The realization space is
  [1   0   1                            x1*x2   1   0             1   1         1         0    1]
  [0   1   1   x1^2 + 3*x1*x2 - 5*x1 - x2 + 2   0   0             0   1        x1        x1   x1]
  [0   0   0                                0   1   1   x1 + x2 - 1   1   -x1 + 1   -x1 + 1   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[x1 + x2 - 1, x1 - 1, x1^2 + x1*x2 - 2*x1 + 1, x1^3*x2 - x1^3 + x1^2*x2^2 - 4*x1^2*x2 + 6*x1^2 + 4*x1*x2 - 7*x1 - x2 + 2, x1 + x2 - 2, x1^2 + x1*x2 - 3*x1 + 1, x1, x1^2*x2 - x1^2 - 3*x1*x2 + 5*x1 + x2 - 2, x1 - x2, x2 - 1, 2*x1^2*x2 - x1^2 + 2*x1*x2^2 - 8*x1*x2 + 5*x1 - x2^2 + 3*x2 - 2, 2*x1^2*x2 - x1^2 + 3*x1*x2^2 - 8*x1*x2 + 5*x1 - x2^2 + 3*x2 - 2, x2, x1^2 + 3*x1*x2 - 5*x1 - x2 + 2, x1^2 + 2*x1*x2 - 5*x1 - x2 + 2, 2*x1 - 1, x1^3 + 2*x1^2*x2 - 6*x1^2 - 4*x1*x2 + 7*x1 + x2 - 2, x1^2 + x1*x2 - 5*x1 + 2, x1^2 + x1*x2 - 4*x1 - x2 + 2, 2*x1 + x2 - 2, x1^3 + 3*x1^2*x2 - 7*x1^2 + 2*x1*x2^2 - 11*x1*x2 + 12*x1 - x2^2 + 4*x2 - 4]