The realization space is
  [1   1   0   1   0   0    1   x1 - 1   x1 - 1          x1 - 1]
  [1   0   1   1   0   1   x1        0      -x1       x1^2 - x1]
  [0   0   0   1   1   1    1       -1       -1   x1^2 - x1 - 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^6 + 5*x1^5 - 9*x1^4 + 6*x1^3 - x1^2)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1^2 - 4*x1 + 1, x1 - 2, x1^2 - 3*x1 + 1, x1 - 1, x1^2 - x1 - 1, 2, 2*x1 - 1]