Three 12 \mathrm{~cm} \times 12 \mathrm{~cm} squares are each cut into two pieces A and B, as shown in the first figure below, by joining the midpoints of two adjacent sides. These six pieces are then attached to a regular hexagon, as shown in the second figure, so as to fold into a polyhedron. What is the volume \left(\right. in \mathrm{cm}^{3} ) of this polyhedron?
