acoplanar

Acoplanar is a geometric term used to describe objects or sets of points that do not lie in the same plane. In three-dimensional space, coplanarity is the property of lying in a single plane, while acoplanarity means the opposite.

In practical terms, any set of four or more points may be acoplanar if there is no single plane that contains all of them. Four points are coplanar if they lie on one plane; if they do not, they are acoplanar. More generally, five or more points are acoplanar when there is no plane that passes through all of them. In coordinate geometry, a set of points is coplanar if there exists a plane that contains every point; otherwise the set is acoplanar.

The concept can extend to other geometric objects. For example, a pair of lines is acoplanar if no single plane contains both lines; such lines are often described as skew lines. Acoplanarity thus expresses a non-planar relationship between objects in space, contrasting with coplanarity, where all members share a common plane.

Etymology-wise, acoplanar comes from a- meaning not and coplanar, indicating non-coplanarity. The term is used in various fields of geometry, including solid geometry, computer graphics, and crystallography, to describe arrangements that cannot be flattened into a single plane. See also coplanar, noncoplanar, and skew lines.