So the technical term for right or left handedness is chirality.
The technical term for evenness or oddness is parity.
Is there a similar term for inside-out-ness vs right-side-out-ness?
EDIT:
I wish to speak of 2 objects. They have no interesting features except that each could be considered 'inside-out' relative to the other. Except there is no 'right' side. I suppose I could arbitrarily designate one side as Right and the other as In, but there are reasons to avoid doing so.
"Object 1 and object 2 differ only in their _."
I tried both chirality and parity but neither fit.
Best Answer
In topology, there is "Orientability", but I haven't studied it to know if it is the right term.
And there is the term "eversion", meaning "to turn inside-out", so the actual answer might be "evertedness", or just "everted".