Volume of a parallelogram = cross-section area times length
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There are many possible shapes. The most general, which has a specific name is a parallelopiped. A cube is a special case of a parallelopiped.
No. It is a parallelopiped. And, if it is a right rectangular prism then it is a cuboid.
A parallelopiped has six faces that are parallelogram - like a cuboid that has been distorted by pushing opposite vertices in opposite directions (the three dimensional equivalent of distorting a rectangle into a parallelogram). A solid with two rectangular faces would be a special case of a parallelopiped.
A parallelopiped, which is the 3-dimensional equivalent of a parallelogram.
An equilateral parallelopiped, each of whose face is a rhombus.