The feast of the Epiphany actually celebrates several different epiphanies (theophanies), including the adoration of the Magi, the baptism of Jesus, and the miracle of the wine at Cana.
The readings at Matins are as follows:
Nocturn I: Isaiah 55:1-4; 60:1-6; 61:10-11; 62:1
Nocturn II: Sermon of Pope St Leo (on the Divinum Officium website, 1960 rubrics)
Nocturn III: Homily of Pope St Gregory (also available at Divinum Officium)
Gospel: Matthew 2:1-12