The realization space is
  [1   1   0   2*x1 - 2   0   1   1        0   2*x1 - 2   x1 - 1        2]
  [1   0   1    -x1 - 1   0   1   0   x1 - 1    -x1 - 1      -x1   x1 + 1]
  [0   0   0          0   1   1   1     2*x1      -2*x1      -x1     2*x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (12*x1^6 - 22*x1^5 + 20*x1^3 - 12*x1^2 + 2*x1)
avoiding the zero loci of the polynomials
RingElem[3*x1 - 1, x1, x1 - 1, x1^2 + 2*x1 - 1, 2*x1 - 1, 2, x1 + 1, x1^2 - 4*x1 + 1, 5*x1 - 1]