Geometric properties of geometric tripotents and split faces in neutral $SFS$-space

The present paper is devoted to the study of geometric properties of split faces of a unit ball of neutral $SFS$-space and to the study of properties of relations in the set of geometric tripotents. Namely, we give the condition under which the complete orthomodular lattice of geometric tripotents is a Boolean algebra and prove that the relations ${{\le }_{r}},\,\,{{\le }_{c}}$ are pre-orders in the set of geometric tripotents.