An abrasive device is defined by a honeycomb or cellular structure which is configured to define the grinding device. The cells of the cellular structure are filled with the normal constituents that make up a grinding wheel such as abrasive grains, a bonding matrix such as an organic resin, and fillers. The bonding matrix acts to bond the abrasive grains together into a uniform mass. The bonding medium is also designed to bond the abrasive and fillers to the walls of the cellular structure.