What does parallelepiped mean?
A parallelepiped is a three-dimensional solid with six parallelogram faces, arranged so that opposite faces are parallel and congruent. A familiar example is a rectangular box, although the mathematical definition also includes oblique forms whose faces meet at angles other than right angles. Because every face of a parallelepiped is a parallelogram, the term generalizes the rectangular prism. It is especially useful in geometry, where it describes the parallel-sided solids that arise in three-dimensional coordinate systems, lattice theory, and crystallography. Architects and engineers may also use the word for substantial glass or metal structures with a broadly boxlike form. In general speech, “box” is more natural, while “parallelepiped” conveys greater geometric precision and can suggest either a rigorously defined solid or a striking, angular architectural shape.
nounA three-dimensional solid with six faces that are parallelograms, whose opposite faces are parallel and equal. In general use, the term often refers to a rectangular prism, but it may also describe an oblique solid whose faces are not rectangles.
- A three-dimensional solid bounded by six parallelogram faces, with each face parallel and equal to the face opposite it.
"The architect designed a glass parallelepiped whose mirrored surfaces echoed the surrounding buildings."
"A unit cube is the simplest example of a rectangular parallelepiped."
"The mathematician represented the lattice in terms of an oblique parallelepiped."
The standard plural adds the ending -s.
"The classroom models consist of several parallelepipeds built from magnetic tiles."
A parallelepiped gives a rectangle’s familiar box form six faces at once—and can twist that familiar shape into an elegant oblique solid.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does parallelepiped come from?
The word comes through Latin from Ancient Greek parallēlēpípedon, a compound formed from parallēlos, meaning “beside one another” or “parallel,” and epípedos, meaning “level” or “flat.” The Greek term referred to a solid with parallel, plane faces. It entered English through mathematical usage and remains associated primarily with the geometry of parallel-sided three-dimensional forms.
How parallelepiped is actually used
In everyday technical and educational use, “parallelepiped” often means a rectangular prism, including a rectangular box. Its strict geometric meaning is broader because the six faces may be parallelograms rather than rectangles. The term is chiefly used in mathematics, architecture, engineering, and crystallography.
Easily confused with parallelepiped
A parallelogram is a flat two-dimensional figure, whereas a parallelepiped is a three-dimensional solid.