Sol. It can easily be seen that the circuit diagram proposed in the problem is a "regular" tetrahedron

Whose edges contain six identical capacitors. Therefore, we conclude from the symmetry considerations that irrespective of the pair of points between which the current source is connected, there always exists an uncharged capacitor in the circuit (the capacitor in the edge crossed with the edge containing the source). For example, if the current source is connected between points A and B in Fig., the capacitor between points C and D will be uncharged since the potentials of points C and D are equal.