Since no one else ever answered this, might as well give it a shot, though note that I am not as well read on this topic as I could be.

Now, without further ado, here is a map of the Four Parts.

Notice anything? A particular pattern for how these provinces are distributed, perhaps?

The Qusqoans (and most Andean peoples) conceptualized geography as something deeply religious and tied to the spiritual world. Space was not understood as something that absolutely existed in a single fixed place relative to all other spaces, but as a sacred array of locations connected and shaped by their social history.

Because of this, the cities of the Andes are almost all heavily planned and marked by expressions of hierarchy directly onto the urban geography. And when the Qusqoans expanded outwards, building a single empire to unite the entire “civilized” world, they naturally extended this behavior to their administrative regions.

Administrative regions, which are, of course, far more concerned with religious significance relative to the Inka capital than any ethnic distinctions. Of note here are that firstly, the Andeans conceptualized their primary cultural identity as ayllus, a sort of communal gift economy and social network, not ethnicities. And secondly, ethnicities and ayllus were often moved around between provinces by central authorities as mitimaes, explicitly to ensure the loyalty of conquered regions and assimilate Inka subjects.

But this doesn’t mean that the lines drawn were coldly precise like colonial African borders, even though the Inka state had the mathematics to implement such a system, at least about as well as any premodern state had the ability to. As I said previously, space and geography were highly ritualized concepts deeply shaped in the Andean ontology by the actions of those who had lived there and their ties to other locations.

As such, if you zoomed in beyond the macro level seen in the image at the beginning of this comment, you’d notice that on the regional level, the borders really are not as rigid as they appear, and the clean lines of the larger map become very messy. This really reflects a fundamental truth of the way the Empire of Four Quarters saw the world: on the on the scale of all the world, there was only one center, and it was Qusqo. But at a smaller level? The people and stories of a region shaped geography just as much as any distant, imperial capital.

Sources

Father Bernabe Cobo, History of the Inca Empire

Terrence D’Altroy, The Incas