Question about Wedge Products

Referencing Message 8953 again:

The wedgie for miracle is given as <<6 -7 -2 -25 -20 15|| and the
"2&g" mapping to primes is given as [<1 1 3 3|, <0 6 -7 -2|] I
understand how <0 6 -7 -2| is chosen, (and I understand how all the
generator values are chosen, for 3&g, 5&g and 7&g) but what I don't
get is how we are all so lucky that <1 1 3 3| for example, are the
period values (where <1 1 3 3| ^ <0 6 -7 -2| = <<6 -7 -2 -25 -20 15||
I'm just having a little trouble wrapping my mind around it, not
even sure why I am stuck:)

Paul Hj