In
geometry, a
parallelepiped is a three-dimensional figure formed by six
parallelograms (the term
rhomboid is also sometimes used with this meaning). By analogy, it relates to a
parallelogram just as a
cube relates to a
square or as a
cuboid to a
rectangle. In
Euclidean geometry, its definition encompasses all four concepts (i.e.,
parallelepiped,
parallelogram,
cube, and
square). In this context of
affine geometry, in which angles are not differentiated, its definition admits only
parallelograms and
parallelepipeds. Three equivalent definitions of
parallelepiped are
The rectangular
cuboid (six
rectangular faces),
cube (six
square faces), and the
rhombohedron (six
rhombus faces) are all specific cases of parallelepiped.
