Topic summary
Parallelepiped
In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms (the term rhomboid is also sometimes used with this meaning). By analogy, it relates to a parallelogram just as a cube relates to a square.
Three equivalent definitions of parallelepiped are
- a hexahedron with three pairs of parallel faces,
- a polyhedron with six faces (hexahedron), each of which is a parallelogram, and
- a prism of which the base is a parallelogram.
The rectangular cuboid (six rectangular faces), cube (six square faces), and the rhombohedron (six rhombus faces) are all special cases of parallelepiped.
Parallelepiped is now usually pronounced or ; traditionally, it was due to its etymology in Ancient Greek (parallēlepípedon) (with a short -i-), meaning a body "having parallel planes".
Parallelepipeds are a subclass of the prismatoids.