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