We present a multiphase, resolved study of the galactic wind extending from the nearby starburst galaxy NGC 4666. For this we use VLT/MUSE observations from the GECKOS program and HI data from the WALLABY survey. We identify both ionised and HI gas in a biconical structure extending to at least 8 kpc from the galaxy disk, with increasing velocity offsets above the midplane in both phases, consistent with a multiphase wind. The measured electron density, using [SII], differs significantly from standard expectations of galactic winds. We find electron density declines from the galaxy centre to kpc, then rises again, remaining high ( cm) out to 5 kpc. We find that HI dominates the mass loading. The total HI mass outflow rate (above kpc) is between , accounting for uncertainties from disk-blurring and group interactions. The total ionised mass outflow rate (traced by H) is between and , depending on assumptions. From ALMA/ACA observations, we place an upper-limit on CO flux in the outflow which correlates to . We also show that the entire outflow is not limited to the bicone, but a secondary starburst at the edge generates a more widespread outflow, which should be included in simulations. The cool gas in NGC 4666 wind has insufficient velocity to escape the halo of a galaxy of its mass, especially because most of the mass is present in the slower atomic phase. This strong biconical wind contributes to gas cycling around the galaxy.

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