  Magnetic properties and underlying magnetic models of the synthetic
A$_2$Cu$_3$O(SO$_4)_3$ fedotovite (A = K) and puninite (A = Na) minerals, as
well as the mixed euchlorine-type NaKCu$_3$O(SO$_4)_3$ are reported. We show
that all these compounds contain magnetic Cu$_6$ hexamer units, which at
temperatures below about 100 K act as single spin-1 entities. Weak interactions
between these magnetic molecules lead to long-range order below $T_N$ = 3.4 K
(A = Na), 4.7 K (A = NaK), and about 3.0 K (A = K). The formation of the
magnetic order is elucidated by ab initio calculations that reveal
two-dimensional inter-hexamer interactions within crystallographic $bc$ planes.
This model indicates the presence of a weakly distorted square lattice of $S=1$
magnetic ions and challenges the earlier description of the
A$_2$Cu$_3$O(SO$_4)_3$ minerals in terms of Haldane spin chains.
