This Homeric epithet for cloth is unknown in meaning and etymology. This is the conclusion of all modern scholars (e.g. Chantraine, Dictionnaire étymologique p.750; Lexikon des frühgriechischen Epos 3.352-53). As Leaf (on Iliad 14.185) saw, it almost certainly refers to a fine weave of linen with a glistering sheen. It is probably then a loanword for the weave or origin of a particular linen, either from a language with triconsonantal stems or from a different Indo-European language, with similar roots but different phonological developments. For example, in Herodotus' day and later, Greece imported a fine linen from Colchis, called sardoniko/n, comparable to Egyptian, apparently through Sardis (Herodotus 2.105; see Rawlinson's commentary, pp. 172-73, with notes on fine Egyptian linen at 142-43, 64, 132-33, cf. 142-43; Strabo 498; Pollux 5.4.26).
It is used five times outside commentary and lexicography, twice in Homer’s Iliad and twice in Apollonius Rhodius, Argonautica. In the Homeric Hymn to Apollo the newborn god is wrapped in a cloak (fa=ros, so also at Apollonius Rhodius Argonautica 4.188) 'bright (white), delicate(ly woven), negatean' (121-22: web address 1). When Hera prepares to seduce Zeus (Iliad 14.166ff.: web address 2), she covers her head with a shawl (krh/demnon) 'beautiful, negatean, as bright as the sun' (184-85). Agamemnon, rising from his dream at Iliad 2.41 (web address 3), dresses for war (or, rather, retreat) meticulously and elegantly. He puts on first a 'soft chiton, beautiful, negatean' (42-43). In the simile for Jason’s appearance as he goes to visit Hypsipyle at Apollonius Rhodius Argonautica 1.775 (web address 4), it is used of the bowers or tents (kalu/bai) in which the Nymphs (or new brides) are crafting a star.
[1] These five purported synonyms of the accusative neuter form (used of a fa=ros in the Apollo Hymn and Apollonius Rhodius) come from Photius nu174 Theodoridis, but obscurity surrounds the last of them. Adler prints eu)fue/s and mentions no variants in the Suda mss; but in the view of Theodoridis the Suda compiler has adopted this suo Marte and he himself prints (for the unsatisfactory paradosis e)nufe/s) Porson's conjecture eu)ufe/s 'well-woven'; cf. under epsilon 3481.
[2] These two sentences are very similar to Eustathius, Commentary on the Iliad p.162.9-12, who reads, more plausibly, a)ge/nhton for mh\ gato/n and a)xeiro/teukton for a)xeiro/kmhton, and adds an impossible analogy to the passive verbal adjective tato/s 'stretched' from tei/nw 'stretch.' There is no possible passive for the verbs of becoming, gi/gnomai, gei/nomai. The idea that the word means 'magical, not crafted by human hands' is attractive, but is equally unacceptable in philology. Apollonius the Sophist, Homeric Lexicon 116.8, citing Apion, has the first of these two etymologies, but, in the place of the second, derives the word from the verb of spinning, ne/w (LSJ 'B'), without explanation. These three explanations are found in various ways repeated in the Homeric scholia on the two passages and at Anecdota Oxoniensia 1.292.15 and Etymologicum Magnum 602.43.
The possibility that the word may have a phonological history in an unknown Greek dialect or other IE language is supported by the modern Macedonian word a)nh/gatos 'new' (O. Hoffmann, Die Makedonen, ihre Sprache und ihr Volkstum, 1906, p.30). Hesychius (alone, alpha361-62) records a passive verb a)gata=sqai, a)ga/thmi, 'be harmed', probably non-Greek, that might account for the initial nh-, which normally precedes a vowel; 'undamaged' is a possible meaning (cf. Leaf on Iliad 2.43).