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