2. For a regular triangular prism $A B C-A^{\prime} B^{\prime} C^{\prime}$, the side edges and the base edges are all 1. Then the volume of the common part of the tetrahedra $A^{\prime} A B C$, $B^{\prime} A B C$, and $C^{\prime} A B C$ is $\qquad$ .
2. $\frac{\sqrt{3}}{36}$.

As shown in Figure 2, by symmetry, the intersection point $O$ of the planes $C_{1} A B$, $A_{1} B C$, and $B A C$ projects onto the center $H$ of the equilateral $\triangle A B C$ on the base $A B C$. Let the midpoints of $A B$ and $B C$ be $D$ and $E$, respectively. Then $O H$ is the intersection line of $\triangle E A A_{1}$ and $\triangle D C C_{1}$. Therefore,
$$
\frac{O H}{C_{1} C}=\frac{D H}{D C}=\frac{1}{3} .
$$

Thus, $O H=\frac{1}{3}$.
Hence, the volume of the common part of the tetrahedra $A^{\prime} A B C$, $B^{\prime} A B C$, and $C^{\prime} A B C$ (i.e., the volume of the tetrahedron $O A B C$) is
$$
V=\frac{1}{3} O H \cdot S_{\triangle \triangle B C}=\frac{1}{3} \times \frac{1}{3} \times \frac{\sqrt{3}}{4}=\frac{\sqrt{3}}{36} .
$$