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   1   1   0        0    1   1   x1*x2 - x2 + 1   x1*x2 - x2 + 1       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[x1*x2 - x2*x3 + x3, x1*x2 - x1 - x2*x3 + 2*x3 - 1, x1 - x3 + 1, x1 - x3, x1, x3 - 1, x2 - 1, x1 + x2*x3 - x2 - 2*x3 + 1, x1*x2^2 - x2^2 + x2 - x3, x1 - 1, x2, x1*x2 - x3, x1*x2 - x2 - x3 + 1, x1*x2 + x2*x3 - x2 - 2*x3 + 1, x1*x2 - x2 + 1, x1*x2^2 - x1*x2 - x2^2 + x2 + x3 - 1, x1*x2 - x3 + 1, x1*x2 + x2*x3 - x2 - x3 + 1, x3, x2*x3 - 2*x3 + 1, x2 - x3, x2 - 2, x1*x2 - x1 - 1, x1 - x2 + 1, x1*x2^2 - x2^2 + x2 - 1, x1*x2 - 1, x1*x2^2 - 2*x1*x2 - x2^2 + 2*x2 - 1]