The narwhal or unicorn whale Monodon monoceros is certainly one of the world's strangest whales - a veritable sea monster. It earns its alternative name from its single extremely long, spiralled, ivory tusk (in reality a greatly enlarged left upper incisor tooth), which was once believed to be the horn of the unicorn, and was known as an alicorn. Usually, only the male produces a tusk, but occasionally a female will also do so. Moreover, as I mentioned in the unicorn chapter of Dr Shuker's Casebook: In Pursuit of Marvels and Mysteries (CFZ Press: Bideford, 2008), even more rarely a narwhal will develop a pair of these tusks. Such individuals are variously termed double-tusked, bidental, or bidentate, and although they are extremely rare, I have details of several examples on file.
For example: in a Proceedings of the Zoological Society of London paper from 1871, J.W. Clark lists no fewer than eleven double-tusked skulls from exceptionally-endowed narwhals. These comprise four specimens in Copenhagen, and one each at the Museums of Hamburg (a female, apparently from Greenland), Christiania (now Oslo), Amsterdam, Weimar, Hull (specifically, the Museum of Fisheries and Shipping), Paris, and Cambridge. Others on record include a second Hull specimen (reported in 1937), a specimen at the U.S. National Museum, one at the Dundee Museum, and at least three at London's Natural History Museum (one of which is currently on public display there).
The first of the London three was purchased by the museum in 1885 (and revealed that the spiral in both tusks twisted in the same direction, in contrast to the paired horns of spiralled-horned antelopes such as the kudu in which the horns' spirals twist in opposite directions); the second was purchased in 1917 for 10 guineas; and the third was presented to the museum in 1934 by a nephew of naturalist Frank Buckland, who in turn had received it from a Captain Gray of Peterhead.