The Manx Cat -- sometimes known as Manks, Stubbin, or "rumpy" (no, really) -- is a domestic cat breed that originated on the Isle of Man.
They carry a natural mutation that usually results in no tail, or at most a stub of a tail (hence, the nicknames). They also have longish rear legs and a roundish head. The Manx has been known since the early 19th century.
Here are some pictures of the beasties.
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