The realization space is
  [1   1   0   x1^2 - 2*x1 + 1   0   1   1        0      x1^2 - 2*x1 + 1   x1 - 1      x1 - 1]
  [1   0   1             -x1^2   0   1   0       x1                -x1^2     x1^2        x1^2]
  [0   0   0                 0   1   1   1   x1 - 1   x1^3 - 2*x1^2 + x1     x1^2   x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^12 + 5*x1^11 - 12*x1^10 + 20*x1^9 - 26*x1^8 + 25*x1^7 - 16*x1^6 + 6*x1^5 - x1^4)
avoiding the zero loci of the polynomials
RingElem[x1^2 - x1 + 1, x1, x1 - 1, 2*x1^2 - 2*x1 + 1, x1^4 - x1^3 + 2*x1^2 - 2*x1 + 1, x1^2 - 2*x1 + 2, 2*x1^2 - x1 + 1, x1^3 + x1^2 - 2*x1 + 1, x1^3 - x1 + 1, x1^3 - 4*x1^2 + 3*x1 - 1, 2*x1 - 1]