The realization space is
  [1   1   0        x1 - 1   0   1   1        0        x1 - 1              1              1]
  [1   0   1   x1^2 - 2*x1   0   1   0   x1 - 1   x1^2 - 2*x1   -x1^2 + 2*x1   -x1^2 + 2*x1]
  [0   0   0             0   1   1   1       -1     x1^2 - x1   -x1^2 + 2*x1             x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^12 - 8*x1^11 + 25*x1^10 - 38*x1^9 + 28*x1^8 - 8*x1^7)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, x1 - 2, x1^2 - 3*x1 + 1, 2*x1^2 - 4*x1 + 1, x1^3 - 2*x1^2 + x1 - 1, x1^2 - x1 - 1, x1^2 - x1 + 1, x1^3 - x1^2 - 2*x1 + 1]