The realization space is
  [1   0   1   x3 - 1   0   1    1        0    1    1]
  [0   1   1      -x2   0   0    0   x2 - 1    1   x2]
  [0   0   0        0   1   1   x1       x3   x3   x3]
in the multivariate polynomial ring in 3 variables over ZZ
avoiding the zero loci of the polynomials
RingElem[x3, x2 - 1, x3 - 1, x1 - x3, x2 + x3 - 1, x1*x2 - x1 + x3, x1, x2, x1 - 1, x2 - 2, x2*x3 - 2*x2 - 2*x3 + 2, x2*x3 - x2 - 2*x3 + 1, x1*x2 - x1 - x2*x3 + 2*x3, x1*x2 + x1*x3 - x1 - x2*x3, x1*x2*x3 - x1*x2 - x1*x3 + x1 - x2*x3]