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In The Library of Babel by Jorge Luis Borges, the speaker describes the Library, as the universe, as

The universe (which others call the Library) is composed of an indefinite and perhaps infinite number of hexagonal galleries, with vast air shafts between, surrounded by very low railings.

This explains how the universe in which the story occurs is made up of hexagons. However, there is also a group of people who believe that the rooms may also be circular as we learn when the speaker says,

The idealists argue that the hexagonal rooms are a necessary from of absolute space or, at least, of our intuition of space. They reason that a triangular or pentagonal room is inconceivable. (The mystics claim that their ecstasy reveals to them a circular chamber containing a great circular book, whose spine is continuous and which follows the complete circle of the walls; but their testimony is suspect; their words, obscure. This cyclical book is God.)

Given that the organization of the library could most likely work with pentagonal rooms, given the vagouness of the specifications. This suggests to me that there is a non-mechanical reason for the choice of the hexagon. So, what is the significance/symbolism of the hexagon?

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Hexagons are a natural pattern found in various orderly structures in nature: for example, the cells of a beehive, or the columns of the Giant's Causeway. By making his Library a hexagonal tessellation, Borges could be attempting to evoke thoughts of the most perfect and ordered natural phenomena.

One geometric reason for the popularity of hexagons is that they tesselate perfectly. Regular hexagons can be used to tile the plane in a natural and periodic pattern, while regular pentagons, heptagons, and octagons can't. Squares can, but if you wanted to design a square room with two doors, that would leave only two walls for books. In order to have a perfectly regular planar tesselation (which is necessary for the natural order and perfection that the Library represents) with more walls of books than doors in each room, the hexagon is the best possible option.

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There may also be a deeper significance in the connection, via hexagonal cells, to bees and their hives and society, as discussed on this awesome website. Like the bees in their hive, the librarians in Babel have little individuality or will to exist outside of their society/home. The bees crawl from cell to cell making honey; the librarians wander from cell to cell examining books. Philosophers from Aristotle to Karl Marx have likened humans to bees in their socieities and activities. Perhaps the library is intended to be likened to a beehive: strictly structured, containing numerous largely similar inhabitants, but full of sweet words instead of sweet honey.

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