  The evidence of the existence of tetra-quark meson and penta-quark fermion
systems has revived interest in the hunt of other multi-quark systems. We
explore the possibility of six-quark cluster configurations with the two
nucleon spin-isospin quantum numbers existing in the nuclear medium. The
investigation of such clusters is feasible if one exploits all the symmetries
involved, in particular orbital, color-spin $SU(6)_{cs}$ and isospin SU(2). We
investigate whether such clusters contribute to neutrinoless double-beta decay
mediated by heavy neutrinos or other exotic particles, since in conventional
nuclear physics the relevant nuclear matrix elements are suppressed due to the
presence of the nuclear hard core.
