The realization space is
  [0   1   1   0   0   1                    x2 - 1                x2 - 1                x2 - 1                    x2 - 1                                    x2^2 - x2]
  [1   0   1   1   0   1   x1*x2 - 2*x1 + 2*x2 - 1   x1*x2 - 2*x1 + x2^2   x1*x2 - 2*x1 + x2^2   x1*x2 - 2*x1 + 2*x2 - 1   2*x1*x2^2 - 5*x1*x2 + 2*x1 + x2^3 + x2 - 1]
  [1   0   1   0   1   0                    x2 - 1             x2^2 - x2            x1*x2 - x1                x1*x2 - x1                                  x2^3 - x2^2]
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[x2 - 1, 2*x1 - 1, 2*x1^2*x2^2 - 5*x1^2*x2 + 2*x1^2 + 5*x1*x2 - 3*x1 - 2*x2^3 + 2*x2^2 - 2*x2 + 1, x1 - x2, x1*x2 - 2*x1 + x2^2 - x2 + 1, 2*x1^2*x2^2 - 5*x1^2*x2 + 2*x1^2 + x1*x2^2 + 2*x1*x2 - x1 - x2^3, x1 - 1, x1*x2 - 2*x1 + 1, 2*x1 - x2 - 1, 2*x1^2*x2^2 - 5*x1^2*x2 + 2*x1^2 + 2*x1*x2^2 + x1*x2 - x1 - x2^4, 2*x1^2*x2^2 - 5*x1^2*x2 + 2*x1^2 + 5*x1*x2 - 3*x1 - x2^4 + x2^3 - x2^2 - x2 + 1, 2*x1^2*x2^2 - 5*x1^2*x2 + 2*x1^2 + x1*x2^2 + 2*x1*x2 - x1 - x2^4 + x2^3 - x2^2, x1^2*x2 - 2*x1^2 + x1*x2^2 - 2*x1*x2 + 3*x1 - x2^3 + x2^2 - 1, x2, x1*x2 - 2*x1 + x2 + 1, x1*x2 - 2*x1 + x2, 2*x2 - 1, 2*x1*x2^2 - 5*x1*x2 + 2*x1 + x2^3 - x2^2 + 2*x2 - 1, 2*x1*x2^2 - 5*x1*x2 + 2*x1 + x2^3 + x2 - 1, 2*x1*x2^2 - 5*x1*x2 + 2*x1 + x2^2 + x2 - 1, x1, x1^2*x2 - 2*x1^2 + 2*x1*x2 - 2*x2^2 + x2, x1^2*x2 - 2*x1^2 + x1*x2 + x1 - 2*x2^2 + 2*x2 - 1, x1*x2 - 2*x1 + 2*x2 - 1, x1 - 2*x2 + 1, x1*x2 - 2*x1 + x2^2, x1^2*x2 - 2*x1^2 + 2*x1 - x2^2 + x2 - 1, x1 - x2^2 + x2 - 1, x1 - x2^2]