Escape from Atlantis by Strathford Hamilton

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In order to try to bring together his bickering family, a single father takes his three rebellious teenagers on a vacation trip to the Bahamas. They inadvertently wind up in the Bermuda Triangle, where they are whisked through a time portal and brought to the mythical island of Atlantis. There they are drawn into a fantastical conflict between the peace-loving population and a would-be tyrant determined to take over the island. In their desperate attempts to return home they encounter mythical creatures, evil magicians, and ancient powers.