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The Greek Goddess of the rainbow was Iris.Iris, she is also the messenger god, along with Hermes, although she did not take his place, and he did not ever take hers.
Alcmene was not a goddess. She was a mortal that was the mother of Hercules. Though she was a mortal, she was very wise for a mortal...for more information go to http://en.wikipedia.org/wiki/Alcmene...
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