The realization space is
  [1   x1^2 - 2*x1 + 1   1   0         x1   x1^2 - 2*x1 + 1   1   0          0   x1 - 1         x1]
  [1              x1^2   0   1   2*x1 - 1       2*x1^2 - x1   1   0   2*x1 - 1        0   2*x1 - 1]
  [1              x1^2   0   0         x1              x1^2   0   1       x1^2    -x1^2       x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-2*x1^16 + 15*x1^15 - 37*x1^14 + 35*x1^13 + 2*x1^12 - 30*x1^11 + 24*x1^10 - 8*x1^9 + x1^8)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, 2*x1 - 1, x1, x1^3 - 5*x1^2 + 4*x1 - 1, x1^2 + 2*x1 - 1, x1^2 - 3*x1 + 1, x1^3 + 2*x1^2 - 3*x1 + 1, x1^2 + x1 - 1, x1^2 - 4*x1 + 2]