Open-3DSIM is an open-source reconstruction platform for three-dimensional structured illumination microscopy. We demonstrate its superior performance for artifact suppression and high-fidelity reconstruction relative to other algorithms on various specimens and over a range of signal-to-noise levels. Open-3DSIM also offers the capacity to extract dipole orientation, paving a new avenue for interpreting subcellular structures in six dimensions (xyzθλt). The platform is available as MATLAB code, a Fiji plugin and an Exe application to maximize user-friendliness.