The wrapping of graphite planes into fullerenes induces, among other i
nteresting properties, an increase of the superconducting temperature
in their corresponding intercalation compounds that has been attribute
d to the cluster structure. This motivates the search for similar beha
viour in other systems. Here we explore the clusters that may be obtai
ned by the folding of CuO2 planes and study their magnetic and electro
nic properties. Natural murdochite mineral proves that, at least in an
interconnected structure, the CuO2 layers fold into cages, while the
BaCuO2 phase can be viewed as a first step towards their separation wi
thin a cationic matrix.