R'lyeh

R'lyeh is a fictional sunken city in the Pacific which is featured in H.P. Lovecraft's short story "The Call of Cthulhu". Trapped within the city is the entity known as Cthulhu.

In Toaru Majutsu no Index, the city can be brought into existence through certain spells based off the Cthulhu Mythos.

Principles
The underwater city of R'lyeh, in which Cthulhu is imprisoned, is said to be sunk at a certain point in the Pacific. The city's architecture is said to be of non-Euclidean geometry.

According to the story, when certain conditions are met, the city would rise to the surface from the bottom of the ocean. When R'lyeh surfaced, it was said that the weak-minded would go insane while poets and artists would receive strange inspiration. These conditions include the positions of the stars and submarine volcanic activity.

As with other spells based on the Cthulhu Mythos, spells involving the city are classed as creating something from nothing - calling into existence something which shouldn't exist.

Necessarius Special Admission Test SS
After obtaining the Necronomicon, Arlands Darkstreet of Dusk Waiting to Awaken took it to an ocean salvage terminal in the Strait of Dover, in order to perform a ceremony to summon R'lyeh and obtain the inspiration his cabal needed. Though the terminal was far from the location where R'lyeh was sunk, Arlands and his men were able to recreate the conditions of the sunken city on it, using lighting and observational equipment to simulate the non-Euclidean geometry of the city and exploding fire ships to simulate the earthquakes heralding the surfacing.

As a result, when the ceremony was carried out, the terminal became the equivalent of R'lyeh itself, with Cthulhu partially appearing before the Amakusa managed to make the evil god leave by interfering with the artificially created conditions which created the twisted landscape synonymous with the sunken city.