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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 *a polyhedron with six faces (hexahedron), each of which is a parallelogram, *a hexahedron with three pairs of parallel faces, 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 , , or ; traditionally it was 〔''Oxford English Dictionary'' 1904; ''Webster's Second International'' 1947〕 in accordance with its etymology in Greek παραλληλ-επίπεδον, a body "having parallel planes". Parallelepipeds are a subclass of the prismatoids. ==Properties== Any of the three pairs of parallel faces can be viewed as the base planes of the prism. A parallelepiped has three sets of four parallel edges; the edges within each set are of equal length. Parallelepipeds result from linear transformations of a cube (for the non-degenerate cases: the bijective linear transformations). Since each face has point symmetry, a parallelepiped is a zonohedron. Also the whole parallelepiped has point symmetry ''Ci'' (see also triclinic). Each face is, seen from the outside, the mirror image of the opposite face. The faces are in general chiral, but the parallelepiped is not. A space-filling tessellation is possible with congruent copies of any parallelepiped. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「parallelepiped」の詳細全文を読む スポンサード リンク
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