6. Three cylinders are tangent to each other on their sides, and their axes are pairwise perpendicular. If the radius of the base of each cylinder is 1, then the radius of the smallest sphere that is tangent to the sides of these three cylinders is ( ). Wanfang Data
(A) $\sqrt{2}-1$
(B) $\frac{\sqrt{2}-1}{2}$
(C) $\frac{\sqrt{5}-1}{2}$
(D) $\frac{\sqrt{5}-1}{4}$
6.(A).

Construct a cube $A B C D-A_{1} B_{1} C_{1} D_{1}$ with an edge length of 2, such that the axes of three cylinders are the edges $A A_{1}$, $B C$, and $C_{1} D_{1}$ of the cube. It is easy to see that the side surfaces of these three cylinders are pairwise tangent, and their axes are also pairwise perpendicular. By the symmetry of the cube, the center of the smallest sphere that is tangent to the side surfaces of these three cylinders must be the center $O$ of the cube. The distance from point $O$ to the edge is equal to the sum of the radius of the small sphere and the radius of the cylinder's base. The calculation yields the radius of the sphere as $\sqrt{2}-1$.