Where does the peripeteia (reversal) occur in the play Oedipus Rex?

Shaketeach is correct, but there is a specific moment that
can be pinpointed as the peripeteia.  The Messenger who comes to tell Oedipus that the
man he believed to be his father, Polybus, is dead and that he will be made king in
Corinth, also happens to be the man who brought the baby Oedipus to King Polybus and his
wife.

The scene that reveals Oedipus' true past goes on for
quite a few pages, drawing out the suspense as Oedipus learns that, according to the
Messenger, he need not be afraid of murder and incest in Corinth since Polybus was not
his natural father.

And yet the unravelling doesn't end
with this news.  Oedipus demands to have the old Herdsman who gave him away to the
Messenger brought forward.  He says:

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With such clues,

I
could not fail to bring my birth to light.
(1058-9)

After more
suspenseful questioning, it is finally revealed that the Herdsman got the child from
Jocasta and gave it to the Messenger.  Finally, Oedipus has his answer.  He says (lines
1181 - 1185):

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O, O, O, they will all
come,

all come out clearly!  Light of the sun, let
me

look upon you no more after
today!

I who first saw the light bred of a
match

accursed, and accursed in my
living

with them I lived with, cursed in my
killing.

This is the exact
moment of
reversal.