We collect here the investigations of boxes with arbitrary dimensions and more generally, problems involving the whole of the real number system. We continue to require, however, that our geodesics meet edges at an angle of 45 degrees. The box triangle, which in the section on number theory represents all shapes of boxes with integral sides, will represent to us now all boxes of any dimensions. We will distinguish between the two by referring to the former as the "discrete box triangle".

We organize the work as follows:

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