The realization space is
  [1   1   0   0          x1 - 1   x1 - 1   0   x1^2 - 1   x1^2 - 1    x1^2 - 1    x1^2 - 1]
  [1   0   1   1   x1^2 + x1 - 1     x1^2   0   x1^2 - 1          0   x1^3 - x1   x1^3 - x1]
  [1   0   1   0          x1 - 1        0   1         -1        -x1         -x1          -1]
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 - x1^13 - 8*x1^12 + 3*x1^11 + 10*x1^10 - 7*x1^9 - 3*x1^8 + 4*x1^7 - x1^6)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, 2*x1 - 1, x1^3 + x1^2 - 2*x1 + 1, x1^2 + x1 - 1, x1 + 1, x1^4 - x1^3 + 2*x1 - 1, x1^3 - x1 + 1, x1^2 - x1 + 1]