The realization space is
  [1   1   0   2   0   1   1          0      2   -2*x1 + 2   -2*x1 + 2]
  [0   1   1   1   0   0   1   2*x1 - 1      1   -2*x1 + 1           1]
  [0   0   0   0   1   1   1      -2*x1   2*x1        2*x1        2*x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (256*x1^6 - 768*x1^5 + 896*x1^4 - 512*x1^3 + 144*x1^2 - 16*x1)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, 2, 3*x1 - 1, 4*x1^2 - 3*x1 + 1, 4*x1 - 1, x1 - 1, 2*x1^2 - 2*x1 + 1, 2*x1^2 - 4*x1 + 1]