The realization space is
  [1   1   0   0   1   1    0             x1 - 1              1               1             x1 - 1]
  [1   0   1   0   1   0    1               x1^2     -x1^2 + x1              x1          x1^2 - x1]
  [0   0   0   1   1   1   x1   x1^3 - x1^2 + x1   -x1^3 + x1^2   x1^2 - x1 + 1   x1^3 - x1^2 + x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (2*x1^7 - 4*x1^6 + 3*x1^5 + x1^4 - 2*x1^3 + x1^2)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1^2 - x1 + 1, x1, x1^3 - x1 + 1, x1^3 - x1^2 + 1, x1^2 - 2*x1 + 2, 2*x1^2 - 2*x1 + 1, x1 + 1]