The script of "The Corbomite Maneuver" made it clear that Balok's pilot vessel was a section of the Fesarius which detached from that mother ship.
The set for the interior of this craft was built on Desilu Stage 9. (Information from "The Corbomite Maneuver" call sheets) Clint Howard – who, in his childhood, played Balok – approved of the set. He remarked, "A great thing about the set is it was built to my size... and everybody else had to hunch down, which I thought was pretty cool." ("Inside the Roddenberry Vault, Part I", Star Trek: The Original Series - The Roddenberry Vault special features)