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Book 1 of the Iliad has the optative form κιχείη. Wikipedia says that ordinarily we expect to see the -η- infix in singular optative forms when the verb is athematic or a contract verb. Neither seems to apply here, so why does this happen here?

I guess the ν in -ανω is a PIE athematic present tense marker, so you could say that κιχάνω is in some sense athematic. But the wiktionary entries for this and other verbs in -ανω don't show endings with η. Is this a Homeric or dialectical thing?

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The dictionary entry for κιχάνω is enormous, so check it out for all its various forms. Simply put, the verb has athematic forms.

The relevant part is in Smyth §688:

The following ω-verbs have in poetry (especially in Homer) second aorists of the μι form: ... Epic κιχάνω (ἐκίχην, κιχήω, κιχείη, κιχῆναι and κιχήμεναι, κιχείς and κιχήμενος; properly from κίχημι)

From Beekes:

From a reduplicated root present *κίχημι (like τίθημι), found in κίχημεν, κιχήτην, etc. (ἐκίχεις after ἐτίθεις), which were taken as aorists when the new present κιχάνω arose.
...
The form κιχάνω arose at a recent date after the analogy of φθάνω to ἔφθην, φθήσομαι; the nasal infix in κιγχάνω was modelled on λαμβάνω, etc., on which see Schwyzer: 6885, 698, as well as Chantraine 1942: 300, 392, 415, 446.

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