How should I call a $n$-th dimensional generalization of a parallelogram? and a $n$-th dimensional (convex) "quadrilateral"?

Question

I have two $n$-dimensional bodies, each given by the interior of $2n$ hyperplanes (of dimension $n-1$), such that

(i) In the first, there are $n$ pairs of parallel hyperplanes (if $n=2$, this is a parallelepiped, or parallelogram)

(ii) In the second, this is not true, but still the interior is convex (if $n=2$, this is a convex quadrilateral).

How should I call these guys?

I am writing an article related to cryptography, an article reference would be much appreciated.