text: In  projective space, a hyperplane does not divide the space into two parts; rather, it takes two hyperplanes to separate points and divide up the space.  The reason for this is that the space essentially "wraps around" so that both sides of a lone hyperplane are connected to each other.
  Applications
  In convex geometry, two disjoint convex sets in n-dimensional Euclidean space are separated by a hyperplane, a result called the hyperplane separation theorem.
  In machine learning, hyperplanes are a key tool to create support vector machines for such tasks as computer vision and natural language processing.
  The datapoint and its predicted value via a linear model is a hyperplane.
  Dihedral angles
  The dihedral angle between two non-parallel hyperplanes of a Euclidean space is the angle between the corresponding normal vectors. The product of the transformations in the two hyperplanes is a rotation whose axis is the subspace of codimension 2 obtained by intersecting the hyperplanes, and whose angle is twice the angle between the hyperplanes.
  Support hyperplanes
  A hyperplane H is called a "support" hyperplane of the polyhedron P if P is contained in one of the two closed half-spaces bounded by H and . The intersection of P and H is defined to be a "face" of the polyhedron. The theory of polyhedra and the dimension of the faces are analyzed by looking at these intersections involving hyperplanes.