4. In the tetrahedron $P-ABC$, it is known that $BC=3$, $CA=4$, $AB=5$. If the dihedral angles between the three lateral faces and the base are all $45^{\circ}$, then the volume of the tetrahedron $P-ABC$ is $\qquad$
4.2.

Let $P O \perp$ plane $A B C$ at point $O, O D \perp B C$ at point $D, O E \perp C A$ at point $E, O F \perp A B$ at point $F$.
Let $O P=h$.
Then $\angle P D O=\angle P E O=\angle P F O=45^{\circ}$.
Thus, $O D=O E=O F=h \cot 45^{\circ}=h$.
In $\triangle A B C$,
$$
\begin{array}{l}
3 O D+4 O E+5 O F=2 S_{\triangle A B C}=12 \\
\Rightarrow 3 h+4 h+5 h=12 \Rightarrow h=1 \\
\Rightarrow V=\frac{1}{3} S h=\frac{1}{3} \times 6 \times 1=2 .
\end{array}
$$