  We present a strong lensing analysis of the cluster PSZ1 G311.65-18.48, based
on Hubble Space Telescope imaging, archival VLT/MUSE spectroscopy, and Chandra
X-ray data. This cool-core cluster (z=0.443) lenses the brightest lensed galaxy
known, dubbed the "Sunburst Arc" (z=2.3703), a Lyman continuum (LyC) emitting
galaxy multiply-imaged 12 times. We identify in this field 14 additional
strongly-lensed galaxies to constrain a strong lens model, and report secure
spectroscopic redshifts of four. We measure a projected cluster core mass of
M(<250 kpc)=2.93+0.01/-0.02x10^14M_sun. The two least-magnified but complete
images of the Sunburst Arc's source galaxy are magnified by ~13x, while the LyC
clump is magnified by ~4-80x. We present time delay predictions and conclusive
evidence that a discrepant clump in the Sunburst Arc, previously claimed to be
a transient, is not variable, thus strengthening the hypothesis that it results
from an exceptionally high magnification. A source plane reconstruction and
analysis of the Sunburst Arc finds its physical size to be 1x2 kpc, and that it
is resolved in three distinct directions in the source plane, 0, 40, and 75
degrees (east of North). We place an upper limit of r <~ 50 pc on the source
plane size of unresolved clumps, and r<~ 32 pc for the LyC clump. Finally, we
report that the Sunburst Arc is likely in a system of two or more galaxies
separated by <~6 kpc in projection. Their interaction may drive star formation
and could play a role in the mechanism responsible for the leaking LyC
radiation.
