In a unit cube $A B C D-A_{1} B_{1} C_{1} D_{1}$, if we use the planes $A B_{1} C$, $B C_{1} D$, $C D_{1} A$, $D A_{1} B$, $A_{1} B C_{1}$, $B_{1} C D_{1}$, $C_{1} D A_{1}$, and $D_{1} A B_{1}$ to cut this unit cube, then the volume of the part containing the center of the cube is $\qquad$ .