Exotic Hadrons and Underlying Z2,3 Symmetries

The recent observation of higher quark combinations, tetraquarks and pentaquarks, is a strong indication of more exotic hadrons. Using Z₂ and Z₃ symmetries and standard model data, a general quark combination producing new hadronic states is proposed in terms of polygon geometries according to the Dynkin diagrams of  _n affine Lie algebras. It has been shown that Z_2,3 invariance is crucial in the determination of the mesonic or the baryonic nature of these states. The hexagonal geometry is considered in some details producing both mesonic and baryonic states. A general class of this family is also presented.