The realization space is
  [1    1   1   0   0   1    1                                           x1    0                                           x1      x1]
  [1   x2   0   1   0   1   x2                                            0    1                                           x2      x2]
  [0    0   0   0   1   1   x2   2*x1*x2 - 10*x2^4 + 17*x2^3 - 10*x2^2 + x2   x1   2*x1*x2 - 10*x2^4 + 17*x2^3 - 10*x2^2 + x2   x1*x2]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal with 4 generators
avoiding the zero loci of the polynomials
RingElem[x1 - x2, x2, 5*x1*x2 - 6*x1 + 2, x1 - 1, x1, 5*x1*x2 - 7*x1 + 2, 5*x1^2*x2 - 6*x1^2 - 5*x1*x2 + 9*x1 - 2, 5*x1^2*x2 - 6*x1^2 - 5*x1*x2^2 + 7*x1*x2 + x1 - 2*x2, x2 - 1, x1*x2 - 2*x1 + 1, x1^2 - 5*x1*x2^2 + 6*x1*x2 - 2*x2, x1^2 - 5*x1*x2 + 6*x1 - 2, x1^2 - 5*x1*x2^2 + 6*x1*x2 - x1 - 2*x2, 5*x1*x2^2 - 7*x1*x2 + x1 + 2*x2, 5*x1*x2^2 - 12*x1*x2 + 6*x1 + 3*x2 - 2, 5*x1*x2 - 7*x1 + 3, x1^2 - 5*x1*x2^2 + 7*x1*x2 - 2*x2, x1^2 - 5*x1*x2 + 7*x1 - 2, x1^2 - 5*x1*x2^2 + 7*x1*x2 - x1 - 2*x2, x1*x2 - x1 - x2, x1*x2 - x1 + 1, 5*x1*x2^2 - 12*x1*x2 + 6*x1 + 2*x2 - 2, 5*x1*x2^2 - 12*x1*x2 + 8*x1 + 2*x2 - 2]