The realization space is
  [1   1   0   0   1   1          0          1        x1 - 1        4*x1^2 - 6*x1 + 2                    1]
  [1   0   1   0   1   0     x1 - 1         x1     x1^2 - x1          4*x1^3 - 4*x1^2       -2*x1^2 + 2*x1]
  [0   0   0   1   1   1   2*x1 - 1   2*x1 - 1   2*x1^2 - x1   8*x1^3 - 8*x1^2 + 2*x1   -4*x1^2 + 4*x1 - 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (128*x1^9 - 704*x1^8 + 1632*x1^7 - 2128*x1^6 + 1728*x1^5 - 896*x1^4 + 288*x1^3 - 52*x1^2 + 4*x1)
avoiding the zero loci of the polynomials
RingElem[2*x1 - 1, 2, 2*x1^2 - 2*x1 + 1, x1, x1 - 1, 3*x1^2 - 3*x1 + 1, 2*x1^2 - 1, 6*x1^3 - 8*x1^2 + 4*x1 - 1, 3*x1 - 2]