In 3-D, a parallelepiped is a Prism whose faces are all Parallelograms. The volume of a 3-D
parallelepiped is given by the Scalar Triple Product

In -D, a parallelepiped is the Polytope spanned by Vectors , ...,
in a Vector Space over the reals,

where for , ..., . In the usual interpretation, the Vector Space is taken as Euclidean Space, and the Content of this parallelepiped is given by

where the sign of the determinant is taken to be the ``orientation'' of the ``oriented volume'' of the parallelepiped.

**References**

Phillips, A. W. and Fisher, I. *Elements of Geometry.* New York: Amer. Book Co., 1896.

© 1996-9

1999-05-26