A given direction is considered to belong to the -th face, whenever the mininum angular distance between the given direction and the normal direction to the -th face ( or 12, depending on whether the cube or the dodecahedron grid is considered, respectively), occurs when . In the case of the cube grid, the six cube faces, corresponding to the six sky regions, are so numbered: face # 1 corresponds to GRBM unit 1, and so on till # 4 facing GRBM 4; then face # 5 refers to the top face (pointing along the same direction of the NFIs), while # 6 faces the opposite direction, i.e. the BeppoSAX local south pole. For the dodecahedron faces, their local coordinates can be read from table .
In the following table the results are reported in two cases: first, by taking into account only the BATSE 4B catalog; second, the three merged catalogs: BATSE 4B, Kommers' and Stern's (4B+K+S, in the table). Both the cube and the dodecahedron grid cases are reported; in the latter case, only the merged catalogs have been considered, otherwise the statistics would be poor.
Finally, one might note that the number of BATSE 4B common bursts (262) reported in table and the number of total bursts, including the BATSE non-triggered catalogs (339), are smaller than the corresponding numbers 283 and 283+79=362, respectively, reported in tables and : actually, some bursts happened when the BeppoSAX spacecraft attitude was not known, during the time interval May - July 1997; hence, for these GRBs, the transformation from celestial to local coordinates was not feasible; owing to this, they have not been taken into account for estimating the GRBM efficiency as a function of the local direction.