Star Trek: Every* Starbase Ranked Worst To Best

The Federation Headquarters in the 32nd Century is probably the most unusual starbase on this list as, technically, it isn't a starbase. The USS Federation is a Pax-class starship, retrofitted to serve as the primary location for Starfleet's command structure, and the Federation's civilian government. 

The ship was designed by Ryan Dening for Star Trek: Discovery's third season, with additional elements later added by Lee Fitzgerald. It closesly resembled a spire with struts extending from it, though it also housed support decks that could be converted into lifeboats - such as the time when the DMA threatened Earth, Titan, and Ni'Var. 

After United Earth seceded from the Federation, the ship relocated from Earth's orbit into deep space, which is where is was found by the USS Discovery. Though United Earth formally reentered the Federation after the incident with 10-C, the ship remained in deep space, rather than taking position in orbit again. It has, however, abandoned the dispersal field that had shielded it for some time, preferring now to operate in the open.