2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153860This paper continues the series begun with works solv-int/9701016 and solv-int/9702004. Here we show how to construct eigenstates for a model based on tetrahedron equation using the tetrahedral Zamolodchikov algebras. This yields, in particular, new eigenstates for the model on infinite lattice -- `perturbed', or `broken', strings.LaTeX, 7 pagesExactly Solvable and Integrable Systemstext