Screening of surfaces that spontaneously reconstruct is important when investigating realistic surfaces. Evaluating the surface energy after macroscopic reconstruction to form pairs of facets is a very fast procedure to identify surfaces that spontaneously reconstruct. This paper discusses a method to identify orientations of pairs of facets that can form on an arbitrary crystal orientation, which can then be used to derive the surface energy after facet reconstruction. Another use of the algorithm is to find possible orientations of terrace surfaces when the vicinal surface orientation is known for a surface with step edges. The algorithm is expected to further accelerate high-throughput calculations of surface properties.