Pasiphaë married Minos and bore him many children. She succumbed, however, to her passion for a bull, and thanks to the ingenuity of Daedalus, who made her a hollow wooden cow, satisfied her desire and subsequently gave birth to the Minotaur. She herself was the daughter of Helios and Perse.
Her name means 'all-shining', from pas, 'all' and phaeno, 'to shine'. 'She who shines for all' is a fine name, whether actually or propitiously, and it ties in well with the name of her father and her mother (perhaps) and her daughter Phaedra. See also Phoenix.