Akropoleis

But the harmost and the Spartan garrison still retained their hold on their Akropoleis, or citadels, as a guarantee that Spartan interests should suffer no serious injury.

Source: wiktionary

The sacred fire, emblem of common, patrilineal ancestry, was kept perpetually burning on the akropoleis of a thousand cities, focusing (“focus” was the Roman word for this flame) the loyalty of a still tribal people.

Source: wiktionary

So the use of the word polis to designate an akropolis was probably restricted to akropoleis that were centres of human habitation. On the other hand, the akropoleis which were called poleis did not have to be the centres of a polis in the political sense of the term, as were e.g. the akropoleis of Athens or Korinth.

Source: wiktionary

Most of the new towns developed on hilltops using the materials from ancient akropoleis.

Source: wiktionary