Parallelepiped

Parallelepiped
Type	Prism Plesiohedron
Faces	6 parallelograms
Edges	12
Vertices	8
Symmetry group	Ci, [2+,2+], (×), order 2
Properties	convex, zonohedron

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 /ˌpærəˌlɛlɪˈpɪpɪd/ or /ˌpærəˌlɛlɪˈpaɪpɪd/; traditionally, it was /ˌpærəlɛlˈɛpɪpɛd/ PARR-ə-lel-EP-ih-ped due to its etymology in Ancient Greek παραλληλεπίπεδον (parallēlepípedon) (with a short -i-), meaning a body "having parallel planes".

Parallelepipeds are a subclass of the prismatoids.