It's good to see I'm not the only one that wonders about this sort of thing! I obsessed about this same problem for about a week. ???
Do you know if that Confrontation stuff is available online anywhere? it's good to see I'm not the only one that wonders about this sort of thing! Everything I'm about to say could be contradicting the source material. I'd love to get a read of it but those White Dwarfs are probably older than me!
Looking at the Planetary Empires Hive City tile
http://goo.gl/sc5J2 it would seem that at least some people in GW feel the same about the multiple spires thing.
So tried to work out the actual space inside one the spires, or to be more precise, inside one of the domes, (I wanted to see if I could justify flyers) and I came to the same conclusion as yourself, namely that the illustration of the spire in the rulebook is waaaay smaller than the background suggests.
Before I dive into this, I have a data sheet with 3D models that I made that do a far better job of explaining what I'm about to say. PM me your email address and I'll send you a copy. It's too big to attach to this post.
My first problem was figuring out exactly how a structure like a spire could support itself. Your figure of 643 cubic miles, I assume, is just the external wall with empty space inside it, but a structure like that could never support itself. The highest we can build at the moment is half a mile (the Burj Khalifa), and a spire is supposed to be 10 miles high! It got me thinking that a hive city, like pretty much everything else in the Imperium, was originally built from super technologically advanced STC data, and
that structure now has had lots of extra stuff added on top of it over the millennia by the Imperium (things like the exterior wall), so much so that it doesn't really resemble the original structure at all anymore. This is the angle I started looking at 'domes' from. The way I see it is that all these domes rest on top of each other in a type of bee-hive-pyramid type thing, with all these connected supports maintaining the structural integrity of the hive, like a big molecular model. Now in the case of a bee-hive, hexagonal prisms work fine in two dimensions, but when you try and expand them into a cone or pyramid shape it falls apart. That got me looking at regular polyhedrons, and which ones would stack the best and provide the most structure, while still maintaining the concept of a 'dome'. I settled on icosahedrons (20-sided, like a D20) because (from what I could tell) they fit the most snugly together. I decided these were roughly a mile high (to make my maths easier) and that they would stack on top of each other in the shape of a regular tetrahedron (4-sided pyramid, like a D4). On top of this basic shape the Imperium would have been able to build all their extra bits and pieces, like the exterior wall, the top of the spire, things like that.
So I worked out that there'd be 120 of these icosahedrons in an STC pattern Hive City, and each of these would have a midradius of 0.5 miles, giving them a volume of 0.514 cubic miles each, for a total space of 61.68 cubic miles. Now my calculations don't take into account the top 5 miles of the spire (it becomes too thin at this point to continue the tetrahedron shape), or the space in between the individual domes, or the space between the outside domes and the exterior wall, which could double that figure again. This is certainly a lot smaller than your figure of 643 cubic miles and because we've no way of knowing how exactly a hive is built, the actual usable space inside a single spire could be any number between our two, or any other number for that matter.
I figured that the living conditions were probably pretty cramped in moat areas of the hive, certainly in the Hive City and the Underhive at least. For my domes, I decided that the top half (half a mile high) would have all the housing/factories/space ports or whatever else that particular dome was dedicated to, and this would be separated by a 'ground level' floor from the bottom half, which would contain all the sewers, power infrastructure, transport tunnels, ventilation etc. I based my population density on Kowloon Walled City, which was the most densely populated place on Earth while it still stood. I estimated that number to be 270,750 people per sq mile per floor. Conveniently the Burj Khalifa, as I said before, is half a mile high and has 209 floors. This makes 56,586,750 people per half dome (if it's all taken up by accommodation and services) x 120 = 6.7 billion inhabitants. When you take out space for factories and space ports and the like, and add in the space made available by the extra space I didn't account for, you're still looking at population figures in the 5+ billion per spire range.
I could go on but I realise this is a bit of an essay already. Like I said though, I can send you a PDF of some 3D models which explain what I'm talking about a lot better.
