In geometry , a
parallelepiped is a three-dimensional figure formed by six parallelogram s. (The term rhomboid is also sometimes used with
Kaynak: Parallelepipedknown as a rectangular cuboid, right cuboid, rectangular box , rectangular hexahedron , right rectangular prism, or rectangular
parallelepipedKaynak: CuboidThe three-dimensional counterpart of a parallelogram is a
parallelepiped . The etymology (in Greek παραλληλ-όγραμμον, a shape "of parallel
Kaynak: ParallelogramIndeed, one can also compute the volume V of a
parallelepiped having a, b and c as sides by using a combination of a cross product
Kaynak: Cross productAs pointed out above, the absolute value of the determinant of real vectors is equal to the volume of the
parallelepiped spanned by those
Kaynak: DeterminantIt is a special case of a
parallelepiped where all edges are the same length. In general the rhombohedron can have three types of rhomboid
Kaynak: RhombohedronComparing this formula with that used to compute the volume of a
parallelepiped , we conclude that the volume of a tetrahedron is equal to
Kaynak: TetrahedronIf a k-form is thought of as measuring the flux through an infinitesimal k-
parallelepiped, then its exterior derivative can be thought of
Kaynak: Exterior derivativeThe term rhomboid is now more often used for a
parallelepiped , a solid figure with six faces in which each face is a parallelogram and
Kaynak: RhomboidThe unit cell is a
parallelepiped defined by the lengths of its edges a, b, c and angles between them α, β, γ as shown in the figure
Kaynak: Fractional coordinatesGeometrically the trivector a ∧ b ∧ c corresponds to the
parallelepiped spanned by a, b, and c, with bivectors a ∧ b, b ∧ c and a ∧ c
Kaynak: Triple productA perfect
parallelepiped is a
parallelepiped with integer-length edges, face diagonals, and body diagonals, but not necessarily with all
Kaynak: Euler brickA three-dimensional orthotope is also called a right rectangular prism , rectangular cuboid , or rectangular
parallelepiped .
Kaynak: Hyperrectanglecoordinate system , where it is indeed visualized as a rectangle (two-dimensional case), rectangular
parallelepiped (three-dimensional case), etc.
Kaynak: Minimum bounding boxextension of the notion of size (length , area , volume ) to shapes more complicated than, for example, a triangle , disk , or
parallelepiped .
Kaynak: Jordan measureThe rhomb (usually a right-
parallelepiped ) is shaped such that light entering one of the small faces is internally reflected twice:
Kaynak: Fresnel rhombMurus Dacicus consisted of two outer walls made out of stone blocks carved in the shape of a rectangular
parallelepiped ; apparently no
Kaynak: Murus Dacicus