Euler Brick calculation

Question

How would you go about calculating Euler bricks from a list of primitive Pythagorean triples. I've tried to find an answer to this online but can't find anything which gives me list of Euler bricks with the longest edge $c<1000$.

Is this not possible to find using pythagorean triples.

Thank you

Answer 1

compare https://en.wikipedia.org/wiki/Euler_brick#Examples

     240     117      44               125     244     267
     275     252     240               348     365     373
     693     480     140               500     707     843
     720     132      85               157     725     732
     792     231     160               281     808     825
    1155    1100    1008              1492    1533    1595
    1584    1020     187              1037    1595    1884
    2340     880     429               979    2379    2500
    2640     855     832              1193    2768    2775
    2992    2475     780              2595    3092    3883
    3120    2035     828              2197    3228    3725
    5984    2295    1560              2775    6184    6409
    6325    5796     528              5820    6347    8579
    6336     748     195               773    6339    6380
    6688    6300    1155              6405    6787    9188
    6732    4576    1755              4901    6957    8140
    8160    4888     495              4913    8175    9512
    9120    1672    1575              2297    9255    9272
    9405    9152    2964              9620    9861   13123
   10725    9828    7840             12572   13285   14547