Octant (solid geometry)

A convention for naming an octant is to give its list of signs, e.g. (+,−,−) or (−,+,−).

The advantages of using the (±,±,±) notation are its unambiguousness, and extensibility for higher dimensions.

The following table shows the sign tuples together with likely ways to enumerate them.

Verbal descriptions are ambiguous, because they depend on the representation of the coordinate system.

In the two depicted representations of a right-hand coordinate system, the first octant could be called right-back-top or right-top-front respectively.

Three axial planes ( x =0, y =0, z =0) divide space into eight octants. The eight (±,±,±) coordinates of the cube vertices are used to denote them. The horizontal plane shows the four quadrants between x - and y -axis. (Vertex numbers are little-endian balanced ternary.)