The realization space is
  [1   1   0   x1^2 - 2*x1 + 1   0   1   1          0      x1^2 - 2*x1 + 1        x1 - 1        x1 - 1]
  [1   0   1      -2*x1^2 + x1   0   1   0   2*x1 - 1         -2*x1^2 + x1   2*x1^2 - x1   2*x1^2 - x1]
  [0   0   0                 0   1   1   1     x1 - 1   x1^3 - 2*x1^2 + x1   2*x1^2 - x1     x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (12*x1^9 - 52*x1^8 + 97*x1^7 - 103*x1^6 + 69*x1^5 - 30*x1^4 + 8*x1^3 - x1^2)
avoiding the zero loci of the polynomials
RingElem[2*x1^2 - 2*x1 + 1, x1, 2*x1 - 1, x1 - 1, 3*x1^2 - 3*x1 + 1, 2*x1^3 - 2*x1 + 1, x1^2 - x1 + 1, 4*x1^2 - 3*x1 + 1, x1^3 - 5*x1^2 + 4*x1 - 1, 3*x1 - 2]