Today we are taking the 2-dimensional floor plans of the Library of Babel to the third dimension. The simplest way is to use a single floor plan and copy it for every level of the library. For instance, last time’s finite hexagon becomes a daunting infinite tower, at least in our imagination.

One could also do the same with several separate hexagons, but the resulting library would consist of several buildings, which, while not explicitly prohibited by Borges, seems unacceptable.

But there is another possibility. For instance, using the arrangement of hexagons in horizontal lines, and repeating them vertically (as on the left above), but then, on the second floor, using the same floor plan albeit rotated by 90º (as in the middle), and then repeating this periodically, we arrive at a single building where it is sometimes necessary to climb up, walk across, and then down again to reach a *different* room on the *same* floor.

Nearby places can sometimes be terribly far away.

In the double floor plan up above on the right we see that this can be done by aligning the vestibules in a square pattern, leaving star-shaped Voids. Below is a partial view of this magnificent library:

The condition that the staircases in the vestibules extend infinitely in both directions is quite limiting, even if one doesn’t require that each staircase can be reached at every floor. A good strategy for designing even more complicated libraries is to begin with a floor plan that includes hexagons and squares, and use on each floor a different subset of these squares and hexagons as vestibules and galleries. For instance, we can start with this Archimedean tiling that has large dodecagonal Voids:

One individual floor then could look like this, seemingly giving each gallery three exits to vestibules with staircases, one of which, however, will be blocked off by a bookshelf on two of its sides:

This floor plan will be rotated by 120º on each subsequent floor (about the center of one of the dodecagonal Voids), creating a single labyrinthian library.

Here is a deliciously maddening view into the resulting skeleton of this library. I haven’t closed off the inaccessible staircases yet, so please watch your step.

Happy are those of us who can get lost in a single book like in this Borgesian library.