Bistriazoles, 1,3-bis(1,2,4-triazol-4-yl)propane (tr(2)pr) and 1,3-bis(1,2,4-triazol-4-yl)adamantane (tr(2)ad), were examined in combination with the rigid tetratopic 1,3,5,7-adamantanetetracarboxylic acid (H(4)-adtc) platform for the construction of neutral heteroleptic copper(II) metal-organic frameworks. Two coordination polymers, [{Cu(4)(OH)(2)(H(2)O)(2)}{Cu(4)(OH)(2)}(tr(2)pr)(2)(H-adtc)(4)]·2H(2)O (1) and [Cu(4)(OH)(2)(tr(2)ad)(2)(H-adtc)(2)(H(2)O)(2)]·3H(2)O (2), were synthesized and structurally characterized. In complexes 1 and 2, the N(1),N(2)-1,2,4-triazolyl (tr) and μ(3)-OH(-) groups serve as complementary bridges between adjacent metal centers supporting the tetranuclear dihydroxo clusters. The structure of 1 represents a unique association of two different kinds of centrosymmetrical {Cu(4)(OH)(2)} units in a tight 3D framework, while in compound 2, another configuration type of acentric tetranuclear metal clusters is organized in a layered 3,6-hexagonal motif. In both cases, the {Cu(4)(OH)(2)} secondary building block and trideprotonated carboxylate H-adtc(3-) can be viewed as covalently bound six- and three-connected nodes that define the net topology. The tr ligands, showing μ(3)- or μ(4)-binding patterns, introduce additional integrating links between the neighboring {Cu(4)(OH)(2)} fragments. A variable-temperature magnetic susceptibility study of 2 demonstrates strong antiferromagnetic intracluster coupling (J(1) = -109 cm(-1) and J(2) = -21 cm(-1)), which combines for the bulk phase with a weak antiferromagnetic intercluster interaction (zj = -2.5 cm(-1)).