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.[a]
Three equivalent definitions of parallelepiped are
a hexahedron with three pairs of parallel faces,
a polyhedron with six faces (hexahedron), each of which is a parallelogram, and
a prism of which the base is a parallelogram.
The rectangular cuboid (six rectangular faces), cube (six square faces), and the rhombohedron (six rhombus faces) are all specific cases of parallelepiped.
"Parallelepiped" is now usually pronounced /ˌpærəˌlɛlɪˈpɪpɪd/ or /ˌpærəˌlɛlɪˈpaɪpɪd/;[1] traditionally it was /ˌpærəlɛlˈɛpɪpɛd/PARR-ə-lel-EP-ih-ped[2] despite its etymology in Greek παραλληλεπίπεδον parallelepipedon, a body "having parallel planes".
Parallelepipeds are a subclass of the prismatoids.
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rhombohedron (six rhombus faces) are all specific cases of parallelepiped. "Parallelepiped" is now usually pronounced /ˌpærəˌlɛlɪˈpɪpɪd/ or /ˌpærəˌlɛlɪˈpaɪpɪd/;...
right angles. This shape is also called rectangular parallelepiped or orthogonal parallelepiped. A rectangular cuboid is a convex polyhedron with six...
corresponds to the parallelepiped spanned by a, b, and c, with bivectors a ∧ b, b ∧ c and a ∧ c matching the parallelogram faces of the parallelepiped. The triple...
of planes and lines dihedral angle and solid angle the cube, cuboid, parallelepiped the tetrahedron and other pyramids prisms octahedron, dodecahedron,...
faces meeting at right angles. Along with the rectangular cuboids, any parallelepiped is a cuboid of this type, as is a right square frustum (the shape formed...
its unit cell, which is a section of the tiling (a parallelogram or parallelepiped) that generates the whole tiling using only translations. There are...
a three-dimensional figure like a cuboid (also called a rectangular parallelepiped), except that its 3 pairs of parallel faces are up to 3 types of rhombi...
652 were edge cuboids, 350,778 were face cuboids. A perfect parallelepiped is a parallelepiped with integer-length edges, face diagonals, and body diagonals...
English. The three-dimensional counterpart of a parallelogram is a parallelepiped. The word comes from the Greek παραλληλό-γραμμον, parallēló-grammon...
It has 6 faces, 12 edges, and 8 vertices. The cube is also a square parallelepiped, an equilateral cuboid, a right rhombohedron, and a 3-zonohedron. It...
with cube shaped samples. This method, now known as the rectangular parallelepiped resonance (RPR) method, was further extended by I. Ohno in 1976. Finally...
n-dimensional dV element is in general a parallelepiped in the new coordinate system, and the n-volume of a parallelepiped is the determinant of its edge vectors...
\right\|\left|\sin \theta \right|.} Indeed, one can also compute the volume V of a parallelepiped having a, b and c as edges by using a combination of a cross product...
three-dimensional figure with six faces which are rhombi. It is a special case of a parallelepiped where all edges are the same length. It can be used to define the rhombohedral...
rhomboid is now more often used for a rhombohedron or a more general parallelepiped, a solid figure with six faces in which each face is a parallelogram...
a right parallelepiped, or in other words, a solid with 6 parallelogram faces (a square is to a cube as a parallelogram is to a parallelepiped). If the...
hypervolume of the n-dimensional parallelepiped the set subtends (also called the covolume of the lattice). This parallelepiped is a fundamental region of the...
tessellate space with their own copies. Cell-transitive parallelohedra: any parallelepiped, as well as the rhombic dodecahedron, the elongated dodecahedron, the...
the crystal structure. The geometry of the unit cell is defined as a parallelepiped, providing six lattice parameters taken as the lengths of the cell edges...
arrive at original solutions for the stability of floating cones, parallelepipeds, and cylinders, in some cases through a full cycle of rotation. His...
compute the volume of a parallelepiped, we conclude that the volume of a tetrahedron is equal to 1/6 of the volume of any parallelepiped that shares three converging...
In geometry, a parallelotope may refer to: A generalization of a parallelepiped and parallelogram A generalization of a parallelohedron and parallelogon...
collection of game tokens made of flattened bone and characterised by a parallelepiped shape. Tesserae lusoriae date to the Republican period. The production...
the sixth century, many Manichaeans saw "the earth" as "a rectangular parallelepiped enclosed by walls of crystal, above which three [sky] domes" existed...
The interpretations of 3D volumes for left: a parallelepiped (Ω in polar sine definition) and right: a cuboid (Π in definition). The interpretation is...
First, the absolute value of the box product is the volume of the parallelepiped which has edges that are defined by the three vectors. Second, the scalar...
eigenvalues. In geometry, the signed n-dimensional volume of a n-dimensional parallelepiped is expressed by a determinant, and the determinant of a linear endomorphism...
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