Intersecting planes

Intersecting planes are planes that intersect along a line.

Planes p and q intersect along line m.

Planes p and q do not intersect along a line. They are parallel.

Polyhedra and intersecting planes

A polyhedron is a closed solid figure formed by many planes or faces intersecting. A polyhedron has at least 4 faces. The faces intersect at line segments called edges. Each face is enclosed by three or more edges forming polygons.


The polyhedra above are an octahedron with 8 faces and a rectangular prism with 6 faces. Each edge formed is the intersection of two plane figures.

3D coordinate plane

When three planes intersect orthogonally, the 3 lines formed by their intersection make up the three-dimensional coordinate plane.

Planes p, q, and r intersect each other at right angles forming the x-axis, y-axis, and z-axis.

A point in the 3D coordinate plane contains the ordered triple of numbers (x, y, z) as opposed to an ordered pair in 2D. With a 3D coordinate plane, it is easier to define points, lines, planes, and objects in space.

See also intersect.