Painting an octahedron

You have 8 different colors, and you wish to paint the 8 faces of a regular octahedron, each in a different color. How many different ways can you do it?

Note: Different implies that for two coloring combinations \(A\) and \(B\), you can't pick up \(A\) and reorient it to make it look exactly like \(B\).


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