11. Given a plane that makes an angle of $\alpha$ with all 12 edges of a cube, then $\sin \alpha=$ $\qquad$
Since the 12 edges of the cube are parallel to $P A, P B, P C$, according to the problem, the angle formed by $P A$ and the plane $A B C$ is $\alpha$. Let the edge length of the cube be $1, P D \perp$ plane $A B C$ at point $D$, it is easy to know $P D=\frac{\sqrt{3}}{3} \Rightarrow \sin \alpha=\frac{P D}{P A}=\frac{\sqrt{3}}{3}$.