Deep equivariant models use symmetries to improve sample efficiency and generalization. However, the assumption of perfect symmetry in many of these models can sometimes be restrictive, especially when the data does not perfectly align with such symmetries. Thus, we introduce relaxed octahedral group convolution for modeling 3D physical systems in this paper. This flexible convolution technique provably allows the model to both maintain the highest level of equivariance that is consistent with data and discover the subtle symmetry-breaking factors in the physical systems. Empirical results validate that our approach can not only provide insights into the symmetry-breaking factors in phase transitions but also achieves superior performance in fluid super-resolution tasks.