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Based on new observations and improved modeling techniques, we havereanalyzed seven Cepheids in the Large Magellanic Cloud. Improved physicalparameters have been determined for the exotic system OGLE LMC-CEP-1718composed of two first-overtone Cepheids and a completely new model was obtainedfor the OGLE LMC-CEP-1812 classical Cepheid. This is now the shortest periodCepheid for which the projection factor is measured. The typical accuracy ofour dynamical masses and radii determinations is 1%. The radii of the sixclassical Cepheids follow period--radius relations in the literature. Our veryaccurate physical parameter measurements allow us to calculate a purelyempirical, tight period--mass--radius relation that agrees well withtheoretical relations derived from non-canonical models. This empiricalrelation is a powerful tool to calculate accurate masses for single Cepheidsfor which precise radii can be obtained from Baade--Wesselink-type analyses.The mass of the type-II Cepheid $\kappa$ Pav, $0.56 \pm 0.08 M_\odot$,determined using this relation is in a very good agreement with theoreticalpredictions. We find large differences between the p-factor values derived forthe Cepheids in our sample. Evidence is presented that a simpleperiod--p-factor relation shows an intrinsic dispersion, hinting at therelevance of other parameters, such as the masses, radii, and radial velocityvariation amplitudes. We also find evidence that the systematic blueshiftexhibited by Cepheids, is primarily correlated with their gravity. Thecompanion star of the Cepheid in the OGLE LMC-CEP-4506 system has a verysimilar temperature and luminosity, and is clearly located inside the Cepheidinstability strip, yet it is not pulsating.

The Araucaria Project: High-precision Cepheid astrophysics from the analysis of variables in double-lined eclipsing binaries