The realization space is
  [1   1   0    x1^2 - 2*x1 + 1   0   1   1        0    x1^2 - 2*x1 + 1    1      x1 - 1]
  [1   0   1   x1^3 - x1^2 + x1   0   1   0   x1 - 1   x1^3 - x1^2 + x1   x1   x1^2 - x1]
  [0   0   0                  0   1   1   1       x1        x1^3 - x1^2   x1        x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (2*x1^12 - 12*x1^11 + 33*x1^10 - 54*x1^9 + 56*x1^8 - 36*x1^7 + 13*x1^6 - 2*x1^5)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, x1^2 - x1 + 1, 2*x1^2 - 2*x1 + 1, x1^3 - x1^2 + 1, x1^2 - 2*x1 + 2, x1^3 - 2*x1^2 + 3*x1 - 1, 2*x1 - 1, x1^3 - x1^2 + 2*x1 - 1, x1^4 - 2*x1^2 + 3*x1 - 1, x1^4 - x1^3 + 2*x1 - 1]