2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153589The tetrahedron equation in a special substitution is reduced to a pair of pentagon and one ten-term equations. Various examples of solutions are found. $O$-doubles of Novikov, which generalize the Heisenberg double of a Hopf algebra, provide a particular algebraic solution to the problem.LaTeX, 10 pagesQuantum Algebratext