Many applications, in mathematics, computer graphics, medical imaging, geophysics and others, have used the representation of solids by their boundary surface, usually polygonal meshes. Those meshes can represent, with high precision, the geometric properties of the boundary surface of solid and also store important topological surface properties as genus, boundary and connected components. Because of the high complexity of such meshes, they are usually processed by the computers using specific data structures. These structures store, beyond the mesh geometry, information about incidence and adjacency relations among the mesh elements. They require computational resources for storage and processing according to the mesh complexity. Even with the development of the computational resources available for handling such structures, very large meshes with millions of elements are hard to store, to process and to exchange through the web. Many recent researches are looking for mesh simplification process that allows to represent the same surface with fewer elements and compression process to encode it in compact ways for transmition and storage. In this work, we develop topological operators, in a concise data structure, for simplifying meshes by the decimation of its cells. One of our goals, with these operators, is to obtain a mesh with a low complexity that preserves the topological properties from the original surface without loosing the control of the geometric proprieties as volume, area and visual aspect.