The crystal structures of [Cu(hat)(H2O)(ox)]·H2O (I), [Cu(hat)(H2O)3(sq)]·3H2O (II) and [Cu(hat)(H2O)2](ClO4)2·4H2O (III) have been determined from X-ray single crystal diffraction data (hat=1,4,5,8,9,12-hexaazatriphenylene, ox=oxalate, sq=squarate=dianion of 3,4-dihydroxy-cyclobut-3-ene-1,2-dione). Compound I crystallises in the triclinic system, space group P1̄ with a=6.6626(10), b=9.2001(14), c=12.9954(19)Å,α=103.301(15), β=91.414(21), γ=105.523(13)°, Z=2; compound II in the orthorhombic system, space group P212121 with a=6.9274(2), b=8.4327(3), c=34.0577(14)Å,Z=4; and compound III in the monoclinic system, space group C2/c with a=22.6652(10), b=9.2220(10), c=16.1400(10)Å,β=106.783(10)°, Z=8. In I chelating hat and oxalate ligands and a coordinated water molecule make up a square pyramidal coordination sphere. The mono-nuclear units so described are, however, connected into dinuclear entities through a weak axial interaction between copper and an oxalate oxygen of a neighbouring molecule. In II copper has a distorted, elongated octahedral coordination geometry, being surrounded by a chelating hat, a mono-dentate squarate and three water molecules. The copper atom in III is bound to two mono-chelating hat units and two water molecules, it is situated on a two-fold axis and features an inverted Jahn–Teller geometry with two short and four intermediate distances at room temperature. X-band ESR spectra of I and II at room temperature exhibit the pattern g∥>g⊥>2.0 corresponding to the dx2−y2 orbital ground state of copper(II) ion in elongated octahedral geometry in these complexes. In the case of complex III the room temperature spectrum exhibits the reverse pattern (g⊥>g∥>2.0); variable temperature X- and Q-band measurements reveal that the inverted spectrum is gradually converted to a normal axial spectrum as the temperature is lowered, signalling that the apparent compressed geometry at room temperature is caused by a 2D dynamic Jahn–Teller effect. Variable-temperature magnetic susceptibility measurements of I reveal the occurrence of a weak antiferromagnetic coupling (J=−1.0(1)cm−1 with the Hamiltonian defined as Ĥ=−JŜA·ŜB) between the copper ions.