Tetraplyoctomy is the art or skill of splitting a hair four ways. Don’t be a mere two-way hair-splitter; grasp your pedantry firmly in both hands and split your hair crosswise into four.
This word has found a secure if niche existence in the lexicons of academics with a sense of humour since it was invented by Umberto Eco in his novel Foucault’s Pendulum, published in English in 1989. In a mocking attempt to reform higher education, one character proposes a School of Comparative Irrelevance, whose aim would be to turn out scholars capable of endlessly increasing the number of unnecessary topics. In it would be a Department of Tetrapyloctomy, whose function would be to inculcate a sense of irrelevance in its students. Another department would study useless techniques, such as Assyrio-Babylonian philately and Aztec Equitation.
The word combines tetra, four, with pilus, hair (as in depilatory), and the ending -tomy, a cutting. As the component parts come respectively from Greek, Latin and Greek it’s a miscegenated linguistic sandwich that no self-respecting scholar would invent, which is no doubt why Umberto Eco found it to be appropriate.