Thread cleared up for clarity. HP (High pinion or reverse cut) differentials turn in the same direction as standard cut (some call them LP or low pinion). You can conceivably take a front and use it as a rear axle (some people have). You can also use a rear D60 (or 44, etc), and add inner "C"s, the correct length tubes and shafts, etc, and turn it into a front axle. This also has been done many times.
You usually can't flip it upside down, as that would cause it to rotate the shafts in the opposite direction as you would need, not to mention the pinion bearing wouldn't get lubed. (this is to clarify the john.colling post above.
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