the art the assembly of blocks according to the invention produces a structure which has an internal network of reinforcing partitions improving its resistance to cracking after optional machining of this structure to form a filter body a material reinforcement can be added at the periphery of the filter body the risk of cracking is thereby further diminished in one embodiment of the invention all the assembled blocks have a reinforcement preferably constant along their whole external surface 16 after assembly the peripheral reinforcements of the blocks thereby form in transverse cross section a grid considerably enhancing the resistance to cracking compared to a filter body that does not have a reinforcement at its periphery more preferably irrespective of the embodiment the thickness of the internal portions of the side walls of the peripheral channels is identical to the thickness of the walls of the internal channels that is which are not peripheral channels of the filter block the efficiency of filtration across all the internal walls of the filter block that is walls which are not in contact with the exterior of the block is thereby substantially the same irrespective of the internal wall considered the fabrication of the filter body is also.