An irregular, tessellated building unit comprises x primary elements, wherein x is an integer equal to or greater than 1. The primary element is a rotational tessellation having a plural pairs of sides extending in a generally radial direction from plural vertices, respectively. In each pair, the two sides are rotationally spaced by an angle that is divided evenly into 360 degrees. Preferably, all of the sides are irregularly shaped. In one preferred embodiment all six sides are irregularly shaped, images of each other and comprise mid-point rotations. As a result, any side of any unit can mate with any other side of any other unit. Optionally, spacers are provided on the sides of each unit. A wide variety of units may be constructed having different numbers and arrangements of primary elements. As all the units are combinations of primary elements, they readily mate with each other. A surface covering comprises a multiplicity of units assembled to form a continuous surface without overlap between units and without substantial gaps between units. A structure, such as a wall or column can be formed of building units of the invention. Because of the irregular side configurations, and different sizes and shapes of individual units, the resulting surface or structure has a natural, non-repeating pattern appearance. Optionally, minor surface and edges variations are made from unit to unit to further enhance the natural appearance of the surface covering or structure.