Slab (geometry)

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

Set definition

A slab can also be defined as a set of points:

$$\{x\in \mathbb {R} ^{n}\mid \alpha \leq n\cdot x\leq \beta \}.$$

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:

$$\{x\in \mathbb {R} ^{n}\mid |n\cdot x|\leq \theta /2\}.$$

Where $\theta =|\alpha -\beta |$ is the thickness of the slab.

See also

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