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