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