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