The realization space is
  [1   1   0   x1^2 - x1 + 1   0   1   1               0      x1^2 - x1 + 1      x1^2 - x1 + 1]
  [1   0   1            x1^2   0   1   0               1               x1^2                 x1]
  [0   0   0               0   1   1   1   x1^2 - x1 + 1   x1^3 - x1^2 + x1   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 - 9*x1^8 + 20*x1^7 - 28*x1^6 + 26*x1^5 - 16*x1^4 + 6*x1^3 - x1^2)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, x1^2 - x1 + 1, x1^3 - 2*x1^2 + 3*x1 - 1, x1^3 - x1^2 + 2*x1 - 1, x1^2 - x1 + 2, x1^2 + 1]