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Superfluid³He is a paradigm for odd-parity Cooper pairing, ranging from neutron stars to uranium-based superconducting compounds. Recently it has been shown that³He, imbibed in anisotropic silica aerogel with either positive or negative strain, preferentially selects either the chiral A-phase or the time-reversal-symmetric B-phase. This control over basic order parameter symmetry provides a useful model for understanding imperfect unconventional superconductors. For both phases, the orbital quantization axis is fixed by the direction of strain. Unexpectedly, at a specific temperatureT_x, the orbital axis flops by 90^∘, but in reverse order for A and B-phases. Aided by diffusion limited cluster aggregation simulations of anisotropic aerogel and small angle X-ray measurements, we are able to classify these aerogels as either “planar and “nematic concluding that the orbital-flop is caused by competition between short and long range structures in these aerogels.