The realization space is
  [1   1   0   0   1   1     0    1         1    1]
  [1   0   1   0   1   0    x2   x1   -x2 + 1   x1]
  [0   0   0   1   1   1   -x1   x1        x1   x2]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal (x1^2 + x2^2 - x2)
avoiding the zero loci of the polynomials
RingElem[x1^2 - x1 + x2^2, x1 - x2, x1 + x2 - 1, x1^2 - 2*x1 + x2^2 - x2 + 1, x1^2 - x1 + x2^2 - 2*x2 + 1, x1 - 1, x1, x1^2 + x2^2, x1^2 - x1 + x2^2 - x2, x2 - 1, x2, x1 + x2, x1^2 + x1*x2 - x2, 2*x1 - 1]