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BACKGROUND: An item has a maximum of 6 degrees of freedom; 3 degrees of translation (motion in a straight line) and 3 degrees of rotation.

The textbook answer to this question is 3 degrees of freedom. What do I mean by the "textbook" answer? I mean that the sphere and spherical bowl fit together correctly so that while the ball will rotate smoothly in any direction, the ball fits tightly enough that it will not move in a straight line in any direction.

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