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