The faces are in general chiral, but the parallelepiped is not.Ī space-filling tessellation is possible with congruent copies of any parallelepiped. Each face is, seen from the outside, the mirror image of the opposite face. Also the whole parallelepiped has point symmetry C i (see also triclinic). Since each face has point symmetry, a parallelepiped is a zonohedron. Parallelepipeds result from linear transformations of a cube (for the non-degenerate cases: the bijective linear transformations). A parallelepiped has three sets of four parallel edges the edges within each set are of equal length. Parallelepipeds are a subclass of the prismatoids.Īny of the three pairs of parallel faces can be viewed as the base planes of the prism. "Parallelepiped" is now usually pronounced / ˌ p ær ə ˌ l ɛ l ɪ ˈ p ɪ p ɪ d/ or / ˌ p ær ə ˌ l ɛ l ɪ ˈ p aɪ p ɪ d/ traditionally it was / ˌ p ær ə l ɛ l ˈ ɛ p ɪ p ɛ d/ PARR-ə-lel- EP-ih-ped in accordance with its etymology in Greek παραλληλεπίπεδον parallelepipedon, a body "having parallel planes". The rectangular cuboid (six rectangular faces), cube (six square faces), and the rhombohedron (six rhombus faces) are all specific cases of parallelepiped.
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