Nowadays for real study cases, the generation of full block structured hexahedral meshes is mainly an interactive and very-time consuming process realized by highly-qualified engineers. To this purpose, they use interactive software where they handle and modify complex block structures with operations like block removal, block insertion, O-grid insertion, propagation of block splitting, propagation of meshing parameters along layers of blocks and so on. Such operations are error-prone and modifying or adding an operation is a very tedious work. In this work, we propose to formally define hexahedral block structures and main associated operations in the model of n-dimensional generalized map. This model provides topological invariant and a systematic handling of geometric data that allows us to ensure the expected robustness.