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