If I would pick a word in my language I would simply call the shape of the necklace multi-interpretabel = multi interpretable in English. As I like to keep things simple.

Anyway, even if after long debates on the object a word of common agreement would be found, we would never be sure that we would actually see that object all alike.

The most elementary things, we can never be sure we see things alike.

One more thing:
Quote:
What word describes the quality of being open to many different interpretations.

The question also could be interpreted differently . What is meant? The quality of the object as being open to many different interpretations or the minds of the observing people as being open to many different interpretations?