Perseus analyses of κορυφῇ:

κορύπτω (butt with the head): aor subj pass 3rd sg
κορυφή (head, top): fem dat sg (attic epic ionic)

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κορύπτω

κορύπτω, fut. -ψω Orac. ap. Luc. JTr. 31:—

A. butt with the head, Theoc. 3.5, perh. to be read in Lucil.1241 Marx; etym. of Κορύβαντες, Str. 10.3.21; butt at, τινα Tz.ad Lyc. 558:—Med., v. κορύσσω ad fin.

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κορῠφή

κορυφή, ἡ, (κόρυς)

A. head, top: hence,

1. crown, top of the head, of a horse, Il. 8.83, X. Eq. 1.11; of a man or god, h.Ap. 309, Pi. O. 7.36, Hdt. 4.187, Sammelb. 6003.8 (iv A. D.): between βρέγμα and ἰνίον, Arist. HA 491a34; τὸ ὀστέον τῆς κ. Hp. VC 2.

3. generally, summit, top, κατὰ κορυφὴν ἐσβαλεῖν ἐς τὴν κάτω Μακεδονίαν straight over the summit, ridge, Th. 2.99, cf. IG 42(1).71.11 (Epid., iv B. C.), OGI 383.125 (Nemrud Dagh, i B. C.); κατὰ κ. [τῆς στήλης] ἔσφαττον (sc. ταύρους) Pl. Criti. 119e; ἵσταται κατὰ κ. ὁ ἥλιος in the zenith, Plu. 2.938a; τὸ κατὰ κ., with or without σημεῖον, the zenith, Gem. 5.64, etc., cf. Plu. Mar. 11, Procl. Hyp. 4.59; ταῖς τῶν κατὰ κ. λίθων ἐμβολαῖς by the stones falling vertically, Plb. 8.7.3.

4. apex, vertex of a triangle, Id. 2.14.8; of the Delta, Pl. Ti. 21e; point of an angle, τὸ ἐπὶ τὴν κ. μέρος Plb. 1.26.16, etc.; apex of a cone, Arist. Mete. 362b3; κατὰ κορυφήν vertically opposite, of angles, Euc. 1.15; of halves of double cone, Apollon. Perg.1 Def.

2. height, excellence of . . , i.e. the choicest, best, κορυφαὶ πολίων Pi. N. 1.15; κ. ἀρετᾶν ib.34, cf. O. 1.13; κ. ἀέθλων, of the Olympic games, Id. O. 2.13, cf. N. 9.9; φιάλαν . . πάγχρυσον κ. κτεάνων Id. O. 7.4; ὁ καιρὸς παντὸς ἔχει κορυφάν is the best of all, Id. P. 9.79.

3. κορυφᾷ Διὸς εἰ κρανθῇ πρᾶγμα his head, i.e. his nod, A. Supp. 92.

4. ἡ τῆς οἰκουμένης κ., of Rome, Lib. Or. 59.19.