Tusk of the narwhal (Monodon monoceros), or horn of the unicorn.

A typical example of the long spiral-shaped left tooth of the male narwhal: the right tooth of the male is normally relatively short, as are both teeth of the female. The spiral is left-handed or anti-clockwise from the animal's point of view. The spiral form of the unicorn's horn mentioned in Aelian's Natural history, book XVI, chapter 20 ("The horn is not smooth but has certain natural spirals [Greek "eligmous", helices] ... that horn is said to be very sharp") led to an association between the tusk of the narwhal and the unicorn's horn (alicorn). Various protective properties have been attributed to the alicorn, such as preserving virginity, acting as an antidote to poisons etc. (information from Ettinghausen and Beer, op. cit., and website of Narwhal tusk discoveries, 2006)