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   0   1   0   2*x1 - 1                x1      -x1         -x1]
  [0   0   0                 0   1   1   1         x1        -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*x1^10 - 20*x1^9 + 45*x1^8 - 52*x1^7 + 31*x1^6 - 9*x1^5 + x1^4)
avoiding the zero loci of the polynomials
RingElem[2*x1 - 1, x1, 2*x1^2 - 2*x1 + 1, 2*x1^3 - 4*x1^2 + 4*x1 - 1, x1^2 - x1 + 1, x1^2 - 3*x1 + 1, x1 - 1, 3*x1 - 1, 3*x1^3 - 5*x1^2 + 4*x1 - 1, 4*x1^3 - 7*x1^2 + 5*x1 - 1, 2*x1^2 - 4*x1 + 1, x1^3 - 2*x1^2 + 3*x1 - 1]