The realization space is
  [1   1   0                 1   0   1   1    0                 1           1           1]
  [1   0   1   x1^2 - 2*x1 + 1   0   1   0   x1   x1^2 - 2*x1 + 1   x1^2 - x1   x1^2 - x1]
  [0   0   0                 0   1   1   1    1            x1 - 1      x1 - 1          x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^7 - 5*x1^6 + 10*x1^5 - 10*x1^4 + 5*x1^3 - x1^2)
avoiding the zero loci of the polynomials
RingElem[x1^2 - x1 - 1, x1, x1 - 1, x1 - 2, x1 + 1, x1^2 - x1 + 1, x1^3 - 2*x1^2 + x1 - 1, x1^2 - 2, x1^2 - 2*x1 + 2]