The realization space is
  [1                 x2   1   0   0   1                 x2    1    0           1    1]
  [1   2*x1*x2 - x1 + 1   0   1   0   1   2*x1*x2 - x1 + 1    0   x2   x1*x2 + 1   x2]
  [0                  0   0   0   1   1   2*x1*x2 - x1 + 1   x1    1          x1    1]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal (2*x1^2*x2 - x1^2 + x1*x2^2 - 3*x1*x2 + 2*x1 + x2 - 1)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1^2*x2 - x1^2 - 2*x1*x2 + 2*x1 + x2 - 1, x1 - 1, x1*x2 - x2 + 1, x2 - 1, x1*x2 - x1 + 1, 2*x1*x2 - x1 - 2*x2 + 2, x1*x2 + 1, 2*x1*x2 - x1 + 1, 2*x1^2*x2 - x1^2 - x1*x2^2 - 2*x1*x2 + 2*x1 - 1, x2, 2*x1*x2^2 - 5*x1*x2 + 2*x1 + 2*x2 - 2, 2*x1*x2 - x1 - x2^2 + 1, 2*x1*x2 - x1 - x2 + 1, 2*x2 - 1, x1*x2^2 + 2*x1*x2 - x1 + 1, x1*x2^2 - 3*x1*x2 + x1 + x2 - 1, 2*x1*x2 - x1 + x2^2 - x2 + 1, 2*x1^2*x2 - x1^2 + x1*x2 + 1, 2*x1^2*x2 - x1^2 - 3*x1*x2 + 2*x1 - 1]