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