2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152594The tetrahedron equation arises as a generalization of the famous Yang--Baxter equation to the 2+1-dimensional quantum field theory and the 3-dimensional statistical mechanics. Very little is still known about its solutions. Here a systematic method is described that does produce non-trivial solutions to the tetrahedron equation with spin-like variables on the links. The essence of the method is the use of the so-called tetrahedral Zamolodchikov algebras.12 pages, to appear in ``Zapiski Nauchnyh Seminarov POMI'', S-Petersburg (English translation of a part of the author's Ph.D. Thesis, S-Petersburg, 1990)High Energy Physics - TheoryGeneral Relativity and Quantum CosmologyAlgebraic Geometrytext