Name for “3D quadrilateral” shape?

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 ?

• I would not call "quadrilateral" what seems to be a solid. "Cuboid" might be a more appropriate name. – Aretino Jan 19 '16 at 18:09
• 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 – Pixel Jan 19 '16 at 18:17
• 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. – Andrew D. Hwang Jan 19 '16 at 18:52
• Thank you Andrew. I will have a think about your comment. – Pixel Jan 19 '16 at 19:19