The celebrated MacKay correspondence says that there is a one to one correspondence between regular polyhedral groups and Dynkin diagrams of types A, D, and E. In this talk, we extend the correspondence to a wider class of objects: the regular polyhedral group is replaced by a regular system of weights (defined as a quadruple of positive integers (a,b,c;h) satisfying some simple arithmetic conditions), while the Dynkin diagram is replaced by the generalized root system associated to a triangulated category of matrix factorizations. Regular systems of weights are classified according to their smallest exponent e:=a+b+c-h. Weight systems with e=1 are classified by their type: A_l, D_l, E_6, E_7 or E_8, and the associated category is shown to be equivalent to the category of representations of the classical Dynkin quiver. For e=0, the weight systems are classified into three elliptic types E~_6, E~_7 and E~_8 corresponding to the three elliptic root systems of types E_6^{(1,1)}, E_7^{(1,1)} and E_8^{(1,1)}. For e=-1, the weight systems are classified into 14+8 (+9) types, and the associated category is shown to be equivalent to the category of representations of a certain wild quiver, which defines an infinite root system corresponding to a lattice of signature (l,2). (This is joint work with H.Kajiura and A. Takahashi)