An interesting little system you've put together ;)

I don't think it can safely be described in terms of objects
orbiting a common center of mass: since all components are roughly
same size and same distance it is an n-body problem for n = 4.

Even ignoring that, it would be a precarious unstable balance
at best. It cannot have formed naturally, although an advanced
(and bored?) civilization might engineer and maintain it.

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