  The crystal and magnetic structures of the spin $S$=1 hexamer cluster
fedotovite-like A$_{2}$Cu$_{3}$O(SO$_4$)$_3$ (A$_2$=K$_2$, NaK, Na$_2$) were
studied by neutron powder diffraction at temperatures 1.6-290 K. The crystal
structures in all compounds are well refined in the monoclinic space group
C2/c. The basic magnetic units of the compounds are copper hexamers which are
coupled by weak superexchange interactions giving rise to three-dimensional
long-range magnetic order below $3.0<T_N<4.7$ K. We have found that for
A$_2$=K$_2$ and NaK the propagation vector of the magnetic structure is
$\textbf{k}$=[0,0,0], and the coupling of the Cu hexamers is ferromagnetic FM
along the $ab$ diagonal and antiferromagnetic along the $bc$-diagonal. In
contrast, for A=Na the propagation vector is $\textbf{k}$=[0,1,0], and the Cu
hexamers are coupled antiferromagnetically AFM along the $ab$ diagonal. The
hexamers are formed by three Cu-pairs arranged along the $b$-axis. The
calculated spin expectation values $\left<{s}\right>$ for the simplest
symmetric spin Hamiltonian (obtained from inelastic neutron spectroscopy) of
the isolated hexamers in the mean field, amounted to $\left<{s}\right>$=3/8 for
side spins Cu1 and Cu2 and $\left<{s}\right>$=1/4 for Cu3 in the middle. The Cu
spins are FM coupled in pairs and AFM between neighboring pairs. The
experimental magnetic moments of the Cu$^{2+}$ ions turn out to be not
completely collinear due to spin frustrations within the weak interhexamer
interactions. The sizes of magnetic moments of Cu in the hexamers determined
from the diffraction data are in fair agreement with the calculated values.
