In geometry, a slab is a region between two parallel lines in the Euclidean plane, ^[1] or between two parallel planes in three-dimensional Euclidean space or between two hyperplanes in higher dimensions. ^[2]

Set definition

A slab can also be defined as a set of points: ^[3]

where ${\displaystyle n}$ is the normal vector of the planes ${\displaystyle n\cdot x=\alpha }$ and ${\displaystyle n\cdot x=\beta }$.

Or, if the slab is centered around the origin: ^[4]

where ${\displaystyle \theta =|\alpha -\beta |}$ is the thickness of the slab.

See also

• Bounding slab
• Convex polytope
• Half-plane
• Hyperplane
• Prismatoid
• Slab decomposition
• Spherical shell

References