Before revision:   This algorithm has several important applications, including Boolean operations over big geometric data, like the detailed geometric modeling of buildings, and the smooth combination of 3D meshes  .
After revision:  We introduce here the idea of arrangement generated by a collection of cellular complexes, producing a cellular decomposition of the embedding space. The algorithm that executes this computation is called Merge of complexes. The arrangements of segment lines in 2D and polygons in 3D are special cases, like the combination of closed triangulated surfaces or meshed models. This algorithm has several important applications, including Boolean operations over big geometric data, like the detailed geometric modeling of buildings, and the smooth combination of 3D meshes .