The realization space is
  [1   0   1   1    1         x1   0            2*x1 - 1          0            2*x1 - 1         x1]
  [0   1   1   1   x1   2*x1 - 1   0                   0   2*x1 - 1         2*x1^2 - x1   2*x1 - 1]
  [0   0   0   1   x1         x1   1   -x1*x2 + 2*x1 - 1      x1*x2   -x1*x2 + 2*x1 - 1      x1*x2]
in the multivariate polynomial ring in 2 variables over ZZ
avoiding the zero loci of the polynomials
RingElem[x1^2*x2 + x1*x2 - 2*x1 + 1, 3*x1*x2 - 2*x1 - x2 + 1, x1 - 1, 2*x1^2*x2 - 2*x1 + 1, 2*x1*x2 - 2*x1 + 1, 2*x1^2 + x1*x2 - 3*x1 + 1, x2 - 1, x1, x2, x1*x2 - 2*x1 + 1, 2*x1 - 1, x1^2*x2 + 2*x1^2 - 3*x1 + 1, 3*x1^2 - 3*x1 + 1, x1 - x2, x1^2*x2 - 2*x1 + 1, x1^2 - x1 + 1, x1^2 + x1*x2 - 2*x1 + 1, x1*x2 - 2*x1 - x2 + 1, x1^2*x2 - 4*x1^2 - x1*x2 + 4*x1 - 1]