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Spoilers 4x05 "The Examples" Preview Photos

They weren't even up to a quarter of the Orion Spur/Arm by Picard's day. Maybe that much had been charted, but physically explored?

Of course, between the Bajor-Idran Wormhole and Voyager's misadventures, that "quarter of the galaxy charted" boast would likely have become fact.
 
The Federation spread across 8,000 light-years as of 2373 and though likely bigger by later centuries I don't think would ever have occupied a full one-quarter of the entire galaxy.
But is that:
8,000 ly across one axis of a 2D chart?
8,000 ly² on the 2D chart?
8,000 ly³ on the 3D chart?

Because that could make quite the difference as to how big the UFP is at that time along with it's borders & shapes.
 
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