The realization space is
  [1   1   0        x1 - 1   0   1   1        0        x1 - 1              1              1]
  [1   0   1   x1^2 - 2*x1   0   1   0   x1 - 2   x1^2 - 2*x1   -x1^2 + 2*x1   -x1^2 + 2*x1]
  [0   0   0             0   1   1   1       -1     x1^2 - x1   -x1^2 + 2*x1             x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^8 + 7*x1^7 - 19*x1^6 + 24*x1^5 - 13*x1^4 + 2*x1^3)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, x1 - 2, x1^2 - 3*x1 + 1, 2*x1^2 - 4*x1 + 1, x1^2 - x1 + 1, x1^3 - 3*x1^2 + 2*x1 + 1, x1^2 - 2*x1 + 2, x1^3 - 2*x1^2 - x1 + 1, x1^3 - 3*x1^2 + 2*x1 - 1, x1 - 3]