Is there a tree of Pythagorean quadruples?

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It is well-known that there is a trinary tree that contains every primitive Pythagorean triple exactly once. It even has a Wikipedia page.

Is there a similar tree that contains each primitive Pythagorean quadruple exactly once?

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You can find the answer in the following paper: http://math.colgate.edu/~integers/u73/u73.pdf