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