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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.

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+1 Outstanding question – JeffSahol Sep 7 '11 at 16:16
The term is inside-outness. You already have it. Also, chirality is a chemistry-specific term, so I think it is somewhat misleading to call it technical. – z7sg Ѫ Sep 7 '11 at 16:29
Oops - just realised OP wants a word to describe the existence of a distinction between "normal" and "everted". I can't cancel the vote to close, but I can say there are so few real-world referents it would stagger me if there's even a specialised scientific term for it. Bear in mind particle physicists co-opted colour and spin for similar contexts, where the original meanings are unrelated to the scientific ones. But those scientific differences are [probably] real, whereas OP's one probably isn't. – FumbleFingers Sep 7 '11 at 16:30
@z7sg Ѫ: If "inside-outness" were ever used, I'm sure most people would take it to mean "eversion". I can't imagine a context where it would mean "the distinction between whether a thing is normal or everted". Would you seriously say "Can you check the inside-outness of my freshly-laundered socks", for example? – FumbleFingers Sep 7 '11 at 16:37
@z7sg Ѫ: chirality is also used in math and physics with similar meaning. – Matthew Scouten Sep 7 '11 at 20:28

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".

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We're definitely on the same page here! I considered evertedness, but I just thought evertivity might have useful echos of parity. On the other hand, there are probably more people who would accept that evertedness is "already" a word, even though if it's ever used it's probably in relation to "degree of eversion" rather than to distinguish "inside-out" from "inside-in". – FumbleFingers Sep 7 '11 at 16:47
Orientability is not the right term. But "orientation" can possibly fit; whether it does depends a bit on what the OP had in mind for the application. – Willie Wong Sep 8 '11 at 17:30
To add to @Willie's comment, orientability is (very loosely speaking) the thing you need for the words "inside" and "outside" make sense. – Ross Churchley Sep 10 '11 at 4:37
+1 I was going to suggest "eversion"; I think this is a reasonable thing to put into your blank: "they differ only in their eversion". – Chinasaur Sep 13 '11 at 4:27

I don't think there's an existing word, but for potential neologisms I'd suggest either evertive orientation or evertivity.

Thanks to @Dan Brumleve for suggesting eversity, which I think is an even better coinage, in that it resonates nicely with parity and chirality

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evertivity is the best I have heard so far. googling pretty much leads back to this question :) – – Matthew Scouten Sep 7 '11 at 20:31
@Matthew Scouten: Now I think further on it, it seems to me that theoretical physicists ought to have a word for the concept. I know it's not exactly what we're talking about here, but the possibility of the universe being open/closed/flat/etc., or even being entirely contained inside a black hole within a different universe, could prompt them to create/find/use a word relevant to us here. – FumbleFingers Sep 7 '11 at 21:08
I am pretty sure I have seen such a word before, but I can not remember it. – Matthew Scouten Sep 8 '11 at 16:15
Came here from math.SE to coin "eversity". – Dan Brumleve Sep 9 '11 at 23:26
@Dan Brumleve: Way ahead of you, man! It's interesting to note that in the math.se page where I asked you guys for help, and in the one about turning shirts inside out that was flagged up to me there, the word eversion was actually used several times. But over here my two variants thereof have thus far collected the grand total of no votes whatsoever. But I'll tack your eversity in my answer if you don't mind - it resonates better with parity, which I think is a plus point. – FumbleFingers Sep 9 '11 at 23:40

The word "containment" may suit your needs.

Example usages

  • The containment of the point is outside the box.
  • The containment of this side of the fence is inside.
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