We present and discuss accurate and densely mapped BVRI lightcurves of the neon Nova Mon 2012, supplemented by the evolution in Stromgren b and y bands and in the integrated flux of relevant emission lines. Our monitoring started with the optical discovery of the nova and extend to day +270, well past the end of the super-soft phase in X-rays. The nova displayed very smoothly evolving lightcurves. A bifurcation between y and V light-curves took place at the start of the SSS phase, and a knee developed toward the end of the SSS phase. The apparent magnitude of the nova at the unobserved optical maximum is constrained to +2.8=<V=<4.2. The appearance, grow in amplitude and then demise of a 0.29585 (+/-0.00002) days orbital modulation of the optical brightness was followed along the nova evolution. The observed modulation has a near-sinusoidal shape and a weak secondary minimum at phase 0.5. We favor an interpretation in terms of super-imposed ellipsoidal distortion of the Roche lobe filling companion and irradiation of its side facing the WD. Similar lightcurves are typical of symbiotic stars where a Roche lobe filling giant is irradiated by a very hot WD. Given the high orbital inclination, mutual occultation between the donor star and the accretion disk could contribute to the observed modulation. The optical+infrared spectral energy distribution of Nova Mon 2012 during the quiescence preceeding the outburst is nicely fitted by a early K-type main-sequence star (~K3V) at 1.5 kpc distance, reddened by E(B-V)=0.38, with a WD companion and an accretion disk contributing to the observed blue excess and moderate Halpha emission. A typical early K-type main-sequence star with a mass of ~0.75 Msun and a radius of ~0.8 Rsun, would fill its Roche lobe for a P=0.29585 day orbital period and a more massive WD companion.
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