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No, you would need extra information. If you are looking for solutions over the real numbers you would need two more facts  volume, height, total edge length, length of long diagonal, proportions of edges... In principle you might get a unique solution in whole numbers: for instance there is only one cuboid with whole number edges and surface area 10. However, 842 cm^2 can be attained with (1,1,210), (2,3,83), (2,15,23) and (3,7,40)  at least. RD  


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