Parallelepipeds (other)

A parallelepiped is a 3-dimensional solid with six faces, where each face is a parallelogram. While the most familiar parallelepiped is the rectangular box (cuboid), there are many other types where the faces are not rectangles. These are called oblique parallelepipeds. The edges of a general parallelepiped are not necessarily perpendicular to each other.

Important properties

• Opposite faces of a parallelepiped are parallel and congruent parallelograms.

• The volume of any parallelepiped can be found using the formula: $V = ext{base area} imes ext{height}$, where the base is any face.

• If the parallelepiped is not a rectangular box, its height is the perpendicular distance between two opposite faces.

• The space diagonal (longest diagonal) can be found using the vectors representing the edges.