Kukulkan's ship
Kukulkan's ship was a highly advanced starship controlled by the winged serpent creature Kukulkan.

History 
Kulkulkan's ship was encountered by the  in 2270, while investigating the alien probe that had visited and scanned several Federation homeworlds. During the encounter, several members of the Enterprise crew were beamed aboard the vessel.

While on board the ship, the crew of the Enterprise were given the chance to solve the riddle of Kukulkan's city, which Humanity on Earth had failed to solve.

After an attack by the Enterprise,  Captain Kirk released a Capellan power-cat. Between the Enterprise and the cat enough damage was caused to the ship to cause Kukulkan to lose control of it. 

After Kirk explained that Humans were not like these other creatures and that they didn't need him, Kukulkan understood and allowed them to leave, with his ship returning in the direction from which it came.  ()

Technical information 

Extremely unorthodox in design, it had a hull composed of crystalline ceramic, and was surrounded by an immense energy field that could project the visage of Kukulkan. The energy field also made the ship impenetrable to Federation sensors.

In all, the ship was twice the size of a Federation  starship. 

Like the probe sent from this ship, it too, presumably, had a highly advanced propulsion system, capable of achieving at least warp 3.

It was also equipped with a powerful probe beam, and transporters that could penetrate deflector shields. Offensive capabilities of the ship included the ability to create a force globe to restrict the movement of its target, which could instantaneously bring a vessel travelling at warp 1 to a dead stop. All of which was controlled by Kukulkan via telepathy. ()

Interior design

Undefined area 
This area of the ship was where Kukulkan's city appeared.

Life room 
The life room contained Kukulkan's zoo, and the machinery to create virtual worlds in the minds of other cognizant beings.  ()

Unnamed starships
Starship classes