A polygon mesh may have a plurality of vertices and a set of polygon faces. Each of the triangles defining candidate planes may include one of the vertices as an endpoint of each line segment. For each of the candidate planes, an area or a number of vertices, referred to as a point count, may be computed. The candidate planes may be ordered by decreasing area or by decreasing point count. A planar face may be selected in accordance with the ordering. The selected planar face may be added to a set of polygon faces for a modified polygon mesh. Non-selected ones of the candidate planes may be excluded, whenever the non-selected candidate plane overlaps in area with an already selected planar polygon face. The selecting and the excluding may be repeated until the modified polygon mesh is formed. The modified polygon mesh may be a tessellation in three dimensions.