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Note how the house was built into the Stepped-Stone Structure. On the left, notice the staircase that leads up to the upper levels of the house, including the roof.
The name, "House of Ahiel," is based upon an inscribed potsherd (ostracon) that was found in it. Because of elite objects found nearby, it is suggested that this was an "upscale" district of Jerusalem!
For a very helpful summary article describing this area, please see Cahill, Jane M. “Jerusalem in David and Solomon's Time.” Biblical Archaeology Review 30 (2004): 20–31, 62–63.