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