A block of dimensions 2, 3, and 5 is (I think) the smallest block with all edges relatively prime. It also has the curious property that the two shorter sides sum to the longer one.
A block of dimensions 3 4 5 is also relatively prime. It has the curious property that the diagonal (hypotenuse) of the 3-by-4 face equals the longest edge. It is also equivalent to two the the above blocks stacked.
As building blocks, can interesting shapes be built exploiting these properties?
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