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