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