In the Oz books, L. Frank Baum says that the Rainbow is the father of Polychrome and her sisters, the sky fairies.
When the Rain King spills water from his basin, the Rainbow scampers to the place to show the gorgeous colors of his glorious bow as soon as the mist of rain has passed and the sky is clear. He sets his bow down on the earth after each rain, and lifts it up again after a while, often leaving Polychrome behind. (The Road to Oz, Tik-Tok of Oz)
Background[]
Although Polychrome frequently references it as being her father, the Rainbow does not appear in the Oz Books as a character until Paul Dana's The Law of Oz and Other Stories.
In Magician of Oz (2009), by James C. Wallace II, the Rainbow, now known as the Great Rainbow, along with his daughter, Polychrome, greets Jamie Diggs, great grandson of O.Z. Diggs, upon his arrival in Oz and transports him to the Red Brick Palace of Glinda, the Good Witch of the South.
In Shadow Demon of Oz (2010), by James C. Wallace II, the Great Rainbow, along with Polychrome, escorts Cap'n Bill, Jamie Diggs, and his best friend Buddy in the balloon of O.Z. Diggs to the Emerald City following their crossing of the Shifting Sands.