I started by building a 3D virtual model of the library. No modelling software or computer could deal with infinite hexagons so I have been selectively editing these images to make them appear infinite. The first view is a section cut looking down the infinite voids within each hexagon.
The second image shows the vast expanse of hexagons all connecting to each other - this is the basic geometry, I have included no detail at this stage:
I then built the hexagonal libraries 2-dimensionally to diagram the spaces in each gallery:
The first diagram shows, in orange, the infinite circulation through the library.
The diagram above shows the infinite load bearing walls (in grey) between each hexagon.
The blue below illustrates the placement of the bookcases, but it unintentionally also manages to show clearly the routes between the rooms, showing how they are straight routes between the spiral staircases.
The image above shows the voids, the 'ventilation' shafts where librarians ultimately jump into after reading so many books of pure gibberish.
The next image shows the floor plan made up of shapes other than hexagons. This three sided, forked shape appears all over the floorplan, but our eyes usually adjust to the hexagon shapes rather than the shapes in between.
This last diagram shows the infinite spiral staircases in every 6th room, connecting each level. The lines between show the geometry of triangles between these vertical circulation spaces. I imagine librarians walking up or down these stairs trying to find an end to their universe, which of course they never will on an infinite staircase.
This is neat. I really like the graphics. Though the story suggests that each hexagonal gallery is identical to every other "...which in turn opens onto another gallery, identical to the first - identical in fact to all" which does two things. It suggests the floor plan is more difficult to conceive of but in doing so makes it a more challenging puzzle. So if the galleries are the same, they should have the same number of doors and the same orientation of entryways.
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