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