A family of Cu(II)-based metal–organic frameworks (MOFs) has been synthesized using three pyridyl-isophthalate ligands, H
2
L
1
(4′-(pyridin-4-yl)biphenyl-3,5-dicarboxylic acid), H
2
L
2
(4′′-(pyridin-4-yl)-1,1′:4′,1′′-terphenyl-3,5-dicarboxylic acid) and H
2
L
3
(5-[4-(pyridin-4-yl)naphthalen-1-yl]benzene-1,3-dicarboxylic acid). Although in each case the pyridyl-isophthalate ligands adopt the same pseudo-octahedral [Cu
2
(O
2
CR)
4
N
2
] paddlewheel coordination modes, the resulting frameworks are structurally diverse, particularly in the case of the complex of Cu(II) with H
2
L
3
, which leads to three distinct supramolecular isomers, each derived from Kagomé and square nets. In contrast to [Cu(L
2
)] and the isomers of [Cu(L
3
)], [Cu(L
1
)] exhibits permanent porosity. Thus, the gas adsorption properties of [Cu(L
1
)] were investigated with N
2
, CO
2
and H
2
, and the material exhibits an isosteric heat of adsorption competitive with leading MOF sorbents for CO
2
. [Cu(L
1
)] displays high H
2
adsorption, with the density in the pores approaching that of liquid H
2
.
This article is part of the themed issue ‘Coordination polymers and metal–organic frameworks: materials by design’.