The realization space is
  [1   0   1   0         1   0         1    1              x1            1]
  [0   1   1   1   -x1 + 1   0   -x1 + 1    1               0   -x1^2 + x1]
  [0   1   1   0         0   1         1   x1   x1^2 - x1 + 1           x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^7 + 3*x1^6 - 3*x1^5 + 3*x1^3 - 3*x1^2 + x1)
avoiding the zero loci of the polynomials
RingElem[x1^2 - x1 + 1, x1 - 1, x1, x1^2 + 1, x1^3 - 2*x1^2 + x1 - 1, x1^3 - x1^2 + 2*x1 - 1, 2*x1^2 - 2*x1 + 1, x1^2 - 2*x1 + 2]