Slab (geometry)

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] $${\displaystyle \{x\in \mathbb {R} ^{n}\mid \alpha \leq n\cdot x\leq \beta \},}$$ 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:^[4] $${\displaystyle \{x\in \mathbb {R} ^{n}\mid |n\cdot x|\leq \theta /2\},}$$ 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