The realization space is
  [1   1   0   0   1   1          0        3*x1 - 2      2   3*x1^2 - 2*x1      2*x1 - 1]
  [0   1   1   0   0   1   2*x1 - 2   2*x1^2 - 2*x1   2*x1   2*x1^3 - x1^2   2*x1^2 - x1]
  [0   0   0   1   1   1         x1            x1^2     x1            x1^3          x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (27*x1^12 - 138*x1^11 + 287*x1^10 - 312*x1^9 + 188*x1^8 - 60*x1^7 + 8*x1^6)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1 - 2, x1, 5*x1^2 - 6*x1 + 2, 3*x1 - 2, 3*x1^2 - 3*x1 + 1, 2*x1 - 1, 7*x1^2 - 10*x1 + 4, 2, 3*x1^2 - 4*x1 + 2]