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