The VMC Survey -- XLVIII. Classical Cepheids unveil the 3D geometry of
  the LMC
  We employed the {\it VISTA near-infrared $YJK_\mathrm{s}$ survey of the
Magellanic System} (VMC), to analyse the $Y,\,J,\,K_\mathrm{s}$ light curves of
$\delta$ Cepheid stars (DCEPs) in the Large Magellanic Cloud (LMC). Our sample
consists of 4408 objects accounting for 97 per cent of the combined list of
OGLE\,IV and {\it Gaia}\,DR2 DCEPs. We determined a variety of
period-luminosity ($PL$) and period-Wesenheit $PW$ relationships for
Fundamental (F) and First Overtone (1O) pulsators. We discovered for the first
time a break in these relationships for 1O DCEPs at $P$=0.58 d. We derived
relative individual distances for DCEPs in the LMC with a precision of $\sim$1
kpc, calculating the position angle of the line of nodes and inclination of the
galaxy: $\theta$=145.6$\pm$1.0 deg and $i$=25.7$\pm$0.4 deg. The bar and the
disc are seen under different viewing angles. We calculated the ages of the
pulsators, finding two main episodes of DCEP formation lasting $\sim$40 Myr
which happened 93 and 159 Myr ago. Likely as a result of its past interactions
with the SMC, the LMC shows a non-planar distribution, with considerable
structuring: the bar is divided into two distinct portions, the eastern and the
western displaced by more than 1 kpc from each other. Similar behaviour is
shown by the spiral arms. The LMC disc appears "flared" and thick, with a disc
scale height of $h\sim 0.97$ kpc. This feature can be explained by strong tidal
interactions with the Milky Way and/or the Small Magellanic Cloud or past
merging events with now disrupted LMC satellites.
