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.
| Parallelepiped | |
|---|---|
| Type | Prism Plesiohedron |
| Faces | 6 parallelograms |
| Edges | 12 |
| Vertices | 8 |
| Symmetry group | Ci, [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/; traditionally it was /ˌpærəlɛlˈɛpɪpɛd/ PARR-ə-lel-EP-ih-ped despite its etymology in Greek παραλληλεπίπεδον parallelepipedon, a body "having parallel planes".
Parallelepipeds are a subclass of the prismatoids.
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