The realization space is
  [1    1   1   0   0   1    1   x1^2 - 2*x1 + 1        0   x1^2 - 2*x1 + 1                 x1]
  [1   x1   0   1   0   1   x1                 0   x1 - 1        -x1^2 + x1   -x1^2 + 3*x1 - 1]
  [0    0   0   0   1   1   x1              x1^2      -x1              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 + 49*x1^14 - 95*x1^13 + 117*x1^12 - 90*x1^11 + 41*x1^10 - 10*x1^9 + x1^8)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, 2*x1 - 1, x1^2 - 3*x1 + 1, x1^3 - 5*x1^2 + 4*x1 - 1, 3*x1 - 1, x1 - 2, 2*x1^2 - 4*x1 + 1, 2]