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