Projective hyperplanes, are used in projective geometry. Partial derivatives extend this idea to tangent hyperplanes to a curve. In higher dimensions, a dihedral angle represents the angle between two hyperplanes. The proper colorings of a graph are those lattice points which avoid forbidden hyperplanes. Each pair of non-parallel hyperplanes intersects to form 24 square faces in a tesseract. The intersection of these hyperplanes is a rational flat, and contains rational singular points. When two parallel hyperplanes are used to produce successive reflections, the result is a translation. They can be realized as a group of reflections with respect to hyperplanes . One important example is the case of arrangements of hyperplanes. Hyperplanes and hyperspheres are examples of hypersurfaces. Faces exist in 3 of 4 hyperplanes of the [4,3,4], formula 4 Coxeter group. There are many hyperplanes that might classify the data. The collection of such hyperplanes for a given graph is called its graphic arrangement. Sometimes one wants to allow repeated hyperplanes in the arrangement. "I" is the intersection of the hyperplanes in "S".