The SiC optical constants are fundamental inputs for radiative transfer (RT) models of astrophysical dust environments. However, previously published values contain errors and do not adequately represent the bulk physical properties of the cubic ({beta}) SiC polytype usually found around carbon stars. We provide new, uncompromised optical constants for {beta}- and {alpha}-SiC derived from single-crystal reflectance spectra and investigate quantitatively (i) whether there is any difference between {alpha}- and {beta}-SiC that can be seen in infrared (IR) spectra and optical functions and (ii) whether weak features from {lambda}~12.5-13.0{mu}m need to be fitted. We measured mid- and far-IR reflectance spectra for two samples of 3C ({beta}-)SiC and four samples of 6H ({alpha}-)SiC. For the latter group, we acquired polarized data (E{perpendicular.to}c, E{parallel.to}c orientations). We calculated the real and imaginary parts of the complex refractive index (n({lambda})+ik({lambda})) and the ideal absorption coefficients via classical dispersion fits to our reflectance spectra.