# 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.[1]

The generalization of an octant is called orthant.

Three axial planes (x = 0, y = 0, z = 0) divide space into eight equal octant domains, each with a coordinate signs from ( − − −) to ( + + + ).

## Naming and numbering

For z > 0, the octants have the same numbers as the corresponding quadrants in the plane.

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.

Number
[citation needed]
Name
[citation needed]
x sign y sign z sign Octal
(+ = 0, zyx)
Octal
(+ = 1, zyx)
I top-front-right + + + 0 7
II top-back-right + + 1 6
III top-back-left + 3 4
IV top-front-left + + 2 5
V bottom-front-right + + 4 3
VI bottom-back-right + 5 2
VII bottom-back-left 7 0
VIII bottom-front-left + 6 1

## References

1. ^ Weisstein, Eric W. "Octant". MathWorld.