If we are talking about 280 BC and earlier, there were some prisons;
1) mines and stone mines (don't know english word) - famous were stone mines around Syracusae (they were probably inspiration for Platon)
2) I'm not absolutely sure but I think there were dungeons too.
Systems of prisons was much more developed into ancient Rome, Hadrian's "Reskrypt" gives us some interesting informations about at least 2 kinds of punishment called mines. Mines were kinds of prisons too.
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