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Theorem 1. If a connected polyhedron K (of arbitrary dimension) is homeomorphic to a Cartesian product A1 × . . .×An, where Ai’s are prime compacta of dimension at most 1, then there is no other topologically different system of prime compacta Y1, . . . , Yk of dimension at most 2 such that Y1 × . . .× Yk is homeomorphic to K. A space X is said to be prime if it has more than one point and only X and the singleton as Cartesian factors. In Theorem 1 the dimension of Yi cannot be greater than 2 (see the examples in [3]–[5]). The 3-dimensional factor of a 6-dimensional torus (in [5]) is not a polyhedron, but the 4-dimensional factors of I (in [3] and [4]) are polyhedra non-homeomorphic to a cube. I do not know if Theorem 1 is true when we assume that the sets Yi are polyhedra of dimension at most 3. The decomposition of a polyhedron into a Cartesian product of 1and 2-dimensional factors is not unique. See the examples in [7]. In [7] we have proved that the decomposition of a compact 3-dimensional polyhedron into a Cartesian product is unique if no factor is an arc. In this paper we present a generalization of that theorem. We prove the following

On decomposition of polyhedra into a Cartesian product of 1-dimensional and 2-dimensional factors