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   0   1   0       x1                x1^3   x1        x1^2]
  [0   0   0                   0   1   1   1   x1 - 1    x1^3 - x1^2 + x1   x1   x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^16 + x1^15 + 3*x1^14 - 10*x1^13 + 14*x1^12 - 11*x1^11 + 5*x1^10 - x1^9)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, x1^2 - x1 + 1, 2*x1^2 - 2*x1 + 1, x1^3 - x1 + 1, 2*x1 - 1, x1^3 + x1^2 - 2*x1 + 1, x1^4 - x1^3 + 2*x1^2 - 2*x1 + 1]