Is there a technical term for insideout-ness?

Solution 1:

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".

Solution 2:

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

Solution 3:

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.

Solution 4:

Based on the example provided in the initial question, it sounds like when both objects are in disparate states of eversion they are not enantiomorphs even though they may share a chiral form otherwise (e.g., a pair of gloves with one inside-out). Depending on the characteristics of those objects, when they are in the same state of eversion they may or may not be enantiomorphs as they may or may not be chiral (e.g., a pair of gloves versus a pair of tube socks). If one says that two objects differ only in their states of eversion, is that intended to signify that everting the non-everted one would result in a pair of enantiomorphs or that it would result in an achiral pair--or is the intention to refrain from such specification? I feel like that is where a lack of clarity in the initial question may have yet to be addressed.