The realization space is
  [1   1   0   0   1   1         0                    -x1 + 1                -x1 + 1              1                      x1 - 2]
  [1   0   1   0   1   0         1               -x1^2 + 2*x1           -x1^2 + 2*x1             x1                 x1^2 - 2*x1]
  [0   0   0   1   1   1   -x1 + 1   x1^3 - 4*x1^2 + 4*x1 - 1   x1^3 - 3*x1^2 + 2*x1   -x1^2 + 2*x1   -x1^3 + 4*x1^2 - 4*x1 + 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^8 + 9*x1^7 - 33*x1^6 + 63*x1^5 - 65*x1^4 + 32*x1^3 - 3*x1^2 - 2*x1)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, x1^2 - 3*x1 + 1, x1^3 - 3*x1^2 + 2*x1 - 1, x1^4 - 4*x1^3 + 6*x1^2 - 5*x1 + 1, x1^2 - 2*x1 + 2, x1^2 - 3*x1 + 3, x1 - 3, x1^3 - 4*x1^2 + 5*x1 - 3, x1 - 2, x1^3 - 4*x1^2 + 5*x1 - 1]