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The Neimark-Sacker-pitchfork bifurcation can only occurs in the symmetric dynamic systems.A three-degree-of-freedom vibro-impact system with symmetry is considered.Due to the symmetry, the Poincaré map P is the second iteration of another virtual implicit map Q.The Neimark-Saker-pitchfork bifurcation of the symmetric fixed point of the Poincaré map P corresponds to the Neimark-Saker-flip bifurcation of the map Q.