We present a numerical study of the structured light produced by a laser beam transmitted by a symmetric pyramidal prism. From the Fresnel diffraction formulation, we obtain expressions for the amplitudes valid for an arbitrary number of prism faces, and for both acute and flat-topped prisms. The expressions are readily evaluated numerically and are a significant advancement over the restrictive plane wave models used in prior work. We consider applications in optical trapping and give examples in which the intensity distributions contain a number of bright spots having similar power, as is suitable for the simultaneous trapping of several particles. We also consider applications in lithography and, under other conditions, obtain results in which uniform periodic intensity patterns are produced. Advantages of employing pyramidal prisms in such applications are their excellent stability and their efficiency in the production of structured light.