Due to its proximity, SN 1987A offers a unique opportunity to directly observe the geometry of a stellar explosion as it unfolds. Here we present spectral and imaging observations of SN 1987A obtained ~10,000 days after the explosion with HST/STIS and VLT/SINFONI at optical and near-infrared wavelengths. These observations allow us to produce the most detailed 3D map of H-alpha to date, the first 3D maps for [Ca II] lambda lambda 7292, 7324, [O I] lambda lambda 6300, 6364 and Mg II lambda lambda 9218, 9244, as well as new maps for [Si I]+[Fe II] 1.644 mu m and He I 2.058 mu m. A comparison with previous observations shows that the [Si I]+[Fe II] flux and morphology have not changed significantly during the past ten years, providing evidence that it is powered by 44Ti. The time-evolution of H-alpha shows that it is predominantly powered by X-rays from the ring, in agreement with previous findings. All lines that have sufficient signal show a similar large-scale 3D structure, with a north-south asymmetry that resembles a broken dipole. This structure correlates with early observations of asymmetries, showing that there is a global asymmetry that extends from the inner core to the outer envelope. On smaller scales, the two brightest lines, H-alpha and [Si I]+[Fe II] 1.644 mu m, show substructures at the level of ~ 200 - 1000 km/s and clear differences in their 3D geometries. We discuss these results in the context of explosion models and the properties of dust in the ejecta.
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