Rogelim
Rogelim is a town in Gilead, named only as the home of Barzillai the Gileadite. It appears at two points in the Absalom narrative — once when Barzillai joins the others bringing supplies to David at Mahanaim, and once when he descends from it to escort the returning king across the Jordan.
The Home of Barzillai
When David arrives at Mahanaim in flight from Absalom, three men provision his camp: "And it came to pass, when David came to Mahanaim, that Shobi the son of Nahash of Rabbah of the sons of Ammon, and Machir the son of Ammiel of Lodebar, and Barzillai the Gileadite of Rogelim, brought beds, and basins, and earthen vessels, and wheat, and barley, and meal, and parched [grain], and beans, and lentils, and parched [pulse], and honey, and butter, and sheep, and cheese of the herd, for David, and for the people who were with him, to eat: for they said, The people are hungry, and weary, and thirsty, in the wilderness" (2 Sam 17:27-29). Rogelim is identified here only by the man it produced — Barzillai the Gileadite, the third of the three providers.
After Absalom's defeat, when David returns toward the Jordan, Rogelim reappears as the place from which Barzillai descends to honor the king: "And Barzillai the Gileadite came down from Rogelim; and he went over the Jordan with the king, to conduct him over the Jordan. Now Barzillai was a very aged man, even 80 years old: and he had provided the king with sustenance while he lay at Mahanaim; for he was a very great man" (2 Sam 19:31-32). The town is the geographical hinge for Barzillai's movements in both directions — out to relieve David in his exile, and down again to send him on his way home.