P-tree Index is an arbitrary bounding polyhedron defined by several hyperplanes Hyperplanes are normal to only certain orientation vectors   Basis vectors along with diagonals is a good choice Map convex polyhedron at -dimensional attribute space to hyperrectangle at -dimensional orientation space Polyhedra intersect if and only if the hyperrectangles intersect Searching involves checking the min and max of each axis in orientation space for intersection Orientation vectors may be added and deleted with no change to the index structure