The realization space is
  [1   1   0    1   0   1   1          0    1         1    1]
  [0   1   1   x1   0   0   1          1   x1   -x3 + 1   x3]
  [0   0   0    0   1   1   1   2*x3 - 1   x2        x3   x3]
in the multivariate polynomial ring in 3 variables over ZZ
within the vanishing set of the ideal
Ideal (2*x3^2 - 2*x3 + 1)
avoiding the zero loci of the polynomials
RingElem[x3, 2*x3 - 1, x3 - 1, x2 - x3, x1 - x2, x1*x3 - x2*x3 + x2 - x3, x2, x1 - x3, x1*x3 - x1 - x2*x3 + x3, 2*x1*x3 - x1 - x2 - 2*x3^2 + 2*x3, 2, 2*x3^2 - 4*x3 + 1, 2*x1*x3 - x1 - 2*x3^2 + 2*x3, x1, x1*x3 - x1 + x3, x1 - 1, x1*x3 + x2*x3 - x2, x1 + x2 - 1, x1 + x3 - 1, x1*x3 - x1 + x2*x3 - 2*x3 + 1, 2*x1*x3 - x1 - x2 + 2*x3^2 - 2*x3 + 1, 2*x1*x3 - x1 + 2*x3^2 - 2*x3 + 1, 2*x3^2 - 1, x1*x3 - x1 - 2*x3 + 1, 2*x1*x3 - x1 - x2, 2*x1*x3 - x1 - x2 - 2*x3 + 1, 2*x1*x3 - x1 - x2 + 1, 2*x1*x3 - x1 - x2 - 2*x3 + 2, x2 - 1, 2*x1*x3 - x1 - 2*x3 + 2, 2*x1*x3 - x1 + 1]