Just topple

A hexagonal pencil placed on an inclined plane with a slope 45-degree at right angles to the generatrix (i.e. the line of intersection of the plane with the horizontal surface) remains at rest the same pencil placed parallel to the generatrix rolls down the plane.

Determine the maximum angle (in degrees) between the axis of the pencil and the generatrix of the inclined plane at which the pencil just topples.

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