Immersive scientific data exploration faces challenges in precise and efficient interaction. Tangible media offer a potential solution; but designers lack clear guidance on choosing the appropriate physical dimensionality (1D, 2D, or 3D) for different tasks. To address this problem, we present a design space structuring the relationship between the representative techniques on scientific data visualization and exploration, tangible interactions, and media dimensionality. We further developed a prototype to empirically explore these relationships according to our design space. In a controlled user study, we compared 1D, 2D, and 3D tangible media across seven core techniques. The results demonstrated that the 3D media (e.g., a box) were preferred when tasks required manipulating the entire volumetric data and acted as a proxy. Regarding the tasks requiring 2D operations or interior localization, the 2D media (e.g., a card) offered superior performance. For single-parameter techniques like histogram-based filtering, the 1D media (e.g., a pen) were overwhelmingly preferred for their simplicity and perceived ease of use.