This picture is quit old although it is possible that I haven't posted it yet:I hope everyone sees what these variants have in common.
Lately I made some more:Their names (or signatures) are: (starting right going clockwise)
A5E8A00145E94
C8200041297
A528A00145C03
21E0200101E10
A5E8200141E13
E8000140003
200001087
28A00145E97
21C8A00045E97
There are 17 variants are missing to make this series complete but I am not sure if they are worth the effort.

They look like the transitions from cube to rhombic dodecahedron (truncated version?)

I've seen the circled one before in the Puzzle Museum here on this site a long time ago. I've tried to find it again, but it seems to have disappeared.

At least one member tried an answer and got it right...

The one you marked is the enclosed cube:
viewtopic.php?f=9&t=3506
which was somewhat reinvented here:
viewtopic.php?f=9&t=8047

The true hero would enumerate the 17 missing variants.
Does anybody want to try?