9. For any 4 vertices $A, B, C, D$ of a cube that do not lie on the same plane, the number of cosine values of the dihedral angle $A-BC-D$ that are less than $\frac{1}{2}$ is

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9.4 .

Among the cosines of the dihedral angles with the body diagonal as the edge,
$$
\begin{array}{l}
\cos \angle A_{1} O_{1} C_{1} \\
=\cos 120^{\circ}=-\frac{1}{2} .
\end{array}
$$

Among the cosines of the dihedral angles with the edge as the edge, only 0 is less than $\frac{1}{2}$.
Among the cosines of the dihedral angles with the face diagonal as the edge,
$$
\begin{array}{l}
\cos \angle A O C_{1} \\
=\frac{\left(\frac{\sqrt{2}}{2}\right)^{2}+\left(1+\frac{1}{2}\right)-(\sqrt{3})^{2}}{2 \times \frac{\sqrt{2}}{2} \times \sqrt{1+\frac{1}{2}}}=-\frac{\sqrt{3}}{3}<\frac{1}{2} \\
\cos \angle A_{1} O C_{1}=\frac{\frac{3}{2}+\frac{3}{2}-2}{2 \sqrt{\frac{3}{2}} \times \sqrt{\frac{3}{2}}}=\frac{1}{3}<\frac{1}{2} .
\end{array}
$$