  We explicitly solved the anomaly-free quantum constraints proposed by Tomlin
and Varadarajan for the weak Euclidean model of canonical loop quantum gravity,
in a large subspace of the model's kinematic Hilbert space which is the space
of the charge network states. In doing so, we first identified the subspace on
which each of the constraints acts convergingly, and then by explicitly
evaluating such actions we found the complete set of the solutions in the
identified subspace. We showed that the space of solutions consists of two
classes of states, with the first class having a property that involves the
condition known from the Minkowski theorem on polyhedra, and the second class
satisfying a weaker form of the spatial diffeomorphism invariance.
