12 A hexagonal prism has a regular hexagon as its base, and its lateral edges are perpendicular to the base. It is known that all vertices of the hexagonal prism lie on the same sphere, and the volume of the hexagonal prism is $\frac{9}{8}$, the perimeter of the base is 3, then the volume of this sphere is . $\qquad$
(12) Since the perimeter of the base of the hexagonal prism is 3, the side length of the base is $\frac{1}{2}$, and the base area is $S = \frac{3 \sqrt{3}}{8}$. Given that the volume of the hexagonal prism is $\frac{9}{8}$, the height is $\sqrt{3}$. The diameter of the sphere is $\sqrt{1^{2}+(\sqrt{3})^{2}}=2$, and the volume of the sphere $V=\frac{4}{3} \pi r^{3}=\frac{4}{3} \pi$.