The realization space is
  [1   1   0       -2*x1   0   1   1         0       -2*x1         1           1]
  [0   1   1   -3*x1 + 1   0   0   1         1   -3*x1 + 1        x1          x1]
  [0   0   0           0   1   1   1   -x1 + 1    4*x1 - 2   -x1 + 1   -2*x1 + 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^2 - 3*x1 + 1, 12*x1^6 - 130*x1^5 + 390*x1^4 - 476*x1^3 + 264*x1^2 - 66*x1 + 6)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, x1^3 - 3*x1^2 + x1 - 1, x1 - 3, x1 - 2, x1^3 - 4*x1^2 + 3*x1 - 1, x1^2 - x1 + 1, x1^3 - 2*x1^2 - x1 + 1, x1^2 - 2*x1 - 1, x1^4 - 3*x1^3 + x1^2 + x1 - 1, 2*x1 - 1, x1^4 - 3*x1^3 + 2*x1^2 - 2*x1 + 1, x1 + 1, x1^3 - x1^2 + 2*x1 - 1, x1^3 - 3*x1^2 + 2*x1 - 1]