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. In Euclidean geometry, its definition encompasses all four concepts (i.e., parallelepiped, parallelogram, cube, and square). In this context of affine geometry, in which angles are not differentiated, its definition admits only parallelograms and parallelepipeds. Three equivalent definitions of parallelepiped are

• a polyhedron with six faces (hexahedron), each of which is a parallelogram,
• a hexahedron with three pairs of parallel faces, 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 specific cases of parallelepiped.

"Parallelepiped" is now usually /ˌpærəlɛlɨˈpɪpɛd/, /ˌpærəlɛlɨˈpaɪpɛd/, or /-pɨd/; traditionally it was /ˌpærəlɛlˈɛpɨpɛd/ PARR-ə-lel-EP-i-ped in accordance with its etymology in Greek παραλληλ-επίπεδον, a body "having parallel planes".

Parallelepipeds are a subclass of the prismatoids.