The realization space is
  [1   1   0   0   1   1        0    1    2*x1 - 1      2*x1 - 1]
  [1   0   1   0   1   0   x1 - 1   x1   x1^2 - x1     x1^2 - x1]
  [0   0   0   1   1   1       x1   x1        x1^2   2*x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (6*x1^9 - 43*x1^8 + 126*x1^7 - 205*x1^6 + 206*x1^5 - 131*x1^4 + 51*x1^3 - 11*x1^2 + x1)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, x1^2 - 3*x1 + 1, x1^3 - 2*x1^2 + 3*x1 - 1, 3*x1 - 1, 2*x1 - 1]