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The island is named "Ship Trap Island" in the story because the island's owner fashioned a trap in the ocean to lure his victims (or "opponents") to the island.
Connell uses a lot of imagery (mostly in the use of similes) to describe his setting and how lush and overgrown this jungle-like island is complete with quicksand, swampy areas, beaches, cliffs, and a mansion with only the finest creature comforts around.
The story takes place on a South American island. Rainsford arrives on the island after having fallen off a yacht in the Carribbean.