Slab (geometry)

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

A slab can also be defined as a set of points: $${\displaystyle \{x\in \mathbb {R} ^{n}\mid \alpha \leq n\cdot x\leq \beta \},}$$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: $${\displaystyle \{x\in \mathbb {R} ^{n}\mid |n\cdot x|\leq \theta /2\},}$$where ${\displaystyle \theta =|\alpha -\beta |}$is the thickness of the slab.