The realization space is
  [1   1    1   0   1   0   x1 - 1    1              -x1 + 1    1                 0]
  [1   0   x1   1   1   0   x1 - 1   x1   x1^3 - 2*x1^2 + x1    0   x1^2 - 2*x1 + 1]
  [0   0    0   0   1   1     x1^2   x1                -x1^2   x1               -x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^12 - 7*x1^11 + 22*x1^10 - 42*x1^9 + 55*x1^8 - 51*x1^7 + 33*x1^6 - 14*x1^5 + 3*x1^4)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 2, x1^2 - 3*x1 + 1, x1^3 - 3*x1^2 + 2*x1 - 1, x1^2 - x1 + 1, x1 - 1, x1^3 - 2*x1^2 + x1 - 1, 2*x1 - 1, x1^2 + 1]