The realization space is
  [1   1   0   0   1   1         0   x1^2 - 3*x1 + 2      x1 - 1   x1^2 - 3*x1 + 2        x1 - 1]
  [0   1   1   0   0   1         1                 1          -1           -x1 + 2   x1^2 - 2*x1]
  [0   0   0   1   1   1   -x1 + 1           -x1 + 1   x1^2 - x1           -x1 + 1     x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^6 + 6*x1^5 - 13*x1^4 + 12*x1^3 - 3*x1^2 - 2*x1 + 1)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, x1^2 - 3*x1 + 1, x1 - 2, x1^2 - x1 - 1, 2*x1^2 - 4*x1 + 1, 2*x1 - 3, x1^2 - x1 + 1]