The insectoid ship was a derelict ship discovered by the USS Enterprise during a 2269 star charting mission. Once operated by ancient insectoids, it was not a recorded galactic starship design. (TAS: "Beyond the Farthest Star")
Three hundred million years ago, the ship found itself drawn to a dead star with large hypergravity. At the star, a malevolent magnetic organism took over the ship. Rather then carrying the lifeform to other worlds, the crew decided to destroy their ship. By unknown means, they succeeded in bursting open all pods of their ship from the inside.
One room in the ship remained intact and protected from the lifeform. Therein the insectoids left a message of warning for those who might encounter their ship.
In 2269, similarly drawn in by the star, the Enterprise encountered the ship. By this time, the ship was a dead hulk. Its temperature was absolute zero and there was no energy store to send radio messages.
However, a slight magnetic flux indicated that the magnetic organism was still present.
When an away team beamed over to the ship, they discovered the history of the ship, but also brought back the organism to the Enterprise. In the early stages of taking over the Enterprise's computers, it activated the phaser banks and vaporized the insectoid ship. (TAS: "Beyond the Farthest Star")
The ship was very large. Its design was described as touched by grace and beauty by Lieutenant Uhura, while doctor McCoy noted it was like nothing he had ever seen. It consisted of a number of interconnected pods. The hexagonal shape of the windows suggested a similarity to honeycombs of Earth's bees, their individual cells shaped exactly like on the ship.
It was constructed of an unknown metal alloy, harder and lighter than any registered metal. Instead of being cast or rolled, the metal appeared to be drawn into filaments and spun like a spider spun its web.
The interior of the pods contained energy accumulating wands that collected energy from motion, sound, light, heat, and magnetism. Within non-breached sections of the ship, artificial gravity was provided which was within two points of Earth normal. The air was similarly close to Earth's. (TAS: "Beyond the Farthest Star")
"For 'Beyond the Farthest Star', Roddenberry wanted a previously unseen design for the derelict spaceship," Kline remembered. "After literally 100 tries, he accepted the 'melons on vines' design you see in the episode. All of the other designs were eventually used in an episode [called "The Time Trap"] that featured a graveyard of lost spacecraft." (Gene Roddenberry's Star Trek: The Original Cast Adventures, p. 156)