2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153855This paper adds two observations to the work solv-int/9701016 where some eigenstates for a model based on tetrahedron equation have been constructed. The first observation is that there exists a more "algebraic" construction of one-particle states, resembling the 1+1-dimensional algebraic Bethe ansatz. The second observation is that the strings introduced in solv-int/9701016 are symmetries of a transfer matrix, rather than just eigenstates.LaTeX, 8 pagesExactly Solvable and Integrable Systemstext