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 | 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/;[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.