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. From any of the hexagons one can see, interminably, the upper and lower floors. The distribution of the galleries is invariable. Twenty shelves, five long shelves per side, cover all the sides except two; their height, which is the distance from floor to ceiling, scarcely exceeds that of a normal bookcase. One of the free sides leads to a narrow hallway which opens onto another gallery, identical to the first and to all the rest. To the left and right of the hallway there are two very small closets. In the first, one may sleep standing up; in the other, satisfy one's fecal necessities. Also through here passes a spiral stairway, which sinks abysmally and soars upwards to remote distances. In the hallway there is a mirror which faithfully duplicates all appearances. Men usually infer from this mirror that the Library is not infinite (if it were, why this illusory duplication?); I prefer to dream that its polished surfaces represent and promise the infinite ... Light is provided by some spherical fruit which bear the name of lamps. There are two, transversally placed, in each hexagon. The light they emit is insufficient, incessant.

I was disappointed to find that my go-to resource for such things, The Dictionary of Imaginary Places, had no illustration to go along with its entry.

One edition of the book had as its cover one of the illustrations of the library by Érik Desmazières, which are gorgeous, but have a wanton disregard for nearly every particular in the text, so we can pretty much just ignore this one:

So there's Alex Warren's take, which is nicely symmetrical:

However, I think there are several major misreadings here.

1. The text pretty clearly states that there is only one door from each hexagon to the hallway. To connect the hexagons as shown here requires two or more doors per room.

2. There is one bookcase on each of 4 walls. Not multiple bookcases, and not on 5 walls.

3. Each shelf of each bookcase contains 35 books of 410 pages. Even assuming rather thick paper, each of those books would be less than 2" thick, yielding a bookcase less than 6' wide. So the rooms are probably a lot smaller than shown.

4. The sleep chamber, lavatory and hallway aren't shown.

This image by Andrew DeGraff has an interesting positioning of the stairs, but makes the same mistakes about the number of doors, and omits the hallways.

Thomas Basbøll thinks that since there can only be one door, the library must consist of pairs of hexagonal rooms, which implies that the library must be a tower, immensely tall but not very wide:

But if Borges had meant a tower, I think he would have said a tower, and probably would have used the word "floor" more often instead of words like "region" and "circuit", and wouldn't have said, "If an eternal traveler were to cross it in any direction..."

I think WillH's comment here has the right idea: if the un-described sixth wall is not a wall at all, and sets of six rooms are arranged into pods, it all works out. "Air shafts between" could be interpreted as "between rooms" rather than "between shelves".

That does leave weirdly-shaped unreachable voids between the pods. But at one point he speaks of "in a hexagon on circuit fifteen ninety-four", and the word "circuit" fits well with this circular arrangement.

Kate and Andrew Bernheimer came up with this one, which has the "circuit of hexagons" idea, but links them all into a circle around a void, and again seems to omit the hallways.

Various other illustrations of it that I've seen seemed to assume that the sleep chamber and lavatory open off of the hallway, but "To the left and right of the hallway there are two very small closets" sounds to me like those closets are on the same wall as the entrance to the hallway, that is, they open into the hexagonal room. So that gives us a minimum length of each wall of about 10' (assuming pre-ADA, sub-OSHA standards of construction). That means the bookcases can't possibly fill the whole wall unless there is a lot of empty space on them, or the books themselves are each like 40" thick.

Where does the spiral staircase go? Again, a lot of illustrators stuck it off of the hallway, but it doesn't read that way to me. It sounds to me like there is a spiral stairway within each of the hexagonal book rooms. It might wrap around the air shaft, but I think that's a tortured interpretation.

Well, I fired up Sketchup and took a crack at my own version of it. Fun fact: Sketchup does very poorly with a vast number of objects, even if those objects are wrapped up in "components", most of which are invisible. The file is 400KB but the thing is using almost 2GB of RAM and hypnowheeling constantly for 90+ seconds at a time. Hooray.

I haven't added the stairwells, and I kind of think the "corridors" need to be longer to earn that word. Also those enormous and oddly-shaped voids between "circuits" of rooms bother me. So I don't think this is quite right either.

Wikipedia says that there are 25^1,312,000 or 1.956 × 10^1,834,097 possible books. That's a lot of books.

with 700 books per room, and the rooms laid out with approximately the same number of rooms on all three axes, I think that means it is roughly 10^611,364 rooms wide and floors tall before you reach the end?

I can't help but think about the weight and pressure of a column of air that high, and what is it sitting on, and how to route the plumbing from all of those toilets, and that toilets imply digestion, so where does the food come from? Is there a section of the library devoted to farming, and metallurgy? But now I'm overthinking a sub-infinite but nearly boundless hill of beans.

Update: Hey folks, the comments on this post have been fantastic. If you've been reading this blog for a while, you know that that is, uh, often not the case. So thank you all for playing along. Anyway, I've done some more Sketchup layouts which you can see in the followup post: