6. As shown in Figure 1, given that the volume of the regular quadrilateral pyramid $P$ $A B C D$ is 1, $E$, $F$, $G$, $H$ are the midpoints of line segments $A B$, $C D$, $P B$, $P C$ respectively. Then the volume of the polyhedron $B E G-C F H$ is $\qquad$
6. $\frac{5}{16}$.
$$
x^{2}+1 \text {, }
$$

Transform the polyhedron. $g(x) \cdots)$ ).
$$
E B G-F C H^{\prime} \text {. }
$$

Then $V_{\text {sinik Bec }} g(f(x))$, and $f(x)$ is $2^{m}$ times
$$
=\frac{3}{4} V_{\text {tetrahedron } P A B D}-\frac{1}{8} V_{\text {tetrahedron } P B C D}=\frac{5}{16} \text {. }
$$