Octant (solid geometry)

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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[edit]

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 Name x y z 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[edit]

See also[edit]