Definition

A rectangular prism (also called a cuboid or box) is a 3-D shape with $6$ rectangular faces in $3$ pairs of parallel, congruent rectangles, $12$ edges, and $8$ corners; volume $V = lwh$ and surface area $SA = 2(lw + lh + wh)$. The space diagonal (longest interior segment) has length $\sqrt{l^2 + w^2 + h^2}$, a 3-D extension of the Pythagorean theorem obtained by applying the theorem first in the base to get $\sqrt{l^2 + w^2}$, then again vertically. Formally, a rectangular prism is the Cartesian product $[0,l] \times [0,w] \times [0,h]$ in $\mathbb{R}^3$, an axis-aligned box whose volume $lwh$ is the determinant of the diagonal matrix $\text{diag}(l,w,h)$, connecting the box to linear algebra; rectangular prisms tile $\mathbb{R}^3$ by translation, unlike most other polyhedra.