332. A sphere of radius $R$ touches the edges of a trihedral angle, all plane angles of which are equal to $60^{\circ}$. The surface of the sphere inside the angle consists of two curvilinear quadrilaterals. Find the areas of these quadrilaterals.
332. Consider a regular octahedron with edge $2 R$. A sphere that touches all its edges has a radius $R$. The surface of the sphere is divided by the surface of the octahedron into eight spherical segments and six curvilinear quadrilaterals, equal to the smaller of the two sought.

$$
\text { Answer: } \frac{2 \pi R^{2}}{3}\left(4 \sqrt{\frac{2}{3}}-3\right), \pi R^{2}\left(\frac{16}{3} \sqrt{\frac{2}{3}}-2\right) \text {. }
$$