The realization space is
  [0   1   1   0   0   1        1            x1 - 2        x1 - 2            x1^2 - 3*x1 + 1      x1^2 - 3*x1 + 1]
  [1   1   0   1   0   0   x1 - 1   x1^2 - 3*x1 + 1   x1^2 - 2*x1   x1^3 - 4*x1^2 + 4*x1 - 1   x1^3 - 3*x1^2 + x1]
  [1   1   0   0   1   1        0                -1            -1                        -x1                  -x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^8 - 8*x1^7 + 25*x1^6 - 37*x1^5 + 24*x1^4 - 2*x1^3 - 4*x1^2 + x1)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, x1 - 2, 2*x1 - 1, x1^3 - 2*x1^2 - x1 + 1, x1^3 - 5*x1^2 + 6*x1 - 1, 2*x1^2 - 4*x1 + 1, x1^3 - 4*x1^2 + 5*x1 - 1, x1^2 - x1 - 1, x1^2 - 3*x1 + 1, x1 - 3]