The realization space is
  [0   1   x1   1   0   0            0   x1   x1^3 - x1^2    1    1]
  [1   1    1   0   1   0            1    1            -1    1    0]
  [1   1    1   0   0   1   -x1^2 + x1   x1     x1^2 - x1   x1   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^12 - 6*x1^11 + 16*x1^10 - 24*x1^9 + 19*x1^8 - 19*x1^6 + 24*x1^5 - 16*x1^4 + 6*x1^3 - x1^2)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1 + 1, x1, x1^4 - x1^3 - x1^2 + x1 - 1, x1^3 - x1 + 1, x1^2 - x1 + 1, x1^4 - 2*x1^3 + x1 - 1, x1^3 - x1^2 + 1, x1^2 + 1, x1^3 - 3*x1^2 + 2*x1 - 1]