Photometric data for 593 Cepheids in the LMC, measured by Udalski et al. in the OGLE survey, augmented by 92 longer period Cepheids from other sources, are analyzed for the P-C and P-L relations, and for the variations of amplitude, light curve shape, and period across the instability strip at constant absolute magnitude. Both the P-C and P-L relations have different slopes for periods smaller and larger than 10 days. The break at 10 days is also seen in the period-amplitude relations, and the compound Fourier combinations of R_21 and Phi_21 introduced by Simon and Lee. The LMC Cepheids are bluer than Galactic Cepheids in the B,V,I color bands, part of which is due to differential Fraunhofer line blanketing and part to real differences in the temperature boundaries of the instability strip. The LMC strip is hotter by between 80K and 350K depending on the period. Hence, both the slopes and (necessarily) the zero points of the P-L relations in B,V,I must differ between LMC and the the Galaxy, and in fact they do. The LMC Cepheids are brighter by up to 0.5 mag at log P=0.4 (2 days) and fainter by 0.2 mag at log P=1.5 (32 days). These facts complicate the use of Cepheid as precision distance indicators until the reason is found for the non-universality of the P-L and P-C relations. The very large data base permits mapping of various Cepheid properties at different positions within the instability strip, both at constant period and at constant absolute magnitude over the range of 2 < P < 40 days and -2 > M_V > -5. (...)
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