Parallelepiped vs. Cuboid — What's the Difference?

Parallelepiped and cuboid are both three-dimensional geometric figures, but they differ in the shapes of their faces and their angular relationships. A parallelepiped is characterized by faces that are parallelograms, meaning opposite faces are parallel and equal in area, but not necessarily right-angled. This allows for a parallelepiped to have a more varied shape, including oblique angles. A cuboid, on the other hand, is a more specific type of parallelepiped where all angles are right angles, and each of its faces is a rectangle. Essentially, a cuboid is a type of parallelepiped but with the additional constraint that all its interior angles are 90 degrees, making it a special case with more symmetry.

In terms of edges, both a parallelepiped and a cuboid have twelve edges, but in a cuboid, opposite edges are not only parallel but also equal in length, and the faces are rectangular (with a special case being all squares, which would make it a cube). The angles between the edges of a cuboid are always right angles, whereas the angles in a parallelepiped can vary, providing a wider range of shapes.

From a spatial perspective, parallelepipeds can encompass a wider variety of forms, including those that are skewed, as long as opposite faces are parallel. Cuboids offer a sense of uniformity and regularity, making them common in everyday life, where boxes and rooms typically resemble cuboids due to their perpendicular edges and flat surfaces.

While both shapes are used in various fields of study, including mathematics, physics, and engineering, their properties and applications can differ significantly. Parallelepipeds are often used in more complex geometrical and physical problems, such as in the study of vectors and crystallography, where the angles and proportions of the sides matter. Cuboids are frequently encountered in more practical, everyday calculations, like determining the volume of containers or rooms.