The realization space is
  [1   1   0   x1^2 - 2*x1 + 1   0   1   1        0   x1^4 - 3*x1^3 + 4*x1^2 - 3*x1 + 1    1      x1 - 1]
  [1   0   1             -x1^2   0   1   0       x1                 -x1^4 + x1^3 - x1^2   x1        x1^2]
  [0   0   0                 0   1   1   1   x1 - 1        -x1^4 + 3*x1^3 - 3*x1^2 + x1   x1   x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (3*x1^12 - 17*x1^11 + 45*x1^10 - 73*x1^9 + 79*x1^8 - 58*x1^7 + 28*x1^6 - 8*x1^5 + x1^4)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, 2*x1^2 - 2*x1 + 1, x1^2 - x1 + 1, x1^3 - x1 + 1, x1^3 - 3*x1^2 + 2*x1 - 1, 2*x1 - 1, x1^4 - 2*x1^3 + 4*x1^2 - 3*x1 + 1, 3*x1^4 - 7*x1^3 + 8*x1^2 - 4*x1 + 1]