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