (In a one-dimensional space, it is a point; in two-dimensional space it is a line; in three-dimensional space, it is an ordinary plane.)
(n) :
(geometry) An n-dimensional generalization of a plane; an affine subspace of dimension n − 1 that splits an n-dimensional space. (In a one-dimensional space, it is a point; in two-dimensional space it is a line; in three-dimensional space, it is an ordinary plane.)