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