$[\quad$ Sphere [Inscribed in a Trihedral Angle of a Cube]

Inside a unit cube, there are eight equal spheres. Each sphere is inscribed in one of the trihedral angles of the cube and touches three spheres corresponding to the adjacent vertices of the cube. Find the radii of the spheres.

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The sum of the diameters of two adjacent spheres is equal to the edge of the cube. The radii are equal to $1 / 4$.