Additive manufacturing offers new available categories of geometries to be built. Among those categories, one can find the well developing field of lattice structures. Attention has been paid on lattice structures for their lightweight and mechanical efficiency ratio, thus leading to more optimized mechanical parts for systems. However this lightness only holds true from a mass related point of view. The files sent to additive manufacturing machines are quite large and can go up to such sizes that machines can freeze and get into malfunction. This is directly related to the lattice structures tendency to be of a high geometric complexity. a large amount of vertices and triangles is necessary to describe them geometrically, thus leading to larger file sizes. With the increasing use of lattice structures, the need for their files to be lighter is also rising. This paper aims at proposing a method for tessellating a certain category of such structures, using topologic and geometric criteria to generate as few as possible triangles, thus leading to lightweight files. The triangulation technique is driven by a chordal error that control the deviation between the exact and tessellated structures. It uses interpolation, boolean as well as triangulation operators. The method is illustrated and discussed through examples from our prototype software.