Re: Divisions, Insignia, Uniforms and Assignment Patches
With BK613's find, we're up to 4 variations of the delta patches
4. Rectangle with open right side
With these known parameters:
1. variations only exist on the delta patch,
2. not everyone wears the delta patch - some use a different design that doesn't have room for same variations
3. the delta patch is seen mixed in on other ships that might have different patches
4. character x can switch back and forth between delta patch variations
Then I guess that it is just
a Starfleet patch. The variation is purely cosmetic.
Or it might be a shift patch. It could indicate which of the three shifts the character is currently assigned to. But that wouldn't account for the other patches that don't have room for variations.
Don't forget Nurse Chapel (as already mentioned above)