Rhene (Ancient Greek: Ῥήνη) in this atlas entry is the nymph paramour of Oileus and mother of his bastard son Medon, who marshals the Phthians in the Iliad when Philoctetes is away. Hyginus also names a nymph Rhene as mother of Ajax the Lesser, though Homer leaves the Locrian captain's mother unnamed. A distinct Cyllenian Rhene is mother of Saon of Samothrace by Hermes.
Adapted from Wikipedia, "Rhene (mythology)" · CC BY-SA 4.0
I.Mother of Medon
In the Catalogue of Ships Homer says that though the Argives beside their ships longed for Philoctetes, they were not leaderless: Medon marshalled them — the bastard son of godlike Oileus whom Rhene bore to the sacker of cities. Scholia and later compilers sometimes give Alcimache instead as Medon's mother; the atlas keeps Rhene as Homer's named parent.
Medon's Phthian command is temporary: he holds the contingent while Philoctetes is stranded on Lemnos, linking Rhene's motherhood to the larger Trojan muster.
II.Ajax the Lesser
Hyginus counts Ajax son of Oileus and the nymph Rhene among the captains at Troy with twenty Locrian ships. Elsewhere Ajax's mother is Eriopis, Oileus' legitimate wife. The atlas records both traditions without collapsing Rhene into Eriopis.
III.Homonyms
This entry (rhene-phthian) is Oileus' paramour and Medon's mother. Another Rhene — a nymph of Mount Cyllene — is lover of Hermes and mother of Saon (or Samon), first king of Samothrace in Dionysius of Halicarnassus and Diodorus; that Cyllenian figure is not this node.