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