The realization space is
  [1   0   1   x1 - 1   0   1           1    0        1   x1 - 1           1]
  [0   1   1       x1   0   0           0    1        1        1          x1]
  [0   0   0        0   1   1   x1^2 - x1   -1   x1 - 1   x1 - 1   x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^7 - 7*x1^6 + 19*x1^5 - 24*x1^4 + 12*x1^3 + x1^2 - 2*x1)
avoiding the zero loci of the polynomials
RingElem[x1^2 - x1 - 1, x1, x1 - 1, x1 + 1, x1^2 - 2, x1 - 2, x1^2 - 2*x1 - 1]