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