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I am interested to know the name of the following solid construction - kind of a deformed cube... but I don't know the name, or even a general name:

  1. Left and right faces parallel with the $yz$ axes
  2. Bottom face parallel with the $xz$ axes
  3. Back face parallel with the $xy$ axes.
  4. Front and top faces not necessarily parallel,

assuming $x=(1, 0, 0),y=(0,1,0),z=(0,0,1)$. If there is no such name, then is "3d quadrilateral" correct ?

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    $\begingroup$ I would not call "quadrilateral" what seems to be a solid. "Cuboid" might be a more appropriate name. $\endgroup$ – Aretino Jan 19 '16 at 18:09
  • $\begingroup$ Just found this: I think maybe polyhedron might cover it (in general). A polyhedron with 6 faces is called a hexahedron. mathworld.wolfram.com/Hexahedron.html $\endgroup$ – Pixel Jan 19 '16 at 18:17
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    $\begingroup$ To my knowledge there's no standard name for such a shape, but if I understand the description your solid is a prism, over a right trapezoid if the top and bottom (or front and back) faces are parallel, over a nameless quadrilateral otherwise. "Quadrilateral prism" is probably self-descriptive, but an appropriate name depends on context and your intended usage. $\endgroup$ – Andrew D. Hwang Jan 19 '16 at 18:52
  • $\begingroup$ Thank you Andrew. I will have a think about your comment. $\endgroup$ – Pixel Jan 19 '16 at 19:19
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This is a right-quadrilateral-based right prism. Say prism for short.

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It is called Triclinic. It is one of the 7 crystal systems. Wiki

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    $\begingroup$ Not at all. This is not a parallelepiped and some angles are right. $\endgroup$ – Yves Daoust Mar 14 at 10:04

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