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