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In Euclidean geometry, a parallelepiped is a three-dimensional figure (a polyhedron) having six sides (a hexahedron or prism). All six sides are parallelograms. Opposing sides are parallel and therefore all opposing sides are also congruent.

Given a parallelepiped whose edges are formed by the vectors \mathbf{v},\mathbf{u},\mathbf{w} , the volume of the parallelepiped is the scalar triple product of the three vectors:

\mathbf{v}\times\mathbf{w}\cdot\mathbf{u}=
\begin{vmatrix}
\mathbf{v}_x&\mathbf{w}_x&\mathbf{u}_x\\
\mathbf{v}_y&\mathbf{w}_y &\mathbf{u}_y\\
\mathbf{v}_z&\mathbf{w}_z &\mathbf{u}_z\\
\end{vmatrix}

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