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Having strayed off course while flying over the South Pacific, American radio commentator Mark Bradley and his photographer and co-pilot Joe Walker prepare to make an emergency landing on an uncharted island, but are startled by a voice broadcast over a loudspeaker, warning them to stay away. When their engines fail, Mark and Joe are forced to land and are met by a man who introduces himself as Dr. Paul and asks how quickly they can repair their aircraft and leave. Despite Paul's accusation that the strangers are an intrusion, Paul's daughters, Venus, Mercuria and sixteen-year-old Urana, are anxious to speak to them, the first young men they have ever seen. After Joe concludes that it will take several days to repair the plane, the protective Paul suggests that Mark and Joe camp alone on the beach but allows them to join his family for meals at their shelter, a fully modernized cave powered by a solar furnace. Paul has educated his girls with the help of a large library and a short wave radio on which they have heard Mark's broadcasts. Paul, an atomic scientist, explains to Mark that he fled civilization with his wife, who has since died, and three small children after the atomic bombing of Hiroshima, certain of the civilized world's imminent demise. Meanwhile, Joe is helping Urana, when he discovers that the lumber used to build a chicken coop is labeled "Paul Lujan, California Institute." Later, Mark talks with Venus about her desire to experience the world and fall in love. On the beach that night after Joe tells him about his discovery, Mark recognizes the name Lujan as a leading authority on atomic power who disappeared over fifteen years ago after atomic bombs devastated Hiroshima. The next day, Mark, anxious to break the story to the outside world, addresses Paul by his full name and announces his plans to run a story about him as soon as he returns. Paul is desperate to protect his privacy and, when Mark insists on running the story, blows up the plane with his flame-throwing revolver, leaving Mark and Joe with little hope of returning to their families. Mark and Joe appeal to the sisters to steal tools from their father to enable them to build a raft, but the girls refuse. Later that day, the girls suggest to their father that he offer a truce and invite Mark and Joe to dinner. While Joe helps the girls cook, Paul shows Mark his process for creating a special isotope from uranium in his laboratory reactor. As Paul continues with his tour, Mark opens the laboratory door, allowing the girls to hear their father warn Mark that he is willing to kill anyone who threatens to expose his work. Unnerved by father's violence, Venus and Mercuria steal tools for Joe and Mark and show them a cove where they can work without Paul's knowledge. During their surreptitious meetings, Mercuria falls in love with Joe and Venus with Mark. One night, naive Urana kisses Mark and explains that she knows all about "love at first sight," having read about it in books, but Mark assures her that there is more to love than what she reads. The next morning, Joe longs openly to stay with Mercuria, but Mark warns him that the raft cannot sustain additional passengers, despite his own love for the "unspoiled and trusting" Venus. Later, Mark spots a shark in the waters where Venus is swimming and bravely attacks and kills the predator. Swooning from the life-threatening incident and Mark's embrace, Venus begs to leave with him. A jealous Urana, having heard Venus' plea, brings her father to the cove, exposing Mark and Joe's escape plans. After Mercuria and Venus vow to stand by the men, Paul returns to the cave with Urana, who questions her father's insistence that the world is doomed to annihilate itself, and tries to hide his gun so that he cannot harm Mark or Joe. Paul, however, finds the gun and, after abducting Joe, forces him to announce over the loudspeaker that he will be set free only if Mercuria and Venus return to the cave. After Paul locks Joe in a storage room, Urana grabs the gun, and in the struggle, the weapon discharges, igniting an explosion that sets the laboratory and dwelling on fire. When Paul attempts to open the storage door to free Joe from the smoke-filled room, he is knocked unconscious by a falling shelf. Alerted by Urana's screams, Mark, Venus and Mercuria rush to the cave where Mark frees Joe while the girls help their father to safety. As the group takes cover behind some boulders at the water's edge, an atomic explosion rocks the island, destroying all life and forming a huge mushroom cloud high above them. Detecting the explosion on their radar, the Royal Australian Atomic Energy Commission contacts the American Air Force to investigate. With his island destroyed, Paul is forced to admit the irony of having escaped the world's atomic madness only to annihilate his own "Garden of Eden." Soon after, as the group spots the Air Force plane and they realize they will soon be rescued, Venus announces, "Here comes your world," but Mark embraces her, and assures her that it is "our world."