The realization space is
  [1   0   1   0   1    0   x1 - 1      x1 - 1   -x1^3 + 2*x1^2 - 2*x1 + 1   -x1^3 + 2*x1^2 - 2*x1 + 1      x1^2 - 2*x1 + 1]
  [0   1   1   0   0    1   x1 - 1   x1^2 - x1                  -x1^2 + x1        x1^4 - 2*x1^3 + x1^2   x1^3 - 2*x1^2 + x1]
  [0   0   0   1   1   -1       x1        x1^2           -x1^3 + x1^2 - x1         -x1^4 + x1^3 - x1^2    -x1^3 + x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (2*x1^9 - 8*x1^8 + 15*x1^7 - 17*x1^6 + 12*x1^5 - 5*x1^4 + x1^3)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1^2 - 2*x1 + 1, x1 - 1, x1^3 + x1^2 - 2*x1 + 1, 3*x1^2 - 3*x1 + 1, x1^3 - x1 + 1, x1^2 - x1 + 1, x1^4 - x1^3 + 2*x1^2 - 2*x1 + 1, 2*x1 - 1]