Question 15. Three $12 \mathrm{~cm} \times 12 \mathrm{~cm}$ squares are each divided into two pieces, $A$ and $B$, by a line connecting the midpoints of two adjacent sides, as shown in the first figure. The six pieces are then attached to the outside of a regular hexagon, as shown in the second figure. The pieces are then folded to form a polyhedron. Find the volume of this polyhedron (in $\mathrm{cm}^3$).
Fold into a polyhedron as shown in the first figure, where the vertices marked with $P, Q, R, S$ have three right angles. From this, we can recognize that this polyhedron is part of a cube. We can imagine obtaining a cube with an edge length of $12 \mathrm{~cm}$, as shown in the second figure, making a section (through the midpoints of the relevant six edges) which divides the cube into two polyhedra like the one in the first figure. The volume of the cube is $12^{3}=1728\left(\mathrm{~cm}^{3}\right)$. Therefore, the volume of the polyhedron in question is $\frac{1728}{2}=864 \mathrm{~cm}^{3}$.