So I was looking at cid and realized you could connect an ike and gad by just the vertices to create a similar shape, with pseudofaces which were diga. I decided to fill them in with actual diga which resulted in a true polytope, albeit degenerate.
This led me to discover a class of polytopes. For example, you can have a 2 cubes connected by the vertices, creating pseudodiga which could be filled in with actual diga. A name for this class would be appreciated.