Difference between revisions of "Parallelepiped"
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| − | A '''parallelepiped''' is a [[prism]] that has [[parallelograms]] for its | + | A '''parallelepiped''' is a [[prism]] that has [[parallelograms]] for its faces. Similarly, a '''parallelepiped''' is equivalently a [[hexahedron]] with six [[parallelogram]]. Specific '''parallelepipeds''' include the [[cube]], the [[cuboid]], and any rectangular [[prism]]. |
==Specific Cases== | ==Specific Cases== | ||
Revision as of 10:47, 9 July 2007
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A parallelepiped is a prism that has parallelograms for its faces. Similarly, a parallelepiped is equivalently a hexahedron with six parallelogram. Specific parallelepipeds include the cube, the cuboid, and any rectangular prism.
Specific Cases
A parallelepiped with all rectangular faces is a cuboid, and a parallelepiped with six rhombus faces is known as a [rhombohedron]]. In an 
dimensional space, a parallelepiped is sometimes referred to as an dimensional parallelepiped, or as an parallelepiped. A cube is a parallelepiped with all square faces.
Volume
The volume of a parallelepiped is the product of area of one of its faces times the perpendicular distance to the corresponding top face. Alternately, if the three edges of a parallelepiped that meet at one vertex are defined as vectors 
and 
with the specific vertex as the origin, then the volume of the parallelepiped is the same as the scalar triple product of the vectors, or 
.
