  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.
