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.

Set definition
A slab can also be defined as a set of points: $$\{x \in \mathbb{R}^n \mid \alpha \le n \cdot x \le \beta \},$$ where $$n$$ is the normal vector of the planes $$n \cdot x = \alpha$$ and $$n \cdot x = \beta$$.

Or, if the slab is centered around the origin: $$\{x \in \mathbb{R}^n \mid |n \cdot x| \le \theta / 2 \},$$ where $$\theta = |\alpha - \beta|$$ is the thickness of the slab.