The realization space is
  [1   1   0       x1^2 - x1 + 1   0   1   1                           0      -x1^5 + 4*x1^4 - 6*x1^3 + 6*x1^2 - 3*x1 + 1         1               x1^2 - x1 + 1]
  [0   1   1   2*x1^2 - 2*x1 + 1   0   0   1   -x1^3 + 3*x1^2 - 2*x1 + 1   -2*x1^5 + 8*x1^4 - 11*x1^3 + 9*x1^2 - 4*x1 + 1   -x1 + 1   -x1^3 + 3*x1^2 - 2*x1 + 1]
  [0   0   0                   0   1   1   1    x1^3 - 2*x1^2 + 2*x1 - 1           2*x1^5 - 4*x1^4 + 5*x1^3 - 3*x1^2 + x1        x1            x1^3 - x1^2 + x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (2*x1^12 - 13*x1^11 + 40*x1^10 - 75*x1^9 + 96*x1^8 - 87*x1^7 + 56*x1^6 - 25*x1^5 + 7*x1^4 - x1^3)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, x1^2 - x1 + 1, 2*x1^2 - 2*x1 + 1, x1^3 - 3*x1^2 + 2*x1 - 1, 2*x1^2 - x1 + 1, 2*x1 - 1, 3*x1^2 - 2*x1 + 1, 2*x1^3 - 5*x1^2 + 4*x1 - 2]