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