10. Given that each face of the tetrahedron is a triangle with side lengths $2, 3, 2 \sqrt{2}$. The volume of this tetrahedron is . $\qquad$
10. $\frac{\sqrt{390}}{4}$

First, prove that the three pairs of opposite edges of this tetrahedron are equal. Then embed this tetrahedron into a rectangular prism, such that the face diagonals of the rectangular prism are the edges of the tetrahedron. The volume of the rectangular prism is three times the volume of the tetrahedron.