6. Inside a cube $A B C D-A_{1} B_{1} C_{1} D_{1}$ with edge length 1, there is a small ball that is tangent to the diagonal segment $A C_{1}$ of the cube. Then the maximum radius of the ball $=$ $\qquad$
荟荥 $\frac{4-\sqrt{6}}{5}$.

Huiying $\frac{4-\sqrt{6}}{5}$.