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Parallelepiped

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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 faces. 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 n-dimensional space, a parallelepiped is sometimes referred to as an n-dimensional parallelepiped, or as an n-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 vector a, b, and c 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 a \cdot (b \times c).


See also

Want to learn how to tackle those tough MATHCOUNTS and AMC counting and probability problems? Check out Art of Problem Solving's Introduction to Counting & Probability by David Patrick.
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