The realization space is
  [1    1   x1 - 1   1   0   x1 - 1   0                           x2    1    0    1]
  [1   x1        0   0   1      -x1   0                           x2   x1   x2   x2]
  [0    1       -1   0   0       -1   1   -2*x1*x3 + x2*x3 + x2 + x3   x3   x3   x3]
in the multivariate polynomial ring in 3 variables over ZZ
within the vanishing set of the ideal
Ideal (2*x1^2*x3 - x1*x2*x3 - x1*x2 - x1*x3 + x2*x3)
avoiding the zero loci of the polynomials
RingElem[x3, x1*x3 - x2, 2*x1*x3 - x2*x3 - x2, x1 - x2, x3 - 1, x1*x3 - x3 + 1, 2*x1*x3 - x2 - x3, x2 - 1, 2*x1*x3 - x2*x3 - x2 - x3, 2*x1^2*x3 - 2*x1*x2*x3 - x1*x2 - x1*x3 + x2^2*x3 + x2, 2*x1^2*x3 - x1*x2*x3 - x1*x2 - 2*x1*x3 + x2*x3 + 1, 2*x1^2*x2*x3 + 2*x1^2*x3 - x1*x2^2*x3 - x1*x2^2 - 2*x1*x2*x3 - x1*x2 - x1*x3 + x2^2*x3 + x2, x2, x1*x2 + x1 - x2, 2*x1*x3 - x2 - x3 + 1, x1, x1*x3 - x2 - x3 + 1, x1 - x2 - 1, x1^2*x3 - x1*x2*x3 - x1*x3 + x2*x3 - x2, x1^2*x3 - x1*x2*x3 + x2*x3 - x2, 2*x1^2*x3 - x1*x2*x3 - x1*x2 - 2*x1*x3 + x2*x3, x1*x3 - x2 - x3, x1 - 1, 2*x1^2*x3 - x1*x2*x3 - x1*x2 - x1*x3 + x2*x3 - x2, 2*x1^3*x3 - x1^2*x2*x3 - x1^2*x2 - x1^2*x3 + 2*x1*x2*x3 - x1*x2 - x2*x3 + x2, 2*x1*x3 - x1 - x3 + 1, 2*x1 - 1, 2*x1^2*x3 - x1*x2*x3 - x1*x2 - x1*x3 + x2, 2*x1^2*x3 - x1*x2*x3 - x1*x2 - 3*x1*x3 + x2*x3 + x3, 2*x1 - x2 - 1]