# Parallelepiped

## Hexahedron with parallelogram faces / From Wikipedia, the free encyclopedia

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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.^{[lower-alpha 1]}

Parallelepiped | |
---|---|

Type | Prism Plesiohedron |

Faces | 6 parallelograms |

Edges | 12 |

Vertices | 8 |

Symmetry group | C_{i}, [2^{+},2^{+}], (×), order 2 |

Properties | convex, zonohedron |

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 specific cases of parallelepiped.

"Parallelepiped" is now usually pronounced /ˌpærəˌlɛlɪˈpɪpɪd/ or /ˌpærəˌlɛlɪˈpaɪpɪd/;^{[1]} traditionally it was /ˌpærəlɛlˈɛpɪpɛd/ *PARR-ə-lel-EP-ih-ped*^{[2]} despite its etymology in Greek παραλληλεπίπεδον *parallelepipedon*, a body "having parallel planes".

Parallelepipeds are a subclass of the prismatoids.