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This study proposes a new method for designing adaptive routing algorithms for three-dimensional (3D) networks-on-chip (NoCs). This method is based on extending the existing 2D turn model adaptive routing to a 3D scenario. A 3D plane-balanced approach with maximal degree of adaptiveness is achieved by applying a well-defined set of rules for different strata of the 3D NoC. The proposed method is applicable to any of the turn models. In this study, the authors employ odd-even turn model as a basis for introducing the proposed strategy. Experimental results show that the new 3D odd-even turn model can achieve up to 28.5% improvement in performance over conventional 3D odd-even approach. The improvement is consistent for different traffic types and selection strategies. The proposed method enables a new avenue to explore adaptive approaches for future large-scale 3D integration.