Birefringence and optical band-gap measurements were performed at 20°C on structurally uniform regions of ZnS crystals. The regions were of one of the following polytype structures: 4L, 6L, 10L, 14L, 24L, 26L, 28L, 40L, 120L; cubic (3L) and hexagonal (2L) regions were also investigated for reference. No stacking disorder was discovered in the regions studied. It was found that the absorption-edge positions (for polarization parallel and perpendicular to the optic axis) as well as the degree of birefringence ∆n depend only on the value of a single structure parameter α. This parameter is defined as the percentage of (00.1) planes stacked in hexagonal order; its values were determined directly by x-ray structure analysis. The absorption edge positions were found to be linear functions of α. This linearity is explained on the basis of Birman's perturbation treatment for electron states with k vectors parallel to the c axis. It implies that in a polytype the perturbation potential caused by partially hexagonal stacking is proportional to α. The degree of birefringence was found to be proportional to α an outline of a simple dispersion treatment is given for the explanation of this proportionality. The established linear relationships between absorption edges, birefringence, and α allow calculation of absorption-edge positions and α values from birefringence measurements. This may facilitate investigations of structure-sensitive properties (e.g., the anomalous photovoltaic effect) of ZnS samples which are composed of regions differing from each other in structure.