Troilism (sometimes spelled triolism) refers to sexual activity in which three persons take part simultaneously.
Origins
Troilism was coined in the 1941 edition of Dorland's Medical Dictionary where it was classified as a paraphilia. It was not clear why this scientific name was chosen.
One examination of the word may indicate a root in the French word trois (three). A similar French term, triolisme, exists in French—the shift between the third and fourth letter is perhaps a mistake. On the other hand, ménage à trois (household of three) was coined in the late 19th century. Although all those terms involve three people, ménage à trois implies a romantic link between all three, which is quite different from troilistic scenarios. In French, a plan à trois, vulgar form and synonym of triolisme, corresponds more closely to a troilistic scenario; a "threesome".
Another possible origin was noted in Take Our Word For It, a webzine published by the non-profit Institute for Etymological Research and Education. Here, it is theorized that troilism comes from Shakespeare's Troilus and Cressida. In it, Ulysses forces Troilus to watch his lover, Cressida, with another man. Troilus promptly dismisses his former love as a whore.