this is wrong by definition. I'm not even going to ask how you got 12, but the perimeter cities will only cover half, and since perimeter cities are the most numerous, the empire will be a bunch of junk cities used to power the core, which is nice i guess, but while you were busy building settlers, someone else has been building military instead. I don't think people realize that an ICS approach has just the same weaknesses as non-overlapping cities -- it is weak in the beginning. And i'm not even going to ask as well where did all that space for all these cities came from, unless it's a huge map vs AI, which, considering the AI isn't expanding beyond ~6 cities anyway, is quite redundant to play.
I saw a graphic about it (on Reddit iirc) that showed one factory touching 12 city centers. I only took a passing glance at it though, so it may be possible that it was flawed. Anyway, the denser the pattern, the more cities you'll be hitting, so since production is so important in the game as it stands, it makes sense to try and maximize it. Hence, the optimal distance from the pov of production alone is 3 tiles. Obviously you cannot hit the max amount in a real game, due to mountains, coasts, fresh water considerations, etc. But it is the *ideal* to strive for, and the closer you get, the better.
As for military, in the beginning your cities will be small enough that production isn't really affected by their close distance, as every city will still have enough tiles to work without significant overlap. Later on (yet before factories) this effect is noticeable, but should be compensated by the sheer number of cities, provided you start building the troops early enough. It is possible to screw this up and be steamrolled, but with the bad AI, it is mostly a threat in multiplayer or on Deity vs Gilgamesh (etc).
There is usually plenty of space to expand to, unless playing on an island map, a crowded map (with extra AIs) or having an unlucky spawn with close neighbors. In the latter case, might as well start early with racking up the denouncements (I view them as a badge of honor these days
), and make them relinquish their inappropriate aspirations to greatness.
I will concede that one 'super city' with a good amount of tiles is useful to have, for military emergencies, building wonders and especially spaceship projects, which are prohibitively expensive for your main 'hive' of small-to-medium sized cities. A desert city that built the Petra is ideal for this purpose, if you can get it ofc.