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.

See also

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