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