The realization space is
  [1   1   0   0   1   1      0           -x1     -x1     -x1^2 + x1             -x1^2 + x1]
  [1   0   1   0   1   0      1            -1      -1              1          x1^2 - x1 + 1]
  [0   0   0   1   1   1   x1^2   x1^3 - x1^2   -x1^2   -x1^3 + x1^2   x1^4 - 2*x1^3 + x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^12 + 4*x1^11 - 7*x1^10 + 7*x1^9 - 5*x1^8 + 3*x1^7 - x1^6)
avoiding the zero loci of the polynomials
RingElem[x1, x1^3 - x1 + 1, x1^2 - x1 + 1, x1 - 1, 2*x1^2 - 2*x1 + 1, x1^4 - 2*x1^3 + x1 - 1, x1^3 - x1^2 + 1, x1^3 - 2*x1^2 + x1 - 1, x1 + 1, x1^2 + 1]