Octant (solid geometry)

An octant in solid geometry is one of the eight divisions of a Euclidean three-dimensional coordinate system defined by the signs of the coordinates. It is similar to the two-dimensional quadrant and the one-dimensional ray. An octant in solid geometry is one of the eight divisions of a Euclidean three-dimensional coordinate system defined by the signs of the coordinates. It is similar to the two-dimensional quadrant and the one-dimensional ray. The generalization of an octant is called orthant. A convention for naming an octant is to give its list of signs, e.g. ( + − − ) or ( − + − ). Octant ( + + + ) is sometimes referred to as the first octant, although similar ordinal name descriptors are not defined for the other seven octants. The advantages of using the ( + − − ) notation are its unambiguousness, and extensibility for higher dimensions.