The realization space is
  [1   1   x2 - 1   0   0   1    1                 x2 - 1                       0         1    1]
  [0   1       -1   1   0   0    1                     -1                      x2        x1   x1]
  [0   0        0   0   1   1   x2   -x1*x2 + x1 + x2 - 1   x1*x2 - x1 - 2*x2 + 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, x1 - 1, x1*x2 - x1 + 1, x1^2*x2 - x1^2 - 2*x1*x2 + x1 - x2^2, x1^2*x2 - x1^2 - 3*x1*x2 + 2*x1 - x2^2 + 2*x2 - 1, x1^2*x2^2 - 2*x1^2*x2 + x1^2 - 2*x1*x2^2 + 4*x1*x2 - 2*x1 - x2^3 + x2^2 - 2*x2 + 1, x1*x2 - x1 - 2*x2 + 1, x1^2*x2 - x1^2 - 2*x1*x2 + x1 - x2^2 + x2, x1^2*x2^2 - 2*x1^2*x2 + x1^2 - 3*x1*x2^2 + 5*x1*x2 - 2*x1 - x2^3 + 2*x2^2 - 3*x2 + 1, x1^2*x2 - x1^2 - 2*x1*x2 + 2*x1 - x2^2 + x2 - 1, x1 + 1, x2, x2 - 1, x1^2*x2^2 - 2*x1^2*x2 + x1^2 - x1*x2^2 + 3*x1*x2 - 2*x1 - x2^2 - x2 + 1, x1^2*x2 - x1^2 - 2*x1*x2 + 2*x1 + x2^2 + x2 - 1, x1*x2 + x1 - 1, x1*x2^2 - 2*x1*x2 + x1 - x2^2 + 3*x2 - 1, x1*x2^2 - 2*x1*x2 + x1 + 2*x2 - 1, x1*x2 - x1 - x2^2 - 2*x2 + 1, x1*x2 - x1 - x2^2 - x2 + 1]