consider $D=10$ supergravity. In [@BPS1] such solutions based on standard intersection rules[^3] were listed. Here we also use the non-standard intersection rule[^4] which gives supersymmetric configurations in which the harmonic functions depend on relative transverse coordinates only. In $D=11$ the three standard intersection rules are $(0|\,2\perp 2)$[^5], $(1|\,2\perp 5)$ and $(3|\,5\perp 5)$ [@PT; @Tse1; @GKT], and the only non-standard rule is $(1|\,5\perp 5)$ [@khuri; @GKT]. The intersection rules in ten dimensions can be derived from these by dimensional reduction plus $T$ and $S$-duality. For concreteness we give the standard and non-standard intersection rules in the table below. References in which the intersection rules are derived from the equations of motion are [@AEH] and [@ETT] for standard and non-standard intersections, respectively.

                     standard                    non-standard
  -------- ----------------------------- -----------------------------
   $D=11$        $(0|M2\perp M2)$        
                 $(1|M2\perp M5)$        
                 $(3|M5\perp M5)$              $(1|M5\perp M5)$
   $D=10$   $(\half(p+q-4)|Dp\perp Dq)$   $(\half(p+q-8)|Dp\perp Dq)$
                 $(1|F1\perp NS5)$       
                $(3|NS5\perp NS5)$            $(1|NS5\perp NS5)$
                 $(0|F1\perp Dp)$        
                $(p-1|NS5\perp Dp)$           $(p-3|NS5\perp Dp)$

  : [*Standard and non-standard intersections in ten and eleven dimensions.*]{}

Since we use both standard and non-standard intersection rules, one has to specify which coordinates each harmonic function depends on. In all cases this is clear by inspection of the intersection and it can be further verified by looking 