  We report on magnetic properties of cubic compound Cu3TeO6 studied by $ac$
and $dc$ susceptibility and neutron powder diffraction for the first time. A
novel magnetic lattice, three dimensional spin web, composed of almost planar
regular hexagons of Cu2+, S =1/2 spins, defines the properties of Cu3TeO6. The
behavior of the magnetic susceptibility in the paramagnetic state at
approximately 170 K is suggestive for a competition between local anisotropies
of Cu2+ hexagons. The resulting frustration is weaker than the
antiferromagnetic nearest-neighbor interaction which leads to a collinear (or
slightly canted) spin arrangement (k=0,0,0) and formation of magnetic domains
below TN=61 K.
