(16) As shown in the figure, the polyhedron is obtained by making a section $A_{1} B C_{1} D_{1}$ through the vertex $B$ of the base of a regular quadrilateral prism, given that $A A_{1}=O C_{1}$, the dihedral angle between the section $A_{1} B C_{1} D_{1}$ and the base $A B C D$ is $45^{\circ}$, $A B=1$, then the volume of this polyhedron is $=$ $\qquad$
16 Extend $D_{1} A_{1} 、 D A 、 D_{1} C_{1} 、 D C$ to complete the polyhedron into a triangular pyramid. The volume of the polyhedron can be found by the difference between the volume of the large triangular pyramid and the volumes of the two smaller triangular pyramids, which is $\frac{\sqrt{2}}{2}$.