We present the results of the first neutron powder and single crystal diffraction studies of the coupled spin tetrahedra systems ${CuTeX}$ (X=Cl, Br). Incommensurate antiferromagnetic order with the propagation vectors ${bf{k}_{Cl}}approx[0.150,0.422,half]$, ${bf{k}_{Br}}approx[0.158,0.354,half]$ sets in below $T_{N}$=18 K for X=Cl and 11 K for X=Br. No simple collinear antiferromagnetic or ferromagnetic arrangements of moments within Cu${}^{2+}$ tetrahedra fit these observations. Fitting the diffraction data to more complex but physically reasonable models with multiple helices leads to a moment of 0.67(1)$mu_B$/Cu${}^{2+}$ at 1.5 K for the Cl-compound. The reason for such a complex ground state may be geometrical frustration of the spins due to the intra- and inter-tetrahedral couplings having similar strengths. The magnetic moment in the Br- compound, calculated assuming it has the same magnetic structure as the Cl compound, is only 0.51(5)$mu_B$/Cu${}^{2+}$ at 1.5 K. In neither compound has any evidence for a structural transition accompanying the magnetic ordering been found.
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