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Shouldn't the statement include that X,Y,Z are integers that are possible maximums? It is a fairly important point no? For example dimensions of 2,2,2 given the statement as it currently is, means there is only 1 possible cube with 8 coordinates.
Where as if we said that 2 is the max integer value for X,Z,Y , we can have more than 1 possible cuboid. For example a 1,1,2 cuboid.