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