We provide theoretical modeling of the optical spectrum of recently synthesized triangular CdS nanocrystals by means of atomistic tight-binding theory. Both zinc blende and wurtzite structures are considered. Optical properties predicted for triangular prisms are very different from the ones obtained for tetrahedral quantum dots when z-polarized light is employed. In particular, the ground transition is dim for triangular prisms, whereas it is bright and highly intense for tetrahedra. The high sensitivity of the fine optical properties on the quantum dot shape allows us to discriminate between truncated tetrahedra and triangular prisms and also to estimate the thickness of the nanocrystals.