The realization space is
  [1   0   1    1   1      x1      x1   0      x1    1    1]
  [0   1   1   x1   1   x2*x3   x2*x3   0   x1*x2   x1   x2]
  [0   0   0    0   1   x2*x3      x1   1   x2*x3   x3   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[x1 - x2, x3, x3 - 1, x2, x2 - 1, x1 - x3, x1 - x3^2, x1*x2 + x1*x3 - x1 - x2*x3^2, x1^2*x3 - x1^2 + x1*x2 - x2*x3^2, x1 - x2*x3, x2 - x3, x1 + x2^2 - x2*x3 - x2, x1^2 - x1*x2 + x2^2 - x2*x3, x1*x3 - x1 + x2 - x3, x1, x1 - 1, x1^2 - x2*x3^2, x1^2 - x2*x3, x1^2 + x1*x3 - x1 - x2*x3^2, x1*x2 + x1 - x2*x3 - x2, x1^3 - x1^2*x2*x3 - x1^2*x2 + x2^2*x3^2, x1^2 - x1*x2*x3 - x1*x2 + x2*x3]