  The recent observation of higher quark combinations, tetraquarks and
pentaquarks, is a strong indication of more exotic hadrons. Using Z_{2} and
Z_{3} 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 \widehat{A}_{n} affine Lie algebras. It has been shown that
Z_{\mathbf{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.
