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