What are the honeycomb-like details under a hamam dome?
They may be muqarnas: tiered architectural details used in transitions and decoration. You can notice them without needing to identify every element of the building.
Related questions
Did Mimar Sinan design hamams in Istanbul?
Yes. Sinan's work includes Istanbul bath architecture, including Zeyrek Çinili Hamam. Do not assume every domed hamam was designed by him.
Why do hamam domes have small openings?
Openings in the dome admit daylight into the bath. Their arrangement varies by building, so there is no single pattern shared by every historic hamam.
What do old tile fragments tell us about a hamam?
They can help explain its decoration and construction history. A surviving fragment is evidence; a complete modern display may also contain reconstruction.