  Up to now, the existence of the the magnetic Neel Long Range Order (NLRO) in
nearest neighbor, spin-1/2 antiferromagnetic (AF) lattice systems has been
examined for seven, from the eleven existing, two-dimensional, uniform
lattices. Plaquettes forming these uniform (Archimedean) lattices (e.g. square,
triangular, kagome) are different regular polygons. An investigation of the
NLRO in the ground state of AF spin systems on the seventh uniform (bipartite)
lattice consisting of squares, hexagons and dodecagons is presented. The NLRO
is shown to occur in this system. A simple conjecture concerning the existence
of the NLRO in the ground state of antiferromagnetic, spin-1/2 systems on two
dimensional, Archimedean lattices, is formulated.
