  In two recent papers (Phys. Rev. A90 (2014), 062121 and Phys. Rev. A91
(2015), 052110) an interesting method of analyzing the violation of Bell
inequalities has been proposed which is based on the theory of finite group
representations. We apply here this method to more complicated example of $S_4$
symmetry. We show how the Bell inequality can be related to the symmetries of
regular tetrahedron. By choosing the orbits of threedimensional representation
of $S_4$ determined by the geometry of tetrahedron we find that the Bell
inequality under consideration is violated in quantum theory. The corresponding
nonlocal game is analyzed.
