2. A regular tetrahedral box with an edge length of 6 contains a smaller regular tetrahedron. If the smaller tetrahedron can rotate freely within the box, then the maximum edge length of the smaller tetrahedron is $\qquad$ .
荅靼 2 .
The small regular tetrahedron can rotate freely inside the box, so the maximum edge length of the small regular tetrahedron is when it is inscribed in the sphere that is inscribed in the large regular tetrahedron. Let the radius of the circumscribed sphere of the large regular tetrahedron be $R$, and the radius of the circumscribed sphere of the small regular tetrahedron (which is the inscribed sphere of the large regular tetrahedron) be $r$. It is easy to know that $r=\frac{1}{3} R$, so the maximum edge length of the small regular tetrahedron is $\frac{1}{3} \times 6=2$.