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Abstract In this article, we continue the study of a certain family of 2-Calabi–Yau tilted algebras, called dimer tree algebras. The terminology comes from the fact that these algebras can also be realized as quotients of dimer algebras on a disk. They are defined by a quiver with potential whose dual graph is a tree, and they are generally of wild representation type. Given such an algebra $$B$$, we construct a polygon $$\mathcal {S}$$ with a checkerboard pattern in its interior, which defines a category $$\text {Diag}(\mathcal {S})$$. The indecomposable objects of $$\text {Diag}(\mathcal {S})$$ are the 2-diagonals in $$\mathcal {S}$$, and its morphisms are certain pivoting moves between the 2-diagonals. We prove that the category $$\text {Diag}(\mathcal {S})$$ is equivalent to the stable syzygy category of the algebra $$B$$. This result was conjectured by the authors in an earlier paper, where it was proved in the special case where every chordless cycle is of length three. As a consequence, we conclude that the number of indecomposable syzygies is finite, and moreover the syzygy category is equivalent to the 2-cluster category of type $$\mathbb {A}$$. In addition, we obtain an explicit description of the projective resolutions, which are periodic. Finally, the number of vertices of the polygon $$\mathcal {S}$$ is a derived invariant and a singular invariant for dimer tree algebras, which can be easily computed form the quiver.