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Let x ≤ cuberoot(45) cm be the length of one edge.

Let x ≤ y ≤ sqrt(45/x) cm be the length of another edge and let z = 45/(xy) cm be the length of the third edge.

Then Volume = x*y*z = x*y*45/(x*y) = 45 cm3 and the way in which the three were defined ensures that x ≤ y ≤ z so that all combinations are distinct.

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