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