Can a oblique antiprism be constructed?
Intuitively, it would seem oblique antiprism exist: Take any right antiprism and translate one of the parallel faces within it's plane.
I'm baffled, though, because Google shows countless models and pictures of (right) antiprisms, but not a single oblique antiprism.
If not: Are all antiprisms right? What are examples of non-right antiprisms?
Update
I found two drawings of skewed antiprisms, which seems to be the same as what I called oblique antiprisms.
I've updated the OP with sketches, but am baffled why I can find almost no reference, discussion, or models (when far more complicated polyhedra models abound), and have still not found a proof or construction of their existence (beyond a convincing sketch).