3. From the 6 face diagonals of the rectangular prism $A B C D-A_{1} B_{1} C_{1} D_{1}$, two tetrahedra $A-B_{1} C D_{1}$ and $A_{1}-B C_{1} D$ can be formed. If the combined volume of the two tetrahedra is 1 (overlapping parts are counted only once), then the volume of the rectangular prism is $\qquad$ .
3.2.

Let the length, width, and height of the rectangular prism be $a$, $b$, and $c$ respectively, then the volume of the rectangular prism $V_{0}=a b c$. The volumes of the two tetrahedra (as shown in Figure 4) are both
$$
\begin{array}{l}
V_{1}=V_{0}-V_{A_{1}-A B D}-V_{A_{1}-B B C_{1}}-V_{A_{1}-D_{1} D C_{1}}-V_{C_{1}-B C D} \\
=V_{0}-4 \times \frac{1}{6} a b c=\frac{1}{3} V_{0} .
\end{array}
$$

The common part of the two tetrahedra is an octahedron with vertices at the centers of the 6 faces (as shown in Figure 5), and its volume is
$$
V_{2}=\frac{1}{3} \times \frac{1}{2} S_{\text {quadrilateral } \triangle B C D} \cdot h=\frac{1}{6} V_{0} .
$$

Therefore, the total volume occupied by the two tetrahedra is
$$
1=2 V_{1}-V_{2}=\frac{2}{3} V_{0}-\frac{1}{6} V_{0}=\frac{1}{2} V_{0} \Rightarrow V_{0}=2 .
$$