The authors generalize the regular homotopy theory of finite graphs [the reviewer, Conf. Semin. Mat. Univ. Bari 153 (1978; Zbl 0418.55011)] to finite simplicial complexes and prove that the classical homotopy groups \(\pi_ n(P)\) of a polyhedron P are isomorphic to the regular groups \(Q_ n(K)\) of any triangulation K of P. In this way minimal triangulations of a polyhedron (i.e. the ones with the least number of vertices), which are sometimes not useful in the case of regular graph homotopy, can always be considered.