(2.5,4)[$r'$]{}

We can now use the wave/monopole rule to find other solutions with near-horizon geometries where some or all of $adS_3 \xx S^3 \xx S^3$ are replaced by their two-dimensional versions. The scheme is as follows:

(11,12) (0,0)[(4,1)[$adS_2 \xx S^2 \xx S^2$ (F)]{}]{} (2,1)[(0,1)[2]{}]{} (2,1)[(2,1)[4]{}]{} (0,3)[(4,1)[$adS_2 \xx S^2 \xx S^3$ (D)]{}]{} (4,3)[(4,1)[$adS_3 \xx S^2 \xx S^2$ (E)]{}]{} (6,4)[(0,1)[2]{}]{} (2,4)[(2,1)[4]{}]{} (4,6)[(4,1)[$adS_3 \xx S^2 \xx S^3$ (C)]{}]{} (1.5,2)[$M$]{} (6.2,5)[$M$]{} (4,1.7)[$W$]{} (4,4.7)[$W$]{} (2,4)[(0,1)[2]{}]{} (0,6)[(4,1)[$adS_2 \xx S^3 \xx S^3$ (B)]{}]{} (6,7)[(0,1)[2]{}]{} (2,7)[(2,1)[4]{}]{} (4,9)[(4,1)[$adS_3 \xx S^3 \xx S^3$ (A)]{}]{} (1.5,5)[$M$]{} (6.2,8)[$M$]{} (4,7.7)[$W$]{} (7.5,10.5)[(4,1)[$\#$ charges]{}]{} (7.5,9)[(4,1)[$3$]{}]{} (7.5,6)[(4,1)[$4$]{}]{} (7.5,3)[(4,1)[$5$]{}]{} (7.5,0)[(4,1)[$6$]{}]{}

They correspond to the following intersections. Adding a wave to solution (A) and dimensionally reducing to type IIA supergravity in the same way as described before for $M2\perp M5$, one finds $$\begin{array}{lcccccccccc}
D0   &   &   &   &   &   &   &   &   &   & \\
D4_1 &   & 2 & 3 & 4 & 5 &   &   &   &   & \\
D4_2 &   &   &   &   &   & 6 & 7 & 8 & 9 & \hspace{2cm} (B) \\
F1   & 1 &   &   &   &   &   &   &   &   &
\end{array}$$ where $H_f=H_0=H_4^{(1)} H_4^{(2)}$, $H_4^{(1)}(x_6, x_7, x_8, x_9)$ and $H_4^{(2)}(x_2, x_3, x_4, x_5)$[^11]. This solution is $1/8$ 