The realization space is
  [1   1   0   2*x1^2 - 2*x1 + 1   0   1   1                   0      2*x1^2 - 2*x1 + 1    1        x1 - 1]
  [1   0   1    x1^3 - x1^2 + x1   0   1   0           x1^2 - x1       x1^3 - x1^2 + x1   x1     x1^2 - x1]
  [0   0   0                   0   1   1   1   2*x1^2 - 2*x1 + 1   2*x1^3 - 2*x1^2 + x1   x1   2*x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (2*x1^17 - 6*x1^16 + 9*x1^15 - 8*x1^14 + 4*x1^13 - x1^12)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, 2*x1 - 1, 2*x1^2 - 2*x1 + 1, 3*x1^2 - 3*x1 + 1, x1^2 - x1 + 1, 3*x1^3 - 5*x1^2 + 4*x1 - 1]