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