Suppose that in Example 16.35 we 2-color the faces of the cube, which is free to move

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Suppose that in Example 16.35 we 2-color the faces of the cube, which is free to move in space.
(a) How many distinct 2-colorings are there for this situation?
(b) If the available colors are red and white, determine the pattern inventory.
(c) How many nonequivalent colorings have three red and three white faces?
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