The realization space is
  [1   1   0   0   x1 - x2   x1 - x2   0          x1 - x2          x1 - x2        x1 - x2        x1 - x2]
  [0   1   1   1       -x1       -x2   0                0          x1 - x2            -x1            -x2]
  [0   1   1   0         0   x1 - x2   1   2*x1*x2 - x2^2   2*x1*x2 - x2^2   x1^2 - 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 - x2 + 1, x1 - x2, x1, x2 - 1, 2*x1 - x2, x2, 2*x1*x2 - x1 - x2^2 + x2, x1^2 + x1*x2 - x1 - x2^2 + x2, x1 - 1, x1^2 - 3*x1*x2 + 2*x1 + x2^2 - x2, x1^2 - 3*x1*x2 + x2^2, x1^2 + 2*x1*x2 - 2*x1 - x2^2 + x2, x1^3 - 6*x1^2*x2 + x1^2 + 5*x1*x2^2 - x1*x2 - x2^3, x1^2 - 3*x1*x2 + x1 + x2^2, x1^2 + 2*x1*x2^2 - 2*x1*x2 - x2^3 + x2^2, 2*x1*x2 - x1 - x2^2, 4*x1^2*x2 - x1^2 - 4*x1*x2^2 + x1*x2 + x2^3]