Editing Parallelepiped (section)

{{Short description|Hexahedron with parallelogram faces}}
{| class=wikitable align="right" 
!bgcolor=#e7dcc3 colspan=2|Parallelepiped
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|align=center colspan=2|[[Image:Parallelepiped 2013-11-29.svg|240px|Parallelepiped]]
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|bgcolor=#e7dcc3|Type||[[Prism (geometry)|Prism]]<BR>[[Plesiohedron]]
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|bgcolor=#e7dcc3|Faces||6 [[parallelogram]]s
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|bgcolor=#e7dcc3|Edges||12
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|bgcolor=#e7dcc3|Vertices||8
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|bgcolor=#e7dcc3|[[List of spherical symmetry groups|Symmetry group]]||[[Point reflection|''C''<sub>''i''</sub>]], [2<sup>+</sup>,2<sup>+</sup>], (&times;), order 2
|-
|bgcolor=#e7dcc3|Properties||convex, [[zonohedron]]
|}

In [[geometry]], a '''parallelepiped''' is a [[three-dimensional figure]] formed by six [[parallelogram]]s (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]].{{efn|In [[Euclidean geometry]], the four concepts&mdash;''parallelepiped'' and ''cube'' in three dimensions, ''parallelogram'' and ''square'' in two dimensions&mdash;are defined, but in the context of a more general [[affine geometry]], in which angles are not differentiated, only ''parallelograms'' and ''parallelepipeds'' exist.}}

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 (geometry)|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 {{IPAc-en|ˌ|p|ær|ə|ˌ|l|ɛ|l|ɪ|ˈ|p|ɪ|p|ɪ|d}} or {{IPAc-en|ˌ|p|ær|ə|ˌ|l|ɛ|l|ɪ|ˈ|p|aɪ|p|ɪ|d}};<ref>{{cite Dictionary.com|parallelepiped}}</ref> traditionally it was {{IPAc-en|ˌ|p|ær|ə|l|ɛ|l|ˈ|ɛ|p|ɪ|p|ɛ|d}} {{respell|PARR|ə|lel|EP|ih|ped}}<ref>''Oxford English Dictionary'' 1904; ''Webster's Second International'' 1947</ref> because of its etymology in [[Ancient Greek|Greek]] παραλληλεπίπεδον ''parallelepipedon'' (with short -i-), a body "having [[parallel planes]]".

Parallelepipeds are a subclass of the [[prismatoid]]s.