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