The realization space is
  [1   1   0        x1 - 1   0   1   1         0        x1^2 - 2*x1 + 1    1         1]
  [1   0   1   2*x1^2 - x1   0   1   0        x1   2*x1^3 - 3*x1^2 + x1   x1   -x1 + 1]
  [0   0   0             0   1   1   1   -x1 + 1         -2*x1^3 + x1^2   x1        x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (32*x1^12 - 136*x1^11 + 244*x1^10 - 236*x1^9 + 124*x1^8 - 24*x1^7 - 9*x1^6 + 6*x1^5 - x1^4)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, x1 - 1, 3*x1^2 - 3*x1 + 1, 2*x1^2 - 2*x1 + 1, 4*x1^2 - 3*x1 + 1, 4*x1^2 - 5*x1 + 2, 2, 5*x1^3 - 7*x1^2 + 4*x1 - 1, 5*x1^2 - 6*x1 + 2, 2*x1^3 - 2*x1 + 1]