An irregularly-shaped building unit includes a front surface, a rear surface opposite of the front surface, and an outer contour surface that extends generally perpendicularly from the front surface to the rear surface. The outer contour surface is irregularly shaped. A plurality of mating sides are disposed on the outer contour surface, where at least two mating sides intersect with a major axis, and at least two mating sides intersect with a minor axis. The major axis and the minor axis are generally perpendicular to each other. Each mating side is a centered rotation about the respective axis that the mating side intersects with.