We present a detailed investigation of the Large Magellanic Cloud (LMC) disk using classical Cepheids. Our analysis is based on optical (I,V; OGLE-IV), near-infrared (NIR: J,H,Ks) and mid-infrared (MIR: w1; WISE) mean magnitudes. By adopting new templates to estimate the NIR mean magnitudes from single-epoch measurements, we build the currently most accurate, largest and homogeneous multi-band dataset of LMC Cepheids. We determine Cepheid individual distances using optical and NIR Period-Wesenheit relations (PWRs), to measure the geometry of the LMC disk and its viewing angles. Cepheid distances based on optical PWRs are precise at 3%, but accurate to 7, while the ones based on NIR PWRs are more accurate (to 3%), but less precise (2%-15%), given the higher photometric error on the observed magnitudes. We found an inclination i=25.05 $pm$ 0.02 (stat.) $pm$ 0.55 (syst.) deg, and a position angle of the lines of nodes P.A.=150.76 $pm$ 0.02(stat.) $pm$ 0.07(syst.) deg. These values agree well with estimates based either on young (Red Supergiants) or on intermediate-age (Asymptotic Giant Branch, Red Clump) stellar tracers, but they significantly differ from evaluations based on old (RR Lyrae) stellar tracers. This indicates that young/intermediate and old stellar populations have different spatial distributions. Finally, by using the reddening-law fitting approach, we provide a reddening map of the LMC disk which is ten times more accurate and two times larger than similar maps in the literature. We also found an LMC true distance modulus of $mu_{0,LMC}=18.48 pm 0.10$ (stat. and syst.) mag, in excellent agreement with the currently most accurate measurement (Pietrzynski et al. 2013).
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