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      -2*x1^2 + x1   0   1   0              x1^2      -2*x1^2 + x1   x1   2*x1^2 - x1]
  [0   0   0                 0   1   1   1   x1^2 - 2*x1 + 1        -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 (4*x1^12 - 30*x1^11 + 94*x1^10 - 162*x1^9 + 169*x1^8 - 110*x1^7 + 44*x1^6 - 10*x1^5 + x1^4)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, 2*x1 - 1, x1^2 - 3*x1 + 1, x1^3 - 4*x1^2 + 3*x1 - 1, 3*x1^2 - 3*x1 + 1, 2*x1^2 - 2*x1 + 1, 2*x1^3 - 6*x1^2 + 4*x1 - 1, x1^3 - 5*x1^2 + 4*x1 - 1]