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