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