The realization space is
  [1   0   1   0   1    0     x2 - 1                                     x1                          x1*x2 - x1                    x2                 x1]
  [0   1   1   0   0    1     x2 - 1   -x1*x2^2 + 5*x1*x2 - 2*x1 - 4*x2 + 2   x1*x2^2 - 3*x1*x2 + x1 + 2*x2 - 1   x1*x2 - x1 - x2 + 1   x1*x2 - 2*x2 + 1]
  [0   0   0   1   1   -1   2*x2 - 1                                  x1*x2                        2*x1*x2 - x1                 x1*x2              x1*x2]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal with 2 generators
avoiding the zero loci of the polynomials
RingElem[x1 - x2, x1*x2 - x1 - 2*x2 + 1, x1 - 1, 2*x2 - 1, x1*x2^2 - 4*x1*x2 + 2*x1 + 2*x2 - 1, x1*x2^4 - 6*x1*x2^3 + 10*x1*x2^2 - 6*x1*x2 + x1 + 4*x2^3 - 10*x2^2 + 6*x2 - 1, x1*x2^4 - 6*x1*x2^3 + 9*x1*x2^2 - 3*x1*x2 + 4*x2^3 - 10*x2^2 + 6*x2 - 1, x2^2 - 3*x2 + 1, x1*x2^3 - 4*x1*x2^2 + 3*x1*x2 - x1 + 2*x2^2 - 3*x2 + 1, x1*x2^2 - 5*x1*x2 + 3*x1 + 4*x2 - 2, x2, x2 - 1, x1*x2^2 - 4*x2^2 + 4*x2 - 1, x1*x2 - 2*x1 - x2 + 1, 2*x1*x2 - 2*x2 + 1, x1*x2 - 2*x2 + 1, x1^2*x2 - x1^2 + x1*x2^3 - 5*x1*x2^2 + x1*x2 + x1 + 4*x2^2 - 2*x2, 2*x1^2*x2^2 - 3*x1^2*x2 + x1^2 + x1*x2^4 - 6*x1*x2^3 + 4*x1*x2^2 + x1*x2 - x1 + 4*x2^3 - 6*x2^2 + 2*x2, x1*x2^2 - 4*x1*x2 + x1 + 3*x2 - 1, x1*x2^3 - 4*x1*x2^2 + x1 + 4*x2^2 - 2*x2, 2*x1^2*x2 - x1^2 + x1*x2^3 - 6*x1*x2^2 + x1*x2 + x1 + 4*x2^2 - 2*x2, 2*x1*x2 - x1 - x2 + 1, x1, x1*x2^2 - 5*x1*x2 + 2*x1 + 4*x2 - 2, x1*x2^3 - 6*x1*x2^2 + 5*x1*x2 - x1 + 4*x2^2 - 6*x2 + 2, x1*x2^3 - 6*x1*x2^2 + 6*x1*x2 - 2*x1 + 4*x2^2 - 6*x2 + 2, x1*x2^3 - 7*x1*x2^2 + 11*x1*x2 - 4*x1 + 4*x2^2 - 6*x2 + 2, x1*x2^2 - 6*x1*x2 + 2*x1 + 4*x2 - 2, x1*x2^2 - 6*x1*x2 + 3*x1 + 4*x2 - 2, 3*x2 - 2]