Exact loop-variables formulation of pure gauge lattice QCD(3) is deriv
ed from the Wilson version of the model. The observation is made that
the resulting model is two-dimensional. This significant feature is sh
own to be a unique property of the gauge field. The model is defined o
n the infinite genus surface which covers regularly the original three
-dimensional lattice. Similar transformation applied to the principal
chiral field model in two and three dimensions for comparison with QCD
. (C) 1997 Elsevier Science B.V.