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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